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# LuxAMDGPU.functional — Method.
julia
functional()

Check if LuxAMDGPU is functional.

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LuxCUDA is meant to be used as a trigger package for all CUDA dependencies in Lux. Users requiring CUDA support should install LuxCUDA and load it alongside Lux.

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API Reference ​

# LuxCUDA.functional — Method.
julia
functional()

Check if LuxCUDA is functional.

source


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# LuxDeviceUtils.gpu_backend! — Function.
julia
gpu_backend!() = gpu_backend!("")
+gpu_backend!(backend) = gpu_backend!(string(backend))
+gpu_backend!(backend::AbstractLuxGPUDevice)
+gpu_backend!(backend::String)

Creates a LocalPreferences.toml file with the desired GPU backend.

If backend == "", then the gpu_backend preference is deleted. Otherwise, backend is validated to be one of the possible backends and the preference is set to backend.

If a new backend is successfully set, then the Julia session must be restarted for the change to take effect.

source


Data Transfer ​

# LuxDeviceUtils.cpu_device — Function.
julia
cpu_device() -> LuxCPUDevice()

Return a LuxCPUDevice object which can be used to transfer data to CPU.

source


# LuxDeviceUtils.gpu_device — Function.
julia
gpu_device(device_id::Union{Nothing, Int}=nothing;
+    force_gpu_usage::Bool=false) -> AbstractLuxDevice()

Selects GPU device based on the following criteria:

  1. If gpu_backend preference is set and the backend is functional on the system, then that device is selected.

  2. Otherwise, an automatic selection algorithm is used. We go over possible device backends in the order specified by supported_gpu_backends() and select the first functional backend.

  3. If no GPU device is functional and force_gpu_usage is false, then cpu_device() is invoked.

  4. If nothing works, an error is thrown.

Arguments

  • device_id::Union{Nothing, Int}: The device id to select. If nothing, then we return the last selected device or if none was selected then we run the autoselection and choose the current device using CUDA.device() or AMDGPU.device() or similar. If Int, then we select the device with the given id. Note that this is 1-indexed, in contrast to the 0-indexed CUDA.jl. For example, id = 4 corresponds to CUDA.device!(3).

Warning

device_id is only applicable for CUDA and AMDGPU backends. For Metal and CPU backends, device_id is ignored and a warning is printed.

Keyword Arguments

  • force_gpu_usage::Bool: If true, then an error is thrown if no functional GPU device is found.

source


Miscellaneous ​

# LuxDeviceUtils.reset_gpu_device! — Function.
julia
reset_gpu_device!()

Resets the selected GPU device. This is useful when automatic GPU selection needs to be run again.

source


# LuxDeviceUtils.supported_gpu_backends — Function.
julia
supported_gpu_backends() -> Tuple{String, ...}

Return a tuple of supported GPU backends.

Warning

This is not the list of functional backends on the system, but rather backends which Lux.jl supports.

Danger

Metal.jl support is extremely experimental and most things are not expected to work.

source


# LuxDeviceUtils.default_device_rng — Function.
julia
default_device_rng(::AbstractLuxDevice)

Returns the default RNG for the device. This can be used to directly generate parameters and states on the device using WeightInitializers.jl.

source


# LuxDeviceUtils.get_device — Function.
julia
get_device(x::AbstractArray) -> AbstractLuxDevice

Returns the device of the array x. Trigger Packages must be loaded for this to return the correct device.

source


+ + + + \ No newline at end of file diff --git a/v0.5.30/api/Building_Blocks/LuxCore.html b/v0.5.30/api/Building_Blocks/LuxCore.html new file mode 100644 index 000000000..10583ddb1 --- /dev/null +++ b/v0.5.30/api/Building_Blocks/LuxCore.html @@ -0,0 +1,25 @@ + + + + + + LuxCore | Lux.jl Documentation + + + + + + + + + + + + + +
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LuxCore ​

LuxCore.jl defines the abstract layers for Lux. Allows users to be compatible with the entirely of Lux.jl without having such a heavy dependency. If you are depending on Lux.jl directly, you do not need to depend on LuxCore.jl (all the functionality is exported via Lux.jl).

Index ​

Abstract Types ​

# LuxCore.AbstractExplicitLayer — Type.
julia
abstract type AbstractExplicitLayer

Abstract Type for all Lux Layers

Users implementing their custom layer, must implement

  • initialparameters(rng::AbstractRNG, layer::CustomAbstractExplicitLayer) – This returns a NamedTuple containing the trainable parameters for the layer.

  • initialstates(rng::AbstractRNG, layer::CustomAbstractExplicitLayer) – This returns a NamedTuple containing the current state for the layer. For most layers this is typically empty. Layers that would potentially contain this include BatchNorm, LSTM, GRU etc.

Optionally:

  • parameterlength(layer::CustomAbstractExplicitLayer) – These can be automatically calculated, but it is recommended that the user defines these.

  • statelength(layer::CustomAbstractExplicitLayer) – These can be automatically calculated, but it is recommended that the user defines these.

See also AbstractExplicitContainerLayer

source


# LuxCore.AbstractExplicitContainerLayer — Type.
julia
abstract type AbstractExplicitContainerLayer{layers} <: AbstractExplicitLayer

Abstract Container Type for certain Lux Layers. layers is a tuple containing fieldnames for the layer, and constructs the parameters and states using those.

Users implementing their custom layer can extend the same functions as in AbstractExplicitLayer.

Tip

Advanced structure manipulation of these layers post construction is possible via Functors.fmap. For a more flexible interface, we recommend using Lux.Experimental.@layer_map.

source


General ​

# LuxCore.apply — Function.
julia
apply(model, x, ps, st)

In most cases this function simply calls model(x, ps, st). However, it is still recommended to call apply instead of model(x, ps, st) directly. Some of the reasons for this include:

  1. For certain types of inputs x, we might want to perform preprocessing before calling model. For eg, if x is an Array of ReverseDiff.TrackedReals this can cause significant regressions in model(x, ps, st) (since it won't hit any of the BLAS dispatches). In those cases, we would automatically convert x to a ReverseDiff.TrackedArray.

  2. Certain user defined inputs need to be applied to specific layers but we want the datatype of propagate through all the layers (even unsupported ones). In these cases, we can unpack the input in apply and pass it to the appropriate layer and then repack it before returning. See the Lux manual on Custom Input Types for a motivating example.

source


# LuxCore.stateless_apply — Function.
julia
stateless_apply(model, x, ps)

Calls apply and only returns the first argument. This function requires that model has an empty state of NamedTuple(). Behavior of other kinds of models are undefined and it is the responsibility of the user to ensure that the model has an empty state.

source


# LuxCore.check_fmap_condition — Function.
julia
check_fmap_condition(cond, tmatch, x) -> Bool

fmaps into the structure x and see if cond is statisfied for any of the leaf elements.

Arguments

  • cond - A function that takes a single argument and returns a Bool.

  • tmatch - A shortcut to check if x is of type tmatch. Can be disabled by passing nothing.

  • x - The structure to check.

Returns

A Boolean Value

source


# LuxCore.contains_lux_layer — Function.
julia
contains_lux_layer(l) -> Bool

Check if the structure l is a Lux AbstractExplicitLayer or a container of such a layer.

source


# LuxCore.display_name — Function.
julia
display_name(layer::AbstractExplicitLayer)

Printed Name of the layer. If the layer has a field name that is used, else the type name is used.

source


# LuxCore.replicate — Function.
julia
replicate(rng::AbstractRNG)

Creates a copy of the rng state depending on its type.

source


# LuxCore.setup — Function.
julia
setup(rng::AbstractRNG, layer)

Shorthand for getting the parameters and states of the layer l. Is equivalent to (initialparameters(rng, l), initialstates(rng, l)).

Warning

This function is not pure, it mutates rng.

source


Parameters ​

# LuxCore.initialparameters — Function.
julia
initialparameters(rng::AbstractRNG, layer)

Generate the initial parameters of the layer l.

source


# LuxCore.parameterlength — Function.
julia
parameterlength(layer)

Return the total number of parameters of the layer l.

source


States ​

# LuxCore.initialstates — Function.
julia
initialstates(rng::AbstractRNG, layer)

Generate the initial states of the layer l.

source


# LuxCore.statelength — Function.
julia
statelength(layer)

Return the total number of states of the layer l.

source


# LuxCore.testmode — Function.
julia
testmode(st::NamedTuple)

Make all occurances of training in state st – Val(false).

source


# LuxCore.trainmode — Function.
julia
trainmode(st::NamedTuple)

Make all occurances of training in state st – Val(true).

source


# LuxCore.update_state — Function.
julia
update_state(st::NamedTuple, key::Symbol, value;
+    layer_check=_default_layer_check(key))

Recursively update all occurances of the key in the state st with the value.

source


Layer size ​

Warning

These specifications have been added very recently and most layers currently do not implement them.

# LuxCore.inputsize — Function.
julia
inputsize(layer)

Return the input size of the layer.

source


# LuxCore.outputsize — Function.
julia
outputsize(layer, x, rng)

Return the output size of the layer. If outputsize(layer) is defined, that method takes precedence, else we compute the layer output to determine the final size.

The fallback implementation of this function assumes the inputs were batched, i.e., if any of the outputs are Arrays, with ndims(A) > 1, it will return size(A)[1:(end - 1)]. If this behavior is undesirable, provide a custom outputsize(layer, x, rng) implementation).

source


+ + + + \ No newline at end of file diff --git a/v0.5.30/api/Building_Blocks/LuxLib.html b/v0.5.30/api/Building_Blocks/LuxLib.html new file mode 100644 index 000000000..58d3b5a00 --- /dev/null +++ b/v0.5.30/api/Building_Blocks/LuxLib.html @@ -0,0 +1,27 @@ + + + + + + LuxLib | Lux.jl Documentation + + + + + + + + + + + + + +
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LuxLib ​

Backend for Lux.jl

Index ​

Dropout ​

# LuxLib.alpha_dropout — Function.
julia
alpha_dropout(rng::AbstractRNG, x, p, ::Val{training})
+alpha_dropout(rng::AbstractRNG, x, p, ::Val{training}, α, A, B)

Alpha Dropout: Dropout ensuring that the mean and variance of the output remains same as the input. For details see [1]. Use the second call signature to avoid recomputing the constants for a fixed dropout probability.

Arguments

  • rng: Random number generator

  • x: Input Array

  • p: Probability of an element to be dropped out

  • Val(training): If true then dropout is applied on x with probability p. Else, x is returned

  • α: -1.7580993408473766. Computed at limit x tends to infinity, selu(x) = -λβ = α

  • A: Scaling factor for the mean

  • B: Scaling factor for the variance

Returns

  • Output Array after applying alpha dropout

  • Updated state for the random number generator

References

[1] Klambauer, Günter, et al. "Self-normalizing neural networks." Advances in neural information processing systems 30 (2017).

source


# LuxLib.dropout — Function.
julia
dropout(rng::AbstractRNG, x, p, ::Val{training}, invp; dims)
+dropout(rng::AbstractRNG, x, mask, p, ::Val{training}, ::Val{update_mask}, invp;
+        dims)

Dropout: Simple Way to prevent Neural Networks for Overfitting. For details see [1].

Arguments

  • rng: Random number generator

  • x: Input Array

  • mask: Dropout Mask. If not used then it is constructed automatically

  • p: Probability of an element to be dropped out

  • Val(training): If true then dropout is applied on x with probability p along dims. Else, x is returned

  • Val(update_mask): If true then the mask is generated and used. Else, the mask provided is directly used

  • invp: Inverse of the probability

Keyword Arguments

  • dims: Dimensions along which dropout is applied

  • invp: Inverse of the probability (1p)

Returns

  • Output Array after applying dropout

  • Dropout Mask (if training == false, the returned value is meaningless)

  • Updated state for the random number generator

References

[1] Srivastava, Nitish, et al. "Dropout: a simple way to prevent neural networks from overfitting." The journal of machine learning research 15.1 (2014): 1929-1958.

source


Normalization ​

# LuxLib.batchnorm — Function.
julia
batchnorm(x, scale, bias, running_mean, running_var; momentum, epsilon, training)

Batch Normalization. For details see [1].

Batch Normalization computes the mean and variance for each D1×...×DN−2×1×DN input slice and normalises the input accordingly.

Arguments

  • x: Input to be Normalized

  • scale: Scale factor (γ) (can be nothing)

  • bias: Bias factor (β) (can be nothing)

  • running_mean: Running mean (can be nothing)

  • running_var: Running variance (can be nothing)

Keyword Arguments

  • momentum: Momentum for updating running mean and variance

  • epsilon: Value added to the denominator for numerical stability

  • training: Set to Val(true) if running in training mode

Returns

Normalized Array of same size as x. And a Named Tuple containing the updated running mean and variance.

Performance Considerations

If the input array is 2D, 4D, or 5D CuArray with element types Float16, Float32 and Float64, then the CUDNN code path will be used. In all other cases, a broadcasting fallback is used which is not highly optimized.

References

[1] Ioffe, Sergey, and Christian Szegedy. "Batch normalization: Accelerating deep network training by reducing internal covariate shift." International conference on machine learning. PMLR, 2015.

source


# LuxLib.groupnorm — Function.
julia
groupnorm(x, scale, bias; groups, epsilon)

Group Normalization. For details see [1].

This op is similar to batch normalization, but statistics are shared across equally-sized groups of channels and not shared across batch dimension. Thus, group normalization does not depend on the batch composition and does not require maintaining internal state for storing statistics.

Arguments

  • x: Input to be Normalized

  • scale: Scale factor (γ) (can be nothing)

  • bias: Bias factor (β) (can be nothing)

Keyword Arguments

  • groups: Number of groups

  • epsilon: Value added to the denominator for numerical stability

Returns

The normalized array is returned.

Performance Considerations

The most common case of this Op – x is a 4D array – is optimized using KernelAbstractions and has a fast custom backwards pass implemented. All other cases have a fallback implementation which is not especially optimized.

We have tested the code path for Float16 and it works, but gradient accumulation is extremely fragile. Hence, for Float16 inputs, it uses the fallback implementation.

If the batch size is small (< 16), then the fallback implementation will be faster than the KA version. However, this customization is not possible using the direct groupnorm interface.

References

[1] Wu, Yuxin, and Kaiming He. "Group normalization." Proceedings of the European conference on computer vision (ECCV). 2018.

source


# LuxLib.instancenorm — Function.
julia
instancenorm(x, scale, bias; epsilon, training)

Instance Normalization. For details see [1].

Instance Normalization computes the mean and variance for each D1×...×DN−2×1×1 input slice and normalises the input accordingly.

Arguments

  • x: Input to be Normalized (must be atleast 3D)

  • scale: Scale factor (γ) (can be nothing)

  • bias: Bias factor (β) (can be nothing)

Keyword Arguments

  • epsilon: Value added to the denominator for numerical stability

  • training: Set to Val(true) if running in training mode

Returns

Normalized Array of same size as x. And a Named Tuple containing the updated running mean and variance.

References

[1] Ulyanov, Dmitry, Andrea Vedaldi, and Victor Lempitsky. "Instance normalization: The missing ingredient for fast stylization." arXiv preprint arXiv:1607.08022 (2016).

source


# LuxLib.layernorm — Function.
julia
layernorm(x, scale, bias; dims, epsilon)

Layer Normalization. For details see [1].

Given an input array x, this layer computes

y=x−E[x]Var[x]+ϵ∗γ+β

Arguments

  • x: Input to be Normalized

  • scale: Scale factor (γ) (can be nothing)

  • bias: Bias factor (β) (can be nothing)

Keyword Arguments

  • dims: Dimensions along which the mean and std of x is computed

  • epsilon: Value added to the denominator for numerical stability

Returns

Normalized Array of same size as x.

References

[1] Ba, Jimmy Lei, Jamie Ryan Kiros, and Geoffrey E. Hinton. "Layer normalization." arXiv preprint arXiv:1607.06450 (2016).

source


+ + + + \ No newline at end of file diff --git a/v0.5.30/api/Building_Blocks/WeightInitializers.html b/v0.5.30/api/Building_Blocks/WeightInitializers.html new file mode 100644 index 000000000..860671083 --- /dev/null +++ b/v0.5.30/api/Building_Blocks/WeightInitializers.html @@ -0,0 +1,78 @@ + + + + + + WeightInitializers | Lux.jl Documentation + + + + + + + + + + + + + +
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WeightInitializers ​

This package is a light dependency providing common weight initialization schemes for deep learning models.

Index ​

API Reference ​

Main Functions ​

# WeightInitializers.glorot_normal — Function.
julia
glorot_normal([::AbstractRNG=_default_rng()], [T=Float32], size...;
+    gain = 1) -> AbstractArray{T, length(size)}

Return an AbstractArray{T} of the given size containing random numbers drawn from a normal distribution with standard deviation gain * sqrt(2 / (fan_in + fan_out)). This method is described in [1] and also known as Xavier initialization.

References

[1] Glorot, Xavier, and Yoshua Bengio. "Understanding the difficulty of training deep feedforward neural networks." Proceedings of the thirteenth international conference on artificial intelligence and statistics. 2010.

source


# WeightInitializers.glorot_uniform — Function.
julia
glorot_uniform([::AbstractRNG=_default_rng()], [T=Float32], size...;
+    gain = 1) -> AbstractArray{T, length(size)}

Return an AbstractArray{T} of the given size containing random numbers drawn from a uniform distribution on the interval [−x,x], where x = gain * sqrt(6 / (fan_in + fan_out)). This method is described in [1] and also known as Xavier initialization.

References

[1] Glorot, Xavier, and Yoshua Bengio. "Understanding the difficulty of training deep feedforward neural networks." Proceedings of the thirteenth international conference on artificial intelligence and statistics. 2010.

source


# WeightInitializers.identity_init — Function.
julia
identity_init([::AbstractRNG=_default_rng()], [T=Float32], size...; gain::Number=1,
+    shift::Union{Integer, Tuple{Integer, Integer}}=0) -> AbstractArray{T}

Constructs an array that aims to provide an identity mapping when used as parameters in most layers of a neural network. The identity mapping is scaled by the gain parameter.

Behavior

  • 1D: Returns a Vector of zeros (useful for biases in layers where input_size == output_size).

  • 2D: Returns an identity matrix (useful for fully connected layers with equal input and output sizes).

  • More than 2D: Returns a tensor where the central slice along the last two dimensions is an identity matrix, and the rest are zeros (useful for convolutional layers, simulating an identity convolution).

Caveats

  • Not all layers will result in an identity mapping when using this initializer. Exceptions include recurrent and normalization layers.

  • Layers must have input_size == output_size for a perfect identity mapping. In cases where this condition is not met, the function pads extra dimensions with zeros.

  • For convolutional layers to achieve an identity mapping, kernel sizes must be odd, and appropriate padding must be applied to ensure the output feature maps are the same size as the input feature maps.

Arguments

  • rng::AbstractRNG: An optional random number generator, included for consistency with other initializers but ignored since the output is deterministic.

  • T::Type{<:Number}: The numeric type of the array elements.

  • size...: The dimensions of the array to be initialized.

  • gain::Number=1: A scaling factor applied to the identity mapping.

  • shift::Union{Integer, Tuple{Integer, Integer}}=0: An integer or a tuple specifying the circular shift applied to the output array.

Returns

  • AbstractArray{T}: An array initialized to represent an identity mapping, scaled by gain and optionally shifted by shift.

Examples

julia
using Random
+
+# Identity matrix for fully connected layer
+identity_matrix = identity_init(MersenneTwister(123), Float32, 5, 5)
+
+# Identity tensor for convolutional layer
+identity_tensor = identity_init(MersenneTwister(123),
+    Float32,        # Bias initialization
+    3,
+    3,
+    5,        # Matrix multiplication
+    5;
+    gain=1.5,
+    shift=(1, 0))

source


# WeightInitializers.kaiming_normal — Function.
julia
kaiming_normal([::AbstractRNG=_default_rng()], [T=Float32], size...;
+    gain = √T(2)) -> AbstractArray{T, length(size)}

Return an AbstractArray{T} of the given size containing random numbers taken from a normal distribution standard deviation gain / sqrt(fan_in)

References

[1] He, Kaiming, et al. "Delving deep into rectifiers: Surpassing human-level performance on imagenet classification." Proceedings of the IEEE international conference on computer vision. 2015.

source


# WeightInitializers.kaiming_uniform — Function.
julia
kaiming_uniform([::AbstractRNG=_default_rng()], [T=Float32], size...;
+    gain = √T(2)) -> AbstractArray{T, length(size)}

Return an AbstractArray{T} of the given size containing random numbers drawn from a uniform distribution on the interval [-x, x], where x = gain * sqrt(3/fan_in).

References

[1] He, Kaiming, et al. "Delving deep into rectifiers: Surpassing human-level performance on imagenet classification." Proceedings of the IEEE international conference on computer vision. 2015.

source


# WeightInitializers.sparse_init — Function.
julia
sparse_init([::AbstractRNG=_default_rng()], [T=Float32], dims::Integer...;
+    sparsity::Number, std::Number=0.01) -> AbstractArray{T}

Creates a sparsely initialized weight matrix with a specified proportion of zeroed elements, using random numbers drawn from a normal distribution for the non-zero elements. This method is introduced in [^Martens2010]. Note: The sparsity parameter controls the proportion of the matrix that will be zeroed. For example, a sparsity of 0.3 means that approximately 30% of the elements will be set to zero. The non-zero elements are distributed according to a normal distribution, scaled by the std parameter.

Arguments

  • rng::AbstractRNG: The random number generator to use.

  • T::Type{<:Number}: The numeric type of the elements in the returned array.

  • dims::Integer...: The dimensions of the weight matrix to be generated.

  • sparsity::Number: The proportion of elements to be zeroed. Must be between 0 and 1.

  • std::Number=0.01: The standard deviation of the normal distribution before applying gain.

Returns

  • AbstractArray{T}: A sparsely initialized weight matrix of dimensions dims and type T.

Examples

julia
using Random
+
+# Initialize a 5x5 sparsely initialized matrix with 30% sparsity
+rng = MersenneTwister(123)
+matrix = sparse_init(rng, Float32, 5, 5; sparsity=0.3, std=0.01)
5×5 Matrix{Float64}:
+  0.0          0.00273815    0.00592403   0.0          0.0
+  0.00459416  -0.000754831  -0.00888936  -0.0077507    0.0
+  0.0         -0.00194229    0.0          0.0         -0.00468489
+  0.0114265    0.0           0.0         -0.00734886   0.00277726
+ -0.00396679   0.0           0.00327215  -0.0071741   -0.00880897

References

[^Martens2010] Martens, J, "Deep learning via Hessian-free optimization" Proceedings of the 27th International Conference on International Conference on Machine Learning. 2010.

source


# WeightInitializers.truncated_normal — Function.
julia
truncated_normal([::AbstractRNG=_default_rng()], [T=Float32], size...; mean = 0,
+    std = 1, lo = -2, hi = 2) -> AbstractArray{T, length(size)}

Return an AbstractArray{T} of the given size where each element is drawn from a truncated normal distribution. The numbers are distributed like filter(x -> lo ≤ x ≤ hi, mean .+ std .* randn(100)).

source


# WeightInitializers.orthogonal — Function.
julia
orthogonal([::AbstractRNG=_default_rng()], [T=Float32], dims::Integer...;
+    gain = 1)  -> AbstractArray{T, length(dims)}

Return an AbstractArray{T} of the given dimensions (dims) which is a (semi) orthogonal matrix, as described in [^Saxe14]

The function constructs an orthogonal or semi-orthogonal matrix depending on the specified dimensions. For two dimensions, it returns a matrix where dims = (rows, cols). For more than two dimensions, it computes an orthogonal matrix of size prod(dims[1:(end - 1)]) by dims[end] before reshaping it to the original dimensions.

Cannot construct a vector, i.e., length(dims) == 1 is forbidden.

Arguments

  • rng::AbstractRNG: Random number generator.

  • T::Type{<:Real}: The type of the elements in the array.

  • dims::Integer...: The dimensions of the array.

  • gain::Number: Scaling factor for the elements of the orthogonal matrix.

References

[^Saxe14] Saxe, McClelland, Ganguli. "Exact solutions to the nonlinear dynamics of learning in deep linear neural networks", ICLR 2014, https://arxiv.org/abs/1312.6120

source


Commonly Used Wrappers ​

# WeightInitializers.zeros16 — Function.
julia
zeros16([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float16, length(size)}

Return an AbstractArray{Float16} of the given size containing an AbstractArray of zeros.

source


# WeightInitializers.ones16 — Function.
julia
ones16([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float16, length(size)}

Return an AbstractArray{Float16} of the given size containing an AbstractArray of ones.

source


# WeightInitializers.rand16 — Function.
julia
rand16([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float16, length(size)}

Return an AbstractArray{Float16} of the given size containing random numbers from a uniform distribution.

source


# WeightInitializers.randn16 — Function.
julia
randn16([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float16, length(size)}

Return an AbstractArray{Float16} of the given size containing random numbers from a standard normal distribution.

source


# WeightInitializers.zeros32 — Function.
julia
zeros32([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float32, length(size)}

Return an AbstractArray{Float32} of the given size containing an AbstractArray of zeros.

source


# WeightInitializers.ones32 — Function.
julia
ones32([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float32, length(size)}

Return an AbstractArray{Float32} of the given size containing an AbstractArray of ones.

source


# WeightInitializers.rand32 — Function.
julia
rand32([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float32, length(size)}

Return an AbstractArray{Float32} of the given size containing random numbers from a uniform distribution.

source


# WeightInitializers.randn32 — Function.
julia
randn32([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float32, length(size)}

Return an AbstractArray{Float32} of the given size containing random numbers from a standard normal distribution.

source


# WeightInitializers.zeros64 — Function.
julia
zeros64([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float64, length(size)}

Return an AbstractArray{Float64} of the given size containing an AbstractArray of zeros.

source


# WeightInitializers.ones64 — Function.
julia
ones64([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float64, length(size)}

Return an AbstractArray{Float64} of the given size containing an AbstractArray of ones.

source


# WeightInitializers.rand64 — Function.
julia
rand64([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float64, length(size)}

Return an AbstractArray{Float64} of the given size containing random numbers from a uniform distribution.

source


# WeightInitializers.randn64 — Function.
julia
randn64([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float64, length(size)}

Return an AbstractArray{Float64} of the given size containing random numbers from a standard normal distribution.

source


# WeightInitializers.zerosC16 — Function.
julia
zerosC16([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF16, length(size)}

Return an AbstractArray{ComplexF16} of the given size containing an AbstractArray of zeros.

source


# WeightInitializers.onesC16 — Function.
julia
onesC16([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF16, length(size)}

Return an AbstractArray{ComplexF16} of the given size containing an AbstractArray of ones.

source


# WeightInitializers.randC16 — Function.
julia
randC16([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF16, length(size)}

Return an AbstractArray{ComplexF16} of the given size containing random numbers from a uniform distribution.

source


# WeightInitializers.randnC16 — Function.
julia
randnC16([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF16, length(size)}

Return an AbstractArray{ComplexF16} of the given size containing random numbers from a standard normal distribution.

source


# WeightInitializers.zerosC32 — Function.
julia
zerosC32([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF32, length(size)}

Return an AbstractArray{ComplexF32} of the given size containing an AbstractArray of zeros.

source


# WeightInitializers.onesC32 — Function.
julia
onesC32([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF32, length(size)}

Return an AbstractArray{ComplexF32} of the given size containing an AbstractArray of ones.

source


# WeightInitializers.randC32 — Function.
julia
randC32([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF32, length(size)}

Return an AbstractArray{ComplexF32} of the given size containing random numbers from a uniform distribution.

source


# WeightInitializers.randnC32 — Function.
julia
randnC32([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF32, length(size)}

Return an AbstractArray{ComplexF32} of the given size containing random numbers from a standard normal distribution.

source


# WeightInitializers.zerosC64 — Function.
julia
zerosC64([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF64, length(size)}

Return an AbstractArray{ComplexF64} of the given size containing an AbstractArray of zeros.

source


# WeightInitializers.onesC64 — Function.
julia
onesC64([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF64, length(size)}

Return an AbstractArray{ComplexF64} of the given size containing an AbstractArray of ones.

source


# WeightInitializers.randC64 — Function.
julia
randC64([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF64, length(size)}

Return an AbstractArray{ComplexF64} of the given size containing random numbers from a uniform distribution.

source


# WeightInitializers.randnC64 — Function.
julia
randnC64([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF64, length(size)}

Return an AbstractArray{ComplexF64} of the given size containing random numbers from a standard normal distribution.

source


+ + + + \ No newline at end of file diff --git a/v0.5.30/api/Domain_Specific_Modeling/Boltz.html b/v0.5.30/api/Domain_Specific_Modeling/Boltz.html new file mode 100644 index 000000000..634d802cd --- /dev/null +++ b/v0.5.30/api/Domain_Specific_Modeling/Boltz.html @@ -0,0 +1,27 @@ + + + + + + Boltz | Lux.jl Documentation + + + + + + + + + + + + + +
Lux.jl Documentation

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Boltz ​

Accelerate ⚡ your ML research using pre-built Deep Learning Models with Lux.

Index ​

Computer Vision Models ​

Classification Models: Native Lux Models ​

MODEL NAMEFUNCTIONNAMEPRETRAINEDTOP 1 ACCURACY (%)TOP 5 ACCURACY (%)
VGGvgg:vgg11✅67.3587.91
VGGvgg:vgg13✅68.4088.48
VGGvgg:vgg16✅70.2489.80
VGGvgg:vgg19✅71.0990.27
VGGvgg:vgg11_bn✅69.0988.94
VGGvgg:vgg13_bn✅69.6689.49
VGGvgg:vgg16_bn✅72.1191.02
VGGvgg:vgg19_bn✅72.9591.32
Vision Transformervision_transformer:tiny🚫
Vision Transformervision_transformer:small🚫
Vision Transformervision_transformer:base🚫
Vision Transformervision_transformer:large🚫
Vision Transformervision_transformer:huge🚫
Vision Transformervision_transformer:giant🚫
Vision Transformervision_transformer:gigantic🚫

Building Blocks ​

# Boltz.ClassTokens — Type.
julia
ClassTokens(dim; init=Lux.zeros32)

Appends class tokens to an input with embedding dimension dim for use in many vision transformer namels.

source


# Boltz.MultiHeadAttention — Type.
julia
MultiHeadAttention(in_planes::Int, number_heads::Int; qkv_bias::Bool=false,
+                   attention_dropout_rate::T=0.0f0,
+                   projection_dropout_rate::T=0.0f0) where {T}

Multi-head self-attention layer

source


# Boltz.ViPosEmbedding — Type.
julia
ViPosEmbedding(embedsize, npatches;
+               init = (rng, dims...) -> randn(rng, Float32, dims...))

Positional embedding layer used by many vision transformer-like namels.

source


# Boltz.transformer_encoder — Function.
julia
transformer_encoder(in_planes, depth, number_heads; mlp_ratio = 4.0f0, dropout = 0.0f0)

Transformer as used in the base ViT architecture. (reference).

Arguments

  • in_planes: number of input channels

  • depth: number of attention blocks

  • number_heads: number of attention heads

  • mlp_ratio: ratio of MLP layers to the number of input channels

  • dropout_rate: dropout rate

source


# Boltz.vgg — Function.
julia
vgg(imsize; config, inchannels, batchnorm = false, nclasses, fcsize, dropout)

Create a VGG model (reference).

Arguments

  • imsize: input image width and height as a tuple

  • config: the configuration for the convolution layers

  • inchannels: number of input channels

  • batchnorm: set to true to use batch normalization after each convolution

  • nclasses: number of output classes

  • fcsize: intermediate fully connected layer size (see Metalhead._vgg_classifier_layers)

  • dropout: dropout level between fully connected layers

source


Non-Public API ​

# Boltz._seconddimmean — Function.
julia
_seconddimmean(x)

Computes the mean of x along dimension 2

source


# Boltz._fast_chunk — Function.
julia
_fast_chunk(x::AbstractArray, ::Val{n}, ::Val{dim})

Type-stable and faster version of MLUtils.chunk

source


# Boltz._flatten_spatial — Function.
julia
_flatten_spatial(x::AbstractArray{T, 4})

Flattens the first 2 dimensions of x, and permutes the remaining dimensions to (2, 1, 3)

source


# Boltz._vgg_block — Function.
julia
_vgg_block(input_filters, output_filters, depth, batchnorm)

A VGG block of convolution layers (reference).

Arguments

  • input_filters: number of input feature maps

  • output_filters: number of output feature maps

  • depth: number of convolution/convolution + batch norm layers

  • batchnorm: set to true to include batch normalization after each convolution

source


# Boltz._vgg_classifier_layers — Function.
julia
_vgg_classifier_layers(imsize, nclasses, fcsize, dropout)

Create VGG classifier (fully connected) layers (reference).

Arguments

  • imsize: tuple (width, height, channels) indicating the size after the convolution layers (see Metalhead._vgg_convolutional_layers)

  • nclasses: number of output classes

  • fcsize: input and output size of the intermediate fully connected layer

  • dropout: the dropout level between each fully connected layer

source


# Boltz._vgg_convolutional_layers — Function.
julia
_vgg_convolutional_layers(config, batchnorm, inchannels)

Create VGG convolution layers (reference).

Arguments

  • config: vector of tuples (output_channels, num_convolutions) for each block (see Metalhead._vgg_block)

  • batchnorm: set to true to include batch normalization after each convolution

  • inchannels: number of input channels

source


Classification Models: Imported from Metalhead.jl ​

Tip

You need to load Flux and Metalhead before using these models.

MODEL NAMEFUNCTIONNAMEPRETRAINEDTOP 1 ACCURACY (%)TOP 5 ACCURACY (%)
AlexNetalexnet:alexnet✅54.4877.72
ResNetresnet:resnet18🚫68.0888.44
ResNetresnet:resnet34🚫72.1390.91
ResNetresnet:resnet50🚫74.5592.36
ResNetresnet:resnet101🚫74.8192.36
ResNetresnet:resnet152🚫77.6393.84
ConvMixerconvmixer:small🚫
ConvMixerconvmixer:base🚫
ConvMixerconvmixer:large🚫
DenseNetdensenet:densenet121🚫
DenseNetdensenet:densenet161🚫
DenseNetdensenet:densenet169🚫
DenseNetdensenet:densenet201🚫
GoogleNetgooglenet:googlenet🚫
MobileNetmobilenet:mobilenet_v1🚫
MobileNetmobilenet:mobilenet_v2🚫
MobileNetmobilenet:mobilenet_v3_small🚫
MobileNetmobilenet:mobilenet_v3_large🚫
ResNeXTresnext:resnext50🚫
ResNeXTresnext:resnext101🚫
ResNeXTresnext:resnext152🚫

These models can be created using <FUNCTION>(<NAME>; pretrained = <PRETRAINED>)

Preprocessing ​

All the pretrained models require that the images be normalized with the parameters mean = [0.485f0, 0.456f0, 0.406f0] and std = [0.229f0, 0.224f0, 0.225f0].

+ + + + \ No newline at end of file diff --git a/v0.5.30/api/Lux/contrib.html b/v0.5.30/api/Lux/contrib.html new file mode 100644 index 000000000..50713cd85 --- /dev/null +++ b/v0.5.30/api/Lux/contrib.html @@ -0,0 +1,125 @@ + + + + + + Experimental Features | Lux.jl Documentation + + + + + + + + + + + + + +
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Experimental Features ​

All features listed on this page are experimental which means:

  1. No SemVer Guarantees. We use code here to iterate fast and most users should wait for these features to be marked non-experimental.

  2. Expect edge-cases and report them. It will help us move these features out of experimental sooner.

  3. None of the features are exported.

Warning

Starting v"0.5.2" all Experimental features need to be accessed via Lux.Experimental.<feature>. Direct access via Lux.<feature> will be removed in v"0.6".

Index ​

Training ​

Helper Functions making it easier to train Lux.jl models.

Lux.Training is meant to be simple and provide extremely basic functionality. We provide basic building blocks which can be seamlessly composed to create complex training pipelines.

# Lux.Experimental.TrainState — Type.
julia
TrainState

Training State containing:

  • model: Lux model.

  • parameters: Trainable Variables of the model.

  • states: Non-trainable Variables of the model.

  • optimizer_state: Optimizer State.

  • step: Number of updates of the parameters made.

source


# Lux.Experimental.compute_gradients — Function.
julia
compute_gradients(ad::ADTypes.AbstractADType, objective_function::Function, data,
+    ts::TrainState)

Compute the gradients of the objective function wrt parameters stored in ts.

Arguments

  • ad: Backend (from ADTypes.jl) used to compute the gradients.

  • objective_function: Objective function. The function must take 4 inputs – model, parameters, states and data. The function must return 3 values – loss, updated_state, and any computed statistics.

  • data: Data used to compute the gradients.

  • ts: Current Training State. See TrainState.

Return

A 4-Tuple containing:

  • grads: Computed Gradients.

  • loss: Loss from the objective function.

  • stats: Any computed statistics from the objective function.

  • ts: Updated Training State.

source


# Lux.Experimental.apply_gradients — Function.
julia
apply_gradients(ts::TrainState, grads)

Update the parameters stored in ts using the gradients grads.

Arguments

  • ts: TrainState object.

  • grads: Gradients of the loss function wrt ts.params.

Returns

Updated TrainState object.

source


Parameter Freezing ​

Info

In the long term, this will be supported via Optimisers.jl.

# Lux.Experimental.FrozenLayer — Type.
julia
FrozenLayer(l::AbstractExplicitLayer, which_params::Union{Tuple, Nothing})

Freeze the parameters with name which_params of the layer l.

Tip

It is always recommended to use the Lux.Experimental.freeze function instead of directly using the FrozenLayer constructor.

Warning

There are no checks for which_params. For example, if the original layer has parameters named (:weight, :bias), and which_paramsis set to(:myweight,) then none of the parameters are frozen and no error is thrown.

Arguments

  • l: Lux AbstractExplicitLayer.

  • which_params: Parameter Names to be Frozen. Can be set to nothing, in which case all parameters are frozen.

Input

  • x: Input to the layer l.

Returns

  • Output of the inner layer l

  • Updated State

Parameters

  • Parameters of the layer l excluding which_params.

States

  • frozen_params: Parameters that are frozen, i.e., which_params.

  • states: The state of the inner layer l.

Note on Internal Layer Implementation

The inner layer should work with NamedTuple parameters. In order to support custom parameter types, users need to implement Lux._merge(::CustomParamType, ::NamedTuple).

Example

julia
m = Lux.Experimental.FrozenLayer(Dense(2 => 2), (:weight,))

See also Lux.Experimental.freeze, Lux.Experimental.unfreeze.

source


# Lux.Experimental.freeze — Function.
julia
freeze(l::AbstractExplicitLayer, which_params::Union{Tuple, Nothing} = nothing)

Constructs a version of l with which_params frozen. If which_params is nothing, then all parameters are frozen.

source

julia
freeze(l::AbstractExplicitLayer, ps, st::NamedTuple,
+       which_params::Union{Tuple, Nothing} = nothing)

Construct a Lux.Experimental.FrozenLayer for l with the current parameters and states. If which_params is nothing, then all parameters are frozen.

source


# Lux.Experimental.unfreeze — Function.
julia
unfreeze(l::FrozenLayer)

Unfreezes the layer l.

source

julia
unfreeze(l::FrozenLayer, ps, st::NamedTuple)

Unwraps a Lux.Experimental.FrozenLayer l with the current parameters and states.

source


For detailed usage example look at the manual page.

Map over Layer ​

# Lux.Experimental.layer_map — Function.
julia
layer_map(f::Function, l::AbstractExplicitLayer, ps, st::NamedTuple,
+          name::String="model")

Map the function f over the model l, with the parameters ps and states st. This is different from Functors.fmap since it zips the layers, parameters, and states and invokes the function on all of them together.

Call Signature for f

  • Must take 4 inputs – AbstractExplicitLayer, Corresponding Parameters, Corresponding States, and the name of the layer.

  • Must return a tuple of 3 elements – AbstractExplicitLayer, new parameters and the new states.

Tip

We recommend using the macro Lux.@layer_map instead of this function. It automatically sets the name of the layer to be the variable name.

Example

julia
using Lux, Random, Setfield
+
+c = Parallel(+; chain=Chain(; dense_1=Dense(2 => 3), bn=BatchNorm(3),
+                              dense_2=Dense(3 => 5)),
+             dense_3=Dense(5 => 1))
+
+rng = Random.default_rng()
+ps, st = Lux.setup(rng, c)
+
+# Makes parameters of Dense Layers inside Chain zero
+function zero_dense_params(l, ps, st, name)
+    if l isa Dense
+        println("zeroing params of $name")
+        @set! ps.weight = zero.(ps.weight)
+        @set! ps.bias = zero.(ps.bias)
+    end
+    return l, ps, st
+end
+
+Lux.layer_map(zero_dense_params, c, ps, st)

source


# Lux.Experimental.@layer_map — Macro.
julia
@layer_map func layer ps st

See the documentation of Lux.Experimental.layer_map for more details. This macro eliminates the need to the set the layer name, and uses the variable name as the starting point.

Example

julia
using Lux, Random, Setfield
+
+c = Parallel(+; chain=Chain(; dense_1=Dense(2 => 3), bn=BatchNorm(3),
+                              dense_2=Dense(3 => 5)),
+             dense_3=Dense(5 => 1))
+
+rng = Random.default_rng()
+ps, st = Lux.setup(rng, c)
+
+# Makes parameters of Dense Layers inside Chain zero
+function zero_dense_params(l, ps, st, name)
+    if l isa Dense
+        println("zeroing params of $name")
+        @set! ps.weight = zero.(ps.weight)
+        @set! ps.bias = zero.(ps.bias)
+    end
+    return l, ps, st
+end
+
+Lux.@layer_map zero_dense_params c ps st

source


Debugging Functionality ​

Model not working properly! Here are some functionalities to help you debug you Lux model.

# Lux.Experimental.@debug_mode — Macro.
julia
@debug_mode layer kwargs...

Recurses into the layer and replaces the inner most non Container Layers with a Lux.Experimental.DebugLayer.

See Lux.Experimental.DebugLayer for details about the Keyword Arguments.

source


# Lux.Experimental.DebugLayer — Type.
julia
DebugLayer(layer::AbstractExplicitLayer; nan_check::Symbol=:both,
+    error_check::Bool=true, location::String="")

Danger

This layer is only meant to be used for debugging. If used for actual training or inference, will lead to extremely bad performance.

A wrapper over Lux layers that adds checks for NaNs and errors. This is useful for debugging.

Arguments

  • layer: The layer to be wrapped.

Keyword Arguments

  • nan_check: Whether to check for NaNs in the input, parameters, and states. Can be :both, :forward, :backward, or :none.

  • error_check: Whether to check for errors in the layer. If true, will throw an error if the layer fails.

  • location: The location of the layer. Use Lux.Experimental.@debug_mode to construct this layer to populate this value correctly.

Inputs

  • x: The input to the layer.

Outputs

  • y: The output of the layer.

  • st: The updated states of the layer.

If nan_check is enabled and NaNs are detected then a DomainError is thrown. If error_check is enabled, then any errors in the layer are thrown with useful information to track where the error originates.

Warning

nan_check for the backward mode only works with ChainRules Compatible Reverse Mode AD Tools currently.

See Lux.Experimental.@debug_mode to construct this layer.

source


Tied Parameters ​

# Lux.Experimental.share_parameters — Function.
julia
share_parameters(ps, sharing)
+share_parameters(ps, sharing, new_parameters)

Updates the parameters in ps with a common set of parameters new_parameters that are shared between each list in the nested list sharing. (That was kind of a mouthful, the example should make it clear).

Arguments

  • ps: Original parameters.

  • sharing: A nested list of lists of accessors of ps which need to shate the parameters (See the example for details). (Each list in the list must be disjoint)

  • new_parameters: If passed the length of new_parameters must be equal to the length of sharing. For each vector in sharing the corresponding parameter in new_parameters will be used. (If not passed, the parameters corresponding to the first element of each vector in sharing will be used).

Returns

Updated Parameters having the same structure as ps.

Example

julia
model = Chain(; d1=Dense(2 => 4, tanh),
+    d3=Chain(; l1=Dense(4 => 2), l2=Dense(2 => 4)), d2=Dense(4 => 2))
+
+ps, st = Lux.setup(Xoshiro(0), model)
+
+# share parameters of (d1 and d3.l1) and (d3.l2 and d2)
+ps = Lux.share_parameters(ps, (("d3.l2", "d1"), ("d2", "d3.l1")))

source


Compact Layer API ​

# Lux.Experimental.@compact — Macro.
julia
@compact(kw...) do x
+    ...
+end
+@compact(forward::Function; name=nothing, dispatch=nothing, parameters...)

Creates a layer by specifying some parameters, in the form of keywords, and (usually as a do block) a function for the forward pass. You may think of @compact as a specialized let block creating local variables that are trainable in Lux. Declared variable names may be used within the body of the forward function. Note that unlike typical Lux models, the forward function doesn't need to explicitly manage states.

Reserved Kwargs:

  1. name: The name of the layer.

  2. dispatch: The constructed layer has the type Lux.Experimental.CompactLuxLayer{dispatch} which can be used for custom dispatches.

Examples

Here is a linear model:

julia
using Lux, Random
+import Lux.Experimental: @compact
+
+r = @compact(w=rand(3)) do x
+    return w .* x
+end
+ps, st = Lux.setup(Xoshiro(0), r)
+r([1, 1, 1], ps, st)  # x is set to [1, 1, 1].

Here is a linear model with bias and activation:

julia
d_in = 5
+d_out = 7
+d = @compact(W=randn(d_out, d_in), b=zeros(d_out), act=relu) do x
+    y = W * x
+    return act.(y .+ b)
+end
+ps, st = Lux.setup(Xoshiro(0), d)
+d(ones(5, 10), ps, st) # 7×10 Matrix as output.
+
+ps_dense = (; weight=ps.W, bias=ps.b)
+first(d([1, 2, 3, 4, 5], ps, st)) ≈
+first(Dense(d_in => d_out, relu)([1, 2, 3, 4, 5], ps_dense, NamedTuple())) # Equivalent to a dense layer

Finally, here is a simple MLP:

julia
n_in = 1
+n_out = 1
+nlayers = 3
+
+model = @compact(w1=Dense(n_in, 128),
+    w2=[Dense(128, 128) for i in 1:nlayers], w3=Dense(128, n_out), act=relu) do x
+    embed = act(w1(x))
+    for w in w2
+        embed = act(w(embed))
+    end
+    out = w3(embed)
+    return out
+end
+
+ps, st = Lux.setup(Xoshiro(0), model)
+
+model(randn(n_in, 32), ps, st)  # 1×32 Matrix as output.

We can train this model just like any Lux model:

julia
using Optimisers, Zygote
+
+x_data = collect(-2.0f0:0.1f0:2.0f0)'
+y_data = 2 .* x_data .- x_data .^ 3
+optim = Optimisers.setup(Adam(), ps)
+
+for epoch in 1:1000
+    loss, gs = Zygote.withgradient(
+        ps -> sum(abs2, first(model(x_data, ps, st)) .- y_data), ps)
+    @show epoch, loss
+    Optimisers.update!(optim, ps, gs[1])
+end

You may also specify a name for the model, which will be used instead of the default printout, which gives a verbatim representation of the code used to construct the model:

julia
model = @compact(w=rand(3), name="Linear(3 => 1)") do x
+    return sum(w .* x)
+end
+
+println(model)  # "Linear(3 => 1)()"

This can be useful when using @compact to hierarchically construct complex models to be used inside a Chain.

Type Stability

If your input function f is type-stable but the generated model is not type stable, it should be treated as a bug. We will appreciate issues if you find such cases.

Parameter Count

Array Parameter don't print the number of parameters on the side. However, they do account for the total number of parameters printed at the bottom.

source


+ + + + \ No newline at end of file diff --git a/v0.5.30/api/Lux/layers.html b/v0.5.30/api/Lux/layers.html new file mode 100644 index 000000000..1ec8b6142 --- /dev/null +++ b/v0.5.30/api/Lux/layers.html @@ -0,0 +1,80 @@ + + + + + + Built-In Layers | Lux.jl Documentation + + + + + + + + + + + + + +
Lux.jl Documentation

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Built-In Layers ​

Index ​

Containers ​

# Lux.BranchLayer — Type.
julia
BranchLayer(layers...)
+BranchLayer(; name=nothing, layers...)

Takes an input x and passes it through all the layers and returns a tuple of the outputs.

Arguments

  • Layers can be specified in two formats:

    • A list of N Lux layers

    • Specified as N keyword arguments.

Keyword Arguments

  • name: Name of the layer (optional)

Inputs

  • x: Will be directly passed to each of the layers

Returns

  • Tuple: (layer_1(x), layer_2(x), ..., layer_N(x)) (naming changes if using the kwargs API)

  • Updated state of the layers

Parameters

  • Parameters of each layer wrapped in a NamedTuple with fields = layer_1, layer_2, ..., layer_N (naming changes if using the kwargs API)

States

  • States of each layer wrapped in a NamedTuple with fields = layer_1, layer_2, ..., layer_N (naming changes if using the kwargs API)

Comparison with Parallel

This is slightly different from Parallel(nothing, layers...)

  • If the input is a tuple, Parallel will pass each element individually to each layer.

  • BranchLayer essentially assumes 1 input comes in and is branched out into N outputs.

Example

An easy way to replicate an input to an NTuple is to do

julia
l = BranchLayer(NoOpLayer(), NoOpLayer(), NoOpLayer())

source


# Lux.Chain — Type.
julia
Chain(layers...; name=nothing, disable_optimizations::Bool = false)
+Chain(; layers..., name=nothing, disable_optimizations::Bool = false)

Collects multiple layers / functions to be called in sequence on a given input.

Arguments

  • Layers can be specified in two formats:

    • A list of N Lux layers

    • Specified as N keyword arguments.

Keyword Arguments

  • disable_optimizations: Prevents any structural optimization

  • name: Name of the layer (optional)

Inputs

Input x is passed sequentially to each layer, and must conform to the input requirements of the internal layers.

Returns

  • Output after sequentially applying all the layers to x

  • Updated model states

Parameters

  • Parameters of each layer wrapped in a NamedTuple with fields = layer_1, layer_2, ..., layer_N (naming changes if using the kwargs API)

States

  • States of each layer wrapped in a NamedTuple with fields = layer_1, layer_2, ..., layer_N (naming changes if using the kwargs API)

Optimizations

Performs a few optimizations to generate reasonable architectures. Can be disabled using keyword argument disable_optimizations.

  • All sublayers are recursively optimized.

  • If a function f is passed as a layer and it doesn't take 3 inputs, it is converted to a WrappedFunction(f) which takes only one input.

  • If the layer is a Chain, it is flattened.

  • NoOpLayers are removed.

  • If there is only 1 layer (left after optimizations), then it is returned without the Chain wrapper.

  • If there are no layers (left after optimizations), a NoOpLayer is returned.

Miscellaneous Properties

  • Allows indexing. We can access the ith layer using m[i]. We can also index using ranges or arrays.

Example

julia
c = Chain(Dense(2, 3, relu), BatchNorm(3), Dense(3, 2))

source


# Lux.PairwiseFusion — Type.
julia
PairwiseFusion(connection, layers...; name=nothing)
+PairwiseFusion(connection; name=nothing, layers...)
x1 → layer1 → y1 ↘
+                  connection → layer2 → y2 ↘
+              x2 ↗                          connection → y3
+                                        x3 ↗

Arguments

  • connection: Takes 2 inputs and combines them

  • layers: AbstractExplicitLayers. Layers can be specified in two formats:

    • A list of N Lux layers

    • Specified as N keyword arguments.

Keyword Arguments

  • name: Name of the layer (optional)

Inputs

Layer behaves differently based on input type:

  1. If the input x is a tuple of length N + 1, then the layers must be a tuple of length N. The computation is as follows
julia
y = x[1]
+for i in 1:N
+    y = connection(x[i + 1], layers[i](y))
+end
  1. Any other kind of input
julia
y = x
+for i in 1:N
+    y = connection(x, layers[i](y))
+end

Returns

  • See Inputs section for how the return value is computed

  • Updated model state for all the contained layers

Parameters

  • Parameters of each layer wrapped in a NamedTuple with fields = layer_1, layer_2, ..., layer_N (naming changes if using the kwargs API)

States

  • States of each layer wrapped in a NamedTuple with fields = layer_1, layer_2, ..., layer_N (naming changes if using the kwargs API)

source


# Lux.Parallel — Type.
julia
Parallel(connection, layers...; name=nothing)
+Parallel(connection; name=nothing, layers...)

Create a layer which passes an input to each path in layers, before reducing the output with connection.

Arguments

  • connection: An N-argument function that is called after passing the input through each layer. If connection = nothing, we return a tuple Parallel(nothing, f, g)(x, y) = (f(x), g(y))

  • Layers can be specified in two formats:

    • A list of N Lux layers

    • Specified as N keyword arguments.

Keyword Arguments

  • name: Name of the layer (optional)

Inputs

  • x: If x is not a tuple, then return is computed as connection([l(x) for l in layers]...). Else one is passed to each layer, thus Parallel(+, f, g)(x, y) = f(x) + g(y).

Returns

  • See the Inputs section for how the output is computed

  • Updated state of the layers

Parameters

  • Parameters of each layer wrapped in a NamedTuple with fields = layer_1, layer_2, ..., layer_N (naming changes if using the kwargs API)

States

  • States of each layer wrapped in a NamedTuple with fields = layer_1, layer_2, ..., layer_N (naming changes if using the kwargs API)

See also SkipConnection which is Parallel with one identity.

source


# Lux.SkipConnection — Type.
julia
SkipConnection(layer, connection; name=nothing)

Create a skip connection which consists of a layer or Chain of consecutive layers and a shortcut connection linking the block's input to the output through a user-supplied 2-argument callable. The first argument to the callable will be propagated through the given layer while the second is the unchanged, "skipped" input.

The simplest "ResNet"-type connection is just SkipConnection(layer, +).

Arguments

  • layer: Layer or Chain of layers to be applied to the input

  • connection:

    • A 2-argument function that takes layer(input) and the input OR

    • An AbstractExplicitLayer that takes (layer(input), input) as input

Keyword Arguments

  • name: Name of the layer (optional)

Inputs

  • x: Will be passed directly to layer

Returns

  • Output of connection(layer(input), input)

  • Updated state of layer

Parameters

  • Parameters of layer OR

  • If connection is an AbstractExplicitLayer, then NamedTuple with fields :layers and :connection

States

  • States of layer OR

  • If connection is an AbstractExplicitLayer, then NamedTuple with fields :layers and :connection

See Parallel for a more general implementation.

source


# Lux.RepeatedLayer — Type.
julia
RepeatedLayer(model; repeats::Val = Val(10), input_injection::Val = Val(false))

Iteratively applies model for repeats number of times. The initial input is passed into the model repeatedly if input_injection = Val(true). This layer unrolls the computation, however, semantically this is same as:

  1. input_injection = Val(false)
julia
res = x
+for i in 1:repeats
+    res, st = model(res, ps, st)
+end
  1. input_injection = Val(true)
julia
res = x
+for i in 1:repeats
+    res, st = model((res, x), ps, st)
+end

It is expected that repeats will be a reasonable number below 20, beyond that compile times for gradients might be unreasonably high.

Arguments

  • model must be an AbstractExplicitLayer

Keyword Arguments

  • repeats: Number of times to apply the model

  • input_injection: If true, then the input is passed to the model along with the output

Inputs

  • x: Input as described above

Returns

  • Output is computed by as described above

  • Updated state of the model

Parameters

  • Parameters of model

States

  • State of model

source


Convolutional Layers ​

# Lux.Conv — Type.
julia
Conv(k::NTuple{N,Integer}, (in_chs => out_chs)::Pair{<:Integer,<:Integer},
+     activation=identity; init_weight=glorot_uniform, init_bias=zeros32, stride=1,
+     pad=0, dilation=1, groups=1, use_bias=true)

Standard convolutional layer.

Image data should be stored in WHCN order (width, height, channels, batch). In other words, a 100 x 100 RGB image would be a 100 x 100 x 3 x 1 array, and a batch of 50 would be a 100 x 100 x 3 x 50 array. This has N = 2 spatial dimensions, and needs a kernel size like (5, 5), a 2-tuple of integers. To take convolutions along N feature dimensions, this layer expects as input an array with ndims(x) == N + 2, where size(x, N + 1) == in_chs is the number of input channels, and size(x, ndims(x)) is the number of observations in a batch.

Warning

Frameworks like Pytorch perform cross-correlation in their convolution layers

Arguments

  • k: Tuple of integers specifying the size of the convolutional kernel. Eg, for 2D convolutions length(k) == 2

  • in_chs: Number of input channels

  • out_chs: Number of input and output channels

  • activation: Activation Function

Keyword Arguments

  • init_weight: Controls the initialization of the weight parameter

  • init_bias: Controls the initialization of the bias parameter

  • stride: Should each be either single integer, or a tuple with N integers

  • dilation: Should each be either single integer, or a tuple with N integers

  • pad: Specifies the number of elements added to the borders of the data array. It can be

    • a single integer for equal padding all around,

    • a tuple of N integers, to apply the same padding at begin/end of each spatial dimension,

    • a tuple of 2*N integers, for asymmetric padding, or

    • the singleton SamePad(), to calculate padding such that size(output,d) == size(x,d) / stride (possibly rounded) for each spatial dimension.

    • Periodic padding can achieved by pre-empting the layer with a WrappedFunction(x -> NNlib.circular_pad(x, N_pad; dims=pad_dims))

  • groups: Expected to be an Int. It specifies the number of groups to divide a convolution into (set groups = in_chs for Depthwise Convolutions). in_chs and out_chs must be divisible by groups.

  • use_bias: Trainable bias can be disabled entirely by setting this to false.

  • allow_fast_activation: If true, then certain activations can be approximated with a faster version. The new activation function will be given by NNlib.fast_act(activation)

Inputs

  • x: Data satisfying ndims(x) == N + 2 && size(x, N - 1) == in_chs, i.e. size(x) = (I_N, ..., I_1, C_in, N)

Returns

  • Output of the convolution y of size (O_N, ..., O_1, C_out, N) where
Oi=⌊Ii+pi+p(i+N)%|p|−di×(ki−1)si+1⌋
  • Empty NamedTuple()

Parameters

  • weight: Convolution kernel

  • bias: Bias (present if use_bias=true)

source


# Lux.ConvTranspose — Type.
julia
ConvTranspose(k::NTuple{N,Integer}, (in_chs => out_chs)::Pair{<:Integer,<:Integer},
+              activation=identity; init_weight=glorot_uniform, init_bias=zeros32,
+              stride=1, pad=0, dilation=1, groups=1, use_bias=true)

Standard convolutional transpose layer.

Arguments

  • k: Tuple of integers specifying the size of the convolutional kernel. Eg, for 2D convolutions length(k) == 2

  • in_chs: Number of input channels

  • out_chs: Number of input and output channels

  • activation: Activation Function

Keyword Arguments

  • init_weight: Controls the initialization of the weight parameter

  • init_bias: Controls the initialization of the bias parameter

  • stride: Should each be either single integer, or a tuple with N integers

  • dilation: Should each be either single integer, or a tuple with N integers

  • pad: Specifies the number of elements added to the borders of the data array. It can be

    • a single integer for equal padding all around,

    • a tuple of N integers, to apply the same padding at begin/end of each spatial dimension,

    • a tuple of 2*N integers, for asymmetric padding, or

    • the singleton SamePad(), to calculate padding such that size(output,d) == size(x,d) * stride (possibly rounded) for each spatial dimension.

  • groups: Expected to be an Int. It specifies the number of groups to divide a convolution into (set groups = in_chs for Depthwise Convolutions). in_chs and out_chs must be divisible by groups.

  • use_bias: Trainable bias can be disabled entirely by setting this to false.

  • allow_fast_activation: If true, then certain activations can be approximated with a faster version. The new activation function will be given by NNlib.fast_act(activation)

Inputs

  • x: Data satisfying ndims(x) == N + 2 && size(x, N - 1) == in_chs, i.e. size(x) = (I_N, ..., I_1, C_in, N)

Returns

  • Output of the convolution transpose y of size (O_N, ..., O_1, C_out, N) where

  • Empty NamedTuple()

Parameters

  • weight: Convolution Transpose kernel

  • bias: Bias (present if use_bias=true)

source


# Lux.CrossCor — Type.
julia
CrossCor(k::NTuple{N,Integer}, (in_chs => out_chs)::Pair{<:Integer,<:Integer},
+         activation=identity; init_weight=glorot_uniform, init_bias=zeros32, stride=1,
+         pad=0, dilation=1, use_bias=true)

Cross Correlation layer.

Image data should be stored in WHCN order (width, height, channels, batch). In other words, a 100 x 100 RGB image would be a 100 x 100 x 3 x 1 array, and a batch of 50 would be a 100 x 100 x 3 x 50 array. This has N = 2 spatial dimensions, and needs a kernel size like (5, 5), a 2-tuple of integers. To take convolutions along N feature dimensions, this layer expects as input an array with ndims(x) == N + 2, where size(x, N + 1) == in_chs is the number of input channels, and size(x, ndims(x)) is the number of observations in a batch.

Arguments

  • k: Tuple of integers specifying the size of the convolutional kernel. Eg, for 2D convolutions length(k) == 2

  • in_chs: Number of input channels

  • out_chs: Number of input and output channels

  • activation: Activation Function

Keyword Arguments

  • init_weight: Controls the initialization of the weight parameter

  • init_bias: Controls the initialization of the bias parameter

  • stride: Should each be either single integer, or a tuple with N integers

  • dilation: Should each be either single integer, or a tuple with N integers

  • pad: Specifies the number of elements added to the borders of the data array. It can be

    • a single integer for equal padding all around,

    • a tuple of N integers, to apply the same padding at begin/end of each spatial dimension,

    • a tuple of 2*N integers, for asymmetric padding, or

    • the singleton SamePad(), to calculate padding such that size(output,d) == size(x,d) / stride (possibly rounded) for each spatial dimension.

  • use_bias: Trainable bias can be disabled entirely by setting this to false.

  • allow_fast_activation: If true, then certain activations can be approximated with a faster version. The new activation function will be given by NNlib.fast_act(activation)

Inputs

  • x: Data satisfying ndims(x) == N + 2 && size(x, N - 1) == in_chs, i.e. size(x) = (I_N, ..., I_1, C_in, N)

Returns

  • Output of the convolution y of size (O_N, ..., O_1, C_out, N) where
Oi=⌊Ii+pi+p(i+N)%|p|−di×(ki−1)si+1⌋
  • Empty NamedTuple()

Parameters

  • weight: Convolution kernel

  • bias: Bias (present if use_bias=true)

source


Dropout Layers ​

# Lux.AlphaDropout — Type.
julia
AlphaDropout(p::Real)

AlphaDropout layer.

Arguments

  • p: Probability of Dropout

    • if p = 0 then NoOpLayer is returned.

    • if p = 1 then WrappedLayer(Base.Fix1(broadcast, zero)) is returned.

Inputs

  • x: Must be an AbstractArray

Returns

  • x with dropout mask applied if training=Val(true) else just x

  • State with updated rng

States

  • rng: Pseudo Random Number Generator

  • training: Used to check if training/inference mode

Call Lux.testmode to switch to test mode.

See also Dropout, VariationalHiddenDropout

source


# Lux.Dropout — Type.
julia
Dropout(p; dims=:)

Dropout layer.

Arguments

  • p: Probability of Dropout (if p = 0 then NoOpLayer is returned)

Keyword Arguments

  • To apply dropout along certain dimension(s), specify the dims keyword. e.g. Dropout(p; dims = 3) will randomly zero out entire channels on WHCN input (also called 2D dropout).

Inputs

  • x: Must be an AbstractArray

Returns

  • x with dropout mask applied if training=Val(true) else just x

  • State with updated rng

States

  • rng: Pseudo Random Number Generator

  • training: Used to check if training/inference mode

Call Lux.testmode to switch to test mode.

See also AlphaDropout, VariationalHiddenDropout

source


# Lux.VariationalHiddenDropout — Type.
julia
VariationalHiddenDropout(p; dims=:)

VariationalHiddenDropout layer. The only difference from Dropout is that the mask is retained until Lux.update_state(l, :update_mask, Val(true)) is called.

Arguments

  • p: Probability of Dropout (if p = 0 then NoOpLayer is returned)

Keyword Arguments

  • To apply dropout along certain dimension(s), specify the dims keyword. e.g. VariationalHiddenDropout(p; dims = 3) will randomly zero out entire channels on WHCN input (also called 2D dropout).

Inputs

  • x: Must be an AbstractArray

Returns

  • x with dropout mask applied if training=Val(true) else just x

  • State with updated rng

States

  • rng: Pseudo Random Number Generator

  • training: Used to check if training/inference mode

  • mask: Dropout mask. Initilly set to nothing. After every run, contains the mask applied in that call

  • update_mask: Stores whether new mask needs to be generated in the current call

Call Lux.testmode to switch to test mode.

See also AlphaDropout, Dropout

source


Pooling Layers ​

# Lux.AdaptiveMaxPool — Type.
julia
AdaptiveMaxPool(out::NTuple)

Adaptive Max Pooling layer. Calculates the necessary window size such that its output has size(y)[1:N] == out.

Arguments

  • out: Size of the first N dimensions for the output

Inputs

  • x: Expects as input an array with ndims(x) == N+2, i.e. channel and batch dimensions, after the N feature dimensions, where N = length(out).

Returns

  • Output of size (out..., C, N)

  • Empty NamedTuple()

See also MaxPool, AdaptiveMeanPool.

source


# Lux.AdaptiveMeanPool — Type.
julia
AdaptiveMeanPool(out::NTuple)

Adaptive Mean Pooling layer. Calculates the necessary window size such that its output has size(y)[1:N] == out.

Arguments

  • out: Size of the first N dimensions for the output

Inputs

  • x: Expects as input an array with ndims(x) == N+2, i.e. channel and batch dimensions, after the N feature dimensions, where N = length(out).

Returns

  • Output of size (out..., C, N)

  • Empty NamedTuple()

See also MeanPool, AdaptiveMaxPool.

source


# Lux.GlobalMaxPool — Type.
julia
GlobalMaxPool()

Global Max Pooling layer. Transforms (w,h,c,b)-shaped input into (1,1,c,b)-shaped output, by performing max pooling on the complete (w,h)-shaped feature maps.

Inputs

  • x: Data satisfying ndims(x) > 2, i.e. size(x) = (I_N, ..., I_1, C, N)

Returns

  • Output of the pooling y of size (1, ..., 1, C, N)

  • Empty NamedTuple()

See also MaxPool, AdaptiveMaxPool, GlobalMeanPool

source


# Lux.GlobalMeanPool — Type.
julia
GlobalMeanPool()

Global Mean Pooling layer. Transforms (w,h,c,b)-shaped input into (1,1,c,b)-shaped output, by performing mean pooling on the complete (w,h)-shaped feature maps.

Inputs

  • x: Data satisfying ndims(x) > 2, i.e. size(x) = (I_N, ..., I_1, C, N)

Returns

  • Output of the pooling y of size (1, ..., 1, C, N)

  • Empty NamedTuple()

See also MeanPool, AdaptiveMeanPool, GlobalMaxPool

source


# Lux.MaxPool — Type.
julia
MaxPool(window::NTuple; pad=0, stride=window)

Max pooling layer, which replaces all pixels in a block of size window with the maximum value.

Arguments

  • window: Tuple of integers specifying the size of the window. Eg, for 2D pooling length(window) == 2

Keyword Arguments

  • stride: Should each be either single integer, or a tuple with N integers

  • pad: Specifies the number of elements added to the borders of the data array. It can be

    • a single integer for equal padding all around,

    • a tuple of N integers, to apply the same padding at begin/end of each spatial dimension,

    • a tuple of 2*N integers, for asymmetric padding, or

    • the singleton SamePad(), to calculate padding such that size(output,d) == size(x,d) / stride (possibly rounded) for each spatial dimension.

Inputs

  • x: Data satisfying ndims(x) == N + 2, i.e. size(x) = (I_N, ..., I_1, C, N)

Returns

  • Output of the pooling y of size (O_N, ..., O_1, C, N) where
Oi=⌊Ii+pi+p(i+N)%|p|−di×(ki−1)si+1⌋
  • Empty NamedTuple()

See also Conv, MeanPool, GlobalMaxPool, AdaptiveMaxPool

source


# Lux.MeanPool — Type.
julia
MeanPool(window::NTuple; pad=0, stride=window)

Mean pooling layer, which replaces all pixels in a block of size window with the mean value.

Arguments

  • window: Tuple of integers specifying the size of the window. Eg, for 2D pooling length(window) == 2

Keyword Arguments

  • stride: Should each be either single integer, or a tuple with N integers

  • pad: Specifies the number of elements added to the borders of the data array. It can be

    • a single integer for equal padding all around,

    • a tuple of N integers, to apply the same padding at begin/end of each spatial dimension,

    • a tuple of 2*N integers, for asymmetric padding, or

    • the singleton SamePad(), to calculate padding such that size(output,d) == size(x,d) / stride (possibly rounded) for each spatial dimension.

Inputs

  • x: Data satisfying ndims(x) == N + 2, i.e. size(x) = (I_N, ..., I_1, C, N)

Returns

  • Output of the pooling y of size (O_N, ..., O_1, C, N) where
Oi=⌊Ii+pi+p(i+N)%|p|−di×(ki−1)si+1⌋
  • Empty NamedTuple()

See also Conv, MaxPool, GlobalMeanPool, AdaptiveMeanPool

source


Recurrent Layers ​

# Lux.GRUCell — Type.
julia
GRUCell((in_dims, out_dims)::Pair{<:Int,<:Int}; use_bias=true, train_state::Bool=false,
+        init_weight::Tuple{Function,Function,Function}=(glorot_uniform, glorot_uniform,
+                                                        glorot_uniform),
+        init_bias::Tuple{Function,Function,Function}=(zeros32, zeros32, zeros32),
+        init_state::Function=zeros32)

Gated Recurrent Unit (GRU) Cell

r=σ(Wir×x+Whr×hprev+bhr)z=σ(Wiz×x+Whz×hprev+bhz)n=tanh⁡(Win×x+bin+r⋅(Whn×hprev+bhn))hnew=(1−z)⋅n+z⋅hprev

Arguments

  • in_dims: Input Dimension

  • out_dims: Output (Hidden State) Dimension

  • use_bias: Set to false to deactivate bias

  • train_state: Trainable initial hidden state can be activated by setting this to true

  • init_bias: Initializer for bias. Must be a tuple containing 3 functions

  • init_weight: Initializer for weight. Must be a tuple containing 3 functions

  • init_state: Initializer for hidden state

Inputs

  • Case 1a: Only a single input x of shape (in_dims, batch_size), train_state is set to false - Creates a hidden state using init_state and proceeds to Case 2.

  • Case 1b: Only a single input x of shape (in_dims, batch_size), train_state is set to true - Repeats hidden_state from parameters to match the shape of x and proceeds to Case 2.

  • Case 2: Tuple (x, (h, )) is provided, then the output and a tuple containing the updated hidden state is returned.

Returns

  • Tuple containing

    • Output hnew of shape (out_dims, batch_size)

    • Tuple containing new hidden state hnew

  • Updated model state

Parameters

  • weight_i: Concatenated Weights to map from input space {Wir,Wiz,Win}.

  • weight_h: Concatenated Weights to map from hidden space {Whr,Whz,Whn}.

  • bias_i: Bias vector (bin; not present if use_bias=false).

  • bias_h: Concatenated Bias vector for the hidden space {bhr,bhz,bhn} (not present if use_bias=false).

  • hidden_state: Initial hidden state vector (not present if train_state=false) {bhr,bhz,bhn}.

States

  • rng: Controls the randomness (if any) in the initial state generation

source


# Lux.LSTMCell — Type.
julia
LSTMCell(in_dims => out_dims; use_bias::Bool=true, train_state::Bool=false,
+         train_memory::Bool=false,
+         init_weight=(glorot_uniform, glorot_uniform, glorot_uniform, glorot_uniform),
+         init_bias=(zeros32, zeros32, ones32, zeros32), init_state=zeros32,
+         init_memory=zeros32)

Long Short-Term (LSTM) Cell

i=σ(Wii×x+Whi×hprev+bi)f=σ(Wif×x+Whf×hprev+bf)g=tanh(Wig×x+Whg×hprev+bg)o=σ(Wio×x+Who×hprev+bo)cnew=f⋅cprev+i⋅ghnew=o⋅tanh(cnew)

Arguments

  • in_dims: Input Dimension

  • out_dims: Output (Hidden State & Memory) Dimension

  • use_bias: Set to false to deactivate bias

  • train_state: Trainable initial hidden state can be activated by setting this to true

  • train_memory: Trainable initial memory can be activated by setting this to true

  • init_bias: Initializer for bias. Must be a tuple containing 4 functions

  • init_weight: Initializer for weight. Must be a tuple containing 4 functions

  • init_state: Initializer for hidden state

  • init_memory: Initializer for memory

Inputs

  • Case 1a: Only a single input x of shape (in_dims, batch_size), train_state is set to false, train_memory is set to false - Creates a hidden state using init_state, hidden memory using init_memory and proceeds to Case 2.

  • Case 1b: Only a single input x of shape (in_dims, batch_size), train_state is set to true, train_memory is set to false - Repeats hidden_state vector from the parameters to match the shape of x, creates hidden memory using init_memory and proceeds to Case 2.

  • Case 1c: Only a single input x of shape (in_dims, batch_size), train_state is set to false, train_memory is set to true - Creates a hidden state using init_state, repeats the memory vector from parameters to match the shape of x and proceeds to Case 2.

  • Case 1d: Only a single input x of shape (in_dims, batch_size), train_state is set to true, train_memory is set to true - Repeats the hidden state and memory vectors from the parameters to match the shape of x and proceeds to Case 2.

  • Case 2: Tuple (x, (h, c)) is provided, then the output and a tuple containing the updated hidden state and memory is returned.

Returns

  • Tuple Containing

    • Output hnew of shape (out_dims, batch_size)

    • Tuple containing new hidden state hnew and new memory cnew

  • Updated model state

Parameters

  • weight_i: Concatenated Weights to map from input space {Wii,Wif,Wig,Wio}.

  • weight_h: Concatenated Weights to map from hidden space {Whi,Whf,Whg,Who}

  • bias: Bias vector (not present if use_bias=false)

  • hidden_state: Initial hidden state vector (not present if train_state=false)

  • memory: Initial memory vector (not present if train_memory=false)

States

  • rng: Controls the randomness (if any) in the initial state generation

source


# Lux.RNNCell — Type.
julia
RNNCell(in_dims => out_dims, activation=tanh; bias::Bool=true,
+        train_state::Bool=false, init_bias=zeros32, init_weight=glorot_uniform,
+        init_state=ones32)

An Elman RNNCell cell with activation (typically set to tanh or relu).

hnew=activation(weightih×x+weighthh×hprev+bias)

Arguments

  • in_dims: Input Dimension

  • out_dims: Output (Hidden State) Dimension

  • activation: Activation function

  • bias: Set to false to deactivate bias

  • train_state: Trainable initial hidden state can be activated by setting this to true

  • init_bias: Initializer for bias

  • init_weight: Initializer for weight

  • init_state: Initializer for hidden state

Inputs

  • Case 1a: Only a single input x of shape (in_dims, batch_size), train_state is set to false - Creates a hidden state using init_state and proceeds to Case 2.

  • Case 1b: Only a single input x of shape (in_dims, batch_size), train_state is set to true - Repeats hidden_state from parameters to match the shape of x and proceeds to Case 2.

  • Case 2: Tuple (x, (h, )) is provided, then the output and a tuple containing the updated hidden state is returned.

Returns

  • Tuple containing

    • Output hnew of shape (out_dims, batch_size)

    • Tuple containing new hidden state hnew

  • Updated model state

Parameters

  • weight_ih: Maps the input to the hidden state.

  • weight_hh: Maps the hidden state to the hidden state.

  • bias: Bias vector (not present if use_bias=false)

  • hidden_state: Initial hidden state vector (not present if train_state=false)

States

  • rng: Controls the randomness (if any) in the initial state generation

source


# Lux.Recurrence — Type.
julia
Recurrence(cell;
+    ordering::AbstractTimeSeriesDataBatchOrdering=BatchLastIndex(),
+    return_sequence::Bool=false)

Wraps a recurrent cell (like RNNCell, LSTMCell, GRUCell) to automatically operate over a sequence of inputs.

Warning

This is completely distinct from Flux.Recur. It doesn't make the cell stateful, rather allows operating on an entire sequence of inputs at once. See StatefulRecurrentCell for functionality similar to Flux.Recur.

Arguments

  • cell: A recurrent cell. See RNNCell, LSTMCell, GRUCell, for how the inputs/outputs of a recurrent cell must be structured.

Keyword Arguments

  • return_sequence: If true returns the entire sequence of outputs, else returns only the last output. Defaults to false.

  • ordering: The ordering of the batch and time dimensions in the input. Defaults to BatchLastIndex(). Alternatively can be set to TimeLastIndex().

Inputs

  • If x is a

    • Tuple or Vector: Each element is fed to the cell sequentially.

    • Array (except a Vector): It is spliced along the penultimate dimension and each slice is fed to the cell sequentially.

Returns

  • Output of the cell for the entire sequence.

  • Update state of the cell.

Parameters

  • Same as cell.

States

  • Same as cell.

Tip

Frameworks like Tensorflow have special implementation of MultiRNNCell to handle sequentially composed RNN Cells. In Lux, one can simple stack multiple Recurrence blocks in a Chain to achieve the same.

Chain(
+    Recurrence(RNNCell(inputsize => latentsize); return_sequence=true),
+    Recurrence(RNNCell(latentsize => latentsize); return_sequence=true),
+    :
+    x -> stack(x; dims=2)
+)

For some discussion on this topic, see https://github.com/LuxDL/Lux.jl/issues/472.

source


# Lux.StatefulRecurrentCell — Type.
julia
StatefulRecurrentCell(cell)

Wraps a recurrent cell (like RNNCell, LSTMCell, GRUCell) and makes it stateful.

Tip

This is very similar to Flux.Recur

To avoid undefined behavior, once the processing of a single sequence of data is complete, update the state with Lux.update_state(st, :carry, nothing).

Arguments

  • cell: A recurrent cell. See RNNCell, LSTMCell, GRUCell, for how the inputs/outputs of a recurrent cell must be structured.

Inputs

  • Input to the cell.

Returns

  • Output of the cell for the entire sequence.

  • Update state of the cell and updated carry.

Parameters

  • Same as cell.

States

  • NamedTuple containing:

    • cell: Same as cell.

    • carry: The carry state of the cell.

source


Linear Layers ​

# Lux.Bilinear — Type.
julia
Bilinear((in1_dims, in2_dims) => out, activation=identity; init_weight=glorot_uniform,
+         init_bias=zeros32, use_bias::Bool=true, allow_fast_activation::Bool=true)
+Bilinear(in12_dims => out, activation=identity; init_weight=glorot_uniform,
+         init_bias=zeros32, use_bias::Bool=true, allow_fast_activation::Bool=true)

Create a fully connected layer between two inputs and an output, and otherwise similar to Dense. Its output, given vectors x & y, is another vector z with, for all i in 1:out:

z[i] = activation(x' * W[i, :, :] * y + bias[i])

If x and y are matrices, then each column of the output z = B(x, y) is of this form, with B the Bilinear layer.

Arguments

  • in1_dims: number of input dimensions of x

  • in2_dims: number of input dimensions of y

  • in12_dims: If specified, then in1_dims = in2_dims = in12_dims

  • out: number of output dimensions

  • activation: activation function

Keyword Arguments

  • init_weight: initializer for the weight matrix (weight = init_weight(rng, out_dims, in1_dims, in2_dims))

  • init_bias: initializer for the bias vector (ignored if use_bias=false)

  • use_bias: Trainable bias can be disabled entirely by setting this to false

  • allow_fast_activation: If true, then certain activations can be approximated with a faster version. The new activation function will be given by NNlib.fast_act(activation)

Input

  • A 2-Tuple containing

    • x must be an AbstractArray with size(x, 1) == in1_dims

    • y must be an AbstractArray with size(y, 1) == in2_dims

  • If the input is an AbstractArray, then x = y

Returns

  • AbstractArray with dimensions (out_dims, size(x, 2))

  • Empty NamedTuple()

Parameters

  • weight: Weight Matrix of size (out_dims, in1_dims, in2_dims)

  • bias: Bias of size (out_dims, 1) (present if use_bias=true)

source


# Lux.Dense — Type.
julia
Dense(in_dims => out_dims, activation=identity; init_weight=glorot_uniform,
+      init_bias=zeros32, use_bias::Bool=true, allow_fast_activation::Bool=true)

Create a traditional fully connected layer, whose forward pass is given by: y = activation.(weight * x .+ bias)

Arguments

  • in_dims: number of input dimensions

  • out_dims: number of output dimensions

  • activation: activation function

Keyword Arguments

  • init_weight: initializer for the weight matrix (weight = init_weight(rng, out_dims, in_dims))

  • init_bias: initializer for the bias vector (ignored if use_bias=false)

  • use_bias: Trainable bias can be disabled entirely by setting this to false

  • allow_fast_activation: If true, then certain activations can be approximated with a faster version. The new activation function will be given by NNlib.fast_act(activation)

Input

  • x must be an AbstractArray with size(x, 1) == in_dims

Returns

  • AbstractArray with dimensions (out_dims, ...) where ... are the dimensions of x

  • Empty NamedTuple()

Parameters

  • weight: Weight Matrix of size (out_dims, in_dims)

  • bias: Bias of size (out_dims, 1) (present if use_bias=true)

source


# Lux.Embedding — Type.
julia
Embedding(in_dims => out_dims; init_weight=randn32)

A lookup table that stores embeddings of dimension out_dims for a vocabulary of size in_dims.

This layer is often used to store word embeddings and retrieve them using indices.

Warning

Unlike Flux.Embedding, this layer does not support using OneHotArray as an input.

Arguments

  • in_dims: number of input dimensions

  • out_dims: number of output dimensions

Keyword Arguments

  • init_weight: initializer for the weight matrix (weight = init_weight(rng, out_dims, in_dims))

Input

  • Integer OR

  • Abstract Vector of Integers OR

  • Abstract Array of Integers

Returns

  • Returns the embedding corresponding to each index in the input. For an N dimensional input, an N + 1 dimensional output is returned.

  • Empty NamedTuple()

source


# Lux.Scale — Type.
julia
Scale(dims, activation=identity; init_weight=ones32, init_bias=zeros32, bias::Bool=true)

Create a Sparsely Connected Layer with a very specific structure (only Diagonal Elements are non-zero). The forward pass is given by: y = activation.(weight .* x .+ bias)

Arguments

  • dims: size of the learnable scale and bias parameters.

  • activation: activation function

Keyword Arguments

  • init_weight: initializer for the weight matrix (weight = init_weight(rng, out_dims, in_dims))

  • init_bias: initializer for the bias vector (ignored if use_bias=false)

  • use_bias: Trainable bias can be disabled entirely by setting this to false

  • allow_fast_activation: If true, then certain activations can be approximated with a faster version. The new activation function will be given by NNlib.fast_act(activation)

Input

  • x must be an Array of size (dims..., B) or (dims...[0], ..., dims[k]) for k ≤ size(dims)

Returns

  • Array of size (dims..., B) or (dims...[0], ..., dims[k]) for k ≤ size(dims)

  • Empty NamedTuple()

Parameters

  • weight: Weight Array of size (dims...)

  • bias: Bias of size (dims...)

source


Misc. Helper Layers ​

# Lux.FlattenLayer — Type.
julia
FlattenLayer(N = nothing)

Flattens the passed array into a matrix.

Arguments

  • N: Flatten the first N dimensions of the input array. If nothing, then all dimensions (except) are flattened. Note that the batch dimension is never flattened.

Inputs

  • x: AbstractArray

Returns

  • AbstractMatrix of size (:, size(x, ndims(x)))

  • Empty NamedTuple()

source


# Lux.Maxout — Type.
julia
Maxout(layers...)
+Maxout(; layers...)
+Maxout(f::Function, n_alts::Int)

This contains a number of internal layers, each of which receives the same input. Its output is the elementwise maximum of the the internal layers' outputs.

Maxout over linear dense layers satisfies the univeral approximation theorem. See [1].

See also Parallel to reduce with other operators.

Arguments

  • Layers can be specified in three formats:

    • A list of N Lux layers

    • Specified as N keyword arguments.

    • A no argument function f and an integer n_alts which specifies the number of layers.

Inputs

  • x: Input that is passed to each of the layers

Returns

  • Output is computed by taking elementwise max of the outputs of the individual layers.

  • Updated state of the layers

Parameters

  • Parameters of each layer wrapped in a NamedTuple with fields = layer_1, layer_2, ..., layer_N (naming changes if using the kwargs API)

States

  • States of each layer wrapped in a NamedTuple with fields = layer_1, layer_2, ..., layer_N (naming changes if using the kwargs API)

References

[1] Goodfellow, Warde-Farley, Mirza, Courville & Bengio "Maxout Networks" https://arxiv.org/abs/1302.4389

source


# Lux.NoOpLayer — Type.
julia
NoOpLayer()

As the name suggests does nothing but allows pretty printing of layers. Whatever input is passed is returned.

source


# Lux.ReshapeLayer — Type.
julia
ReshapeLayer(dims)

Reshapes the passed array to have a size of (dims..., :)

Arguments

  • dims: The new dimensions of the array (excluding the last dimension).

Inputs

  • x: AbstractArray of any shape which can be reshaped in (dims..., size(x, ndims(x)))

Returns

  • AbstractArray of size (dims..., size(x, ndims(x)))

  • Empty NamedTuple()

source


# Lux.SelectDim — Type.
julia
SelectDim(dim, i)

Return a view of all the data of the input x where the index for dimension dim equals i. Equivalent to view(x,:,:,...,i,:,:,...) where i is in position d.

Arguments

  • dim: Dimension for indexing

  • i: Index for dimension dim

Inputs

  • x: AbstractArray that can be indexed with view(x,:,:,...,i,:,:,...)

Returns

  • view(x,:,:,...,i,:,:,...) where i is in position d

  • Empty NamedTuple()

source


# Lux.WrappedFunction — Type.
julia
WrappedFunction(f)

Wraps a stateless and parameter less function. Might be used when a function is added to Chain. For example, Chain(x -> relu.(x)) would not work and the right thing to do would be Chain((x, ps, st) -> (relu.(x), st)). An easier thing to do would be Chain(WrappedFunction(Base.Fix1(broadcast, relu)))

Arguments

  • f::Function: A stateless and parameterless function

Inputs

  • x: s.t hasmethod(f, (typeof(x),)) is true

Returns

  • Output of f(x)

  • Empty NamedTuple()

source


Normalization Layers ​

# Lux.BatchNorm — Type.
julia
BatchNorm(chs::Integer, activation=identity; init_bias=zeros32, init_scale=ones32,
+          affine=true, track_stats=true, epsilon=1f-5, momentum=0.1f0,
+          allow_fast_activation::Bool=true)

Batch Normalization layer.

BatchNorm computes the mean and variance for each D1×...×DN−2×1×DN input slice and normalises the input accordingly.

Arguments

  • chs: Size of the channel dimension in your data. Given an array with N dimensions, call the N-1th the channel dimension. For a batch of feature vectors this is just the data dimension, for WHCN images it's the usual channel dimension.

  • activation: After normalization, elementwise activation activation is applied.

Keyword Arguments

  • If track_stats=true, accumulates mean and variance statistics in training phase that will be used to renormalize the input in test phase.

  • epsilon: a value added to the denominator for numerical stability

  • momentum: the value used for the running_mean and running_var computation

  • allow_fast_activation: If true, then certain activations can be approximated with a faster version. The new activation function will be given by NNlib.fast_act(activation)

  • If affine=true, it also applies a shift and a rescale to the input through to learnable per-channel bias and scale parameters.

    • init_bias: Controls how the bias is initiliazed

    • init_scale: Controls how the scale is initiliazed

Inputs

  • x: Array where size(x, N - 1) = chs and ndims(x) > 2

Returns

  • y: Normalized Array

  • Update model state

Parameters

  • affine=true

    • bias: Bias of shape (chs,)

    • scale: Scale of shape (chs,)

  • affine=false - Empty NamedTuple()

States

  • Statistics if track_stats=true

    • running_mean: Running mean of shape (chs,)

    • running_var: Running variance of shape (chs,)

  • Statistics if track_stats=false

    • running_mean: nothing

    • running_var: nothing

  • training: Used to check if training/inference mode

Use Lux.testmode during inference.

Example

julia
m = Chain(Dense(784 => 64), BatchNorm(64, relu), Dense(64 => 10), BatchNorm(10))

Warning

Passing a batch size of 1, during training will result in NaNs.

See also BatchNorm, InstanceNorm, LayerNorm, WeightNorm

source


# Lux.GroupNorm — Type.
julia
GroupNorm(chs::Integer, groups::Integer, activation=identity; init_bias=zeros32,
+          init_scale=ones32, affine=true, epsilon=1f-5,
+          allow_fast_activation::Bool=true)

Group Normalization layer.

Arguments

  • chs: Size of the channel dimension in your data. Given an array with N dimensions, call the N-1th the channel dimension. For a batch of feature vectors this is just the data dimension, for WHCN images it's the usual channel dimension.

  • groups is the number of groups along which the statistics are computed. The number of channels must be an integer multiple of the number of groups.

  • activation: After normalization, elementwise activation activation is applied.

Keyword Arguments

  • epsilon: a value added to the denominator for numerical stability

  • allow_fast_activation: If true, then certain activations can be approximated with a faster version. The new activation function will be given by NNlib.fast_act(activation)

  • If affine=true, it also applies a shift and a rescale to the input through to learnable per-channel bias and scale parameters.

    • init_bias: Controls how the bias is initiliazed

    • init_scale: Controls how the scale is initiliazed

Inputs

  • x: Array where size(x, N - 1) = chs and ndims(x) > 2

Returns

  • y: Normalized Array

  • Update model state

Parameters

  • affine=true

    • bias: Bias of shape (chs,)

    • scale: Scale of shape (chs,)

  • affine=false - Empty NamedTuple()

States

  • training: Used to check if training/inference mode

Use Lux.testmode during inference.

Example

julia
m = Chain(Dense(784 => 64), GroupNorm(64, 4, relu), Dense(64 => 10), GroupNorm(10, 5))

See also GroupNorm, InstanceNorm, LayerNorm, WeightNorm

source


# Lux.InstanceNorm — Type.
julia
InstanceNorm(chs::Integer, activation=identity; init_bias=zeros32, init_scale=ones32,
+             affine=true, epsilon=1f-5, allow_fast_activation::Bool=true)

Instance Normalization. For details see [1].

Instance Normalization computes the mean and variance for each D1×...×DN−2×1×1` input slice and normalises the input accordingly.

Arguments

  • chs: Size of the channel dimension in your data. Given an array with N dimensions, call the N-1th the channel dimension. For a batch of feature vectors this is just the data dimension, for WHCN images it's the usual channel dimension.

  • activation: After normalization, elementwise activation activation is applied.

Keyword Arguments

  • epsilon: a value added to the denominator for numerical stability

  • allow_fast_activation: If true, then certain activations can be approximated with a faster version. The new activation function will be given by NNlib.fast_act(activation)

  • If affine=true, it also applies a shift and a rescale to the input through to learnable per-channel bias and scale parameters.

    • init_bias: Controls how the bias is initiliazed

    • init_scale: Controls how the scale is initiliazed

Inputs

  • x: Array where size(x, N - 1) = chs and ndims(x) > 2

Returns

  • y: Normalized Array

  • Update model state

Parameters

  • affine=true

    • bias: Bias of shape (chs,)

    • scale: Scale of shape (chs,)

  • affine=false - Empty NamedTuple()

States

  • training: Used to check if training/inference mode

Use Lux.testmode during inference.

Example

julia
m = Chain(Dense(784 => 64), InstanceNorm(64, relu), Dense(64 => 10), InstanceNorm(10, 5))

References

[1] Ulyanov, Dmitry, Andrea Vedaldi, and Victor Lempitsky. "Instance normalization: The missing ingredient for fast stylization." arXiv preprint arXiv:1607.08022 (2016).

See also BatchNorm, GroupNorm, LayerNorm, WeightNorm

source


# Lux.LayerNorm — Type.
julia
LayerNorm(shape::NTuple{N, Int}, activation=identity; epsilon=1f-5, dims=Colon(),
+          affine::Bool=true, init_bias=zeros32, init_scale=ones32,)

Computes mean and standard deviation over the whole input array, and uses these to normalize the whole array. Optionally applies an elementwise affine transformation afterwards.

Given an input array x, this layer computes

y=x−E[x]Var[x]+ϵ∗γ+β

where γ & β are trainable parameters if affine=true.

Warning

As of v0.5.0, the doc used to say affine::Bool=false, but the code actually had affine::Bool=true as the default. Now the doc reflects the code, so please check whether your assumptions about the default (if made) were invalid.

Arguments

  • shape: Broadcastable shape of input array excluding the batch dimension.

  • activation: After normalization, elementwise activation activation is applied.

Keyword Arguments

  • allow_fast_activation: If true, then certain activations can be approximated with a faster version. The new activation function will be given by NNlib.fast_act(activation)

  • epsilon: a value added to the denominator for numerical stability.

  • dims: Dimensions to normalize the array over.

  • If affine=true, it also applies a shift and a rescale to the input through to learnable per-channel bias and scale parameters.

    • init_bias: Controls how the bias is initiliazed

    • init_scale: Controls how the scale is initiliazed

Inputs

  • x: AbstractArray

Returns

  • y: Normalized Array

  • Empty NamedTuple()

Parameters

  • affine=false: Empty NamedTuple()

  • affine=true

    • bias: Bias of shape (shape..., 1)

    • scale: Scale of shape (shape..., 1)

source


# Lux.WeightNorm — Type.
julia
WeightNorm(layer::AbstractExplicitLayer, which_params::NTuple{N,Symbol},
+           dims::Union{Tuple,Nothing}=nothing)

Applies weight normalization to a parameter in the given layer.

w=gv∥v∥

Weight normalization is a reparameterization that decouples the magnitude of a weight tensor from its direction. This updates the parameters in which_params (e.g. weight) using two parameters: one specifying the magnitude (e.g. weight_g) and one specifying the direction (e.g. weight_v).

Arguments

  • layer whose parameters are being reparameterized

  • which_params: parameter names for the parameters being reparameterized

  • By default, a norm over the entire array is computed. Pass dims to modify the dimension.

Inputs

  • x: Should be of valid type for input to layer

Returns

  • Output from layer

  • Updated model state of layer

Parameters

  • normalized: Parameters of layer that are being normalized

  • unnormalized: Parameters of layer that are not being normalized

States

  • Same as that of layer

source


Upsampling ​

# Lux.PixelShuffle — Function.
julia
PixelShuffle(r::Int)

Pixel shuffling layer with upscale factor r. Usually used for generating higher resolution images while upscaling them.

See NNlib.pixel_shuffle for more details.

PixelShuffle is not a Layer, rather it returns a WrappedFunction with the function set to Base.Fix2(pixel_shuffle, r)

Arguments

  • r: Upscale factor

Inputs

  • x: For 4D-arrays representing N images, the operation converts input size(x) == (W, H, r² x C, N) to output of size (r x W, r x H, C, N). For D-dimensional data, it expects ndims(x) == D + 2 with channel and batch dimensions, and divides the number of channels by rᴰ.

Returns

  • Output of size (r x W, r x H, C, N) for 4D-arrays, and (r x W, r x H, ..., C, N) for D-dimensional data, where D = ndims(x) - 2

source


# Lux.Upsample — Type.
julia
Upsample(mode = :nearest; [scale, size]) 
+Upsample(scale, mode = :nearest)

Upsampling Layer.

Layer Construction

Option 1

  • mode: Set to :nearest, :linear, :bilinear or :trilinear

Exactly one of two keywords must be specified:

  • If scale is a number, this applies to all but the last two dimensions (channel and batch) of the input. It may also be a tuple, to control dimensions individually.

  • Alternatively, keyword size accepts a tuple, to directly specify the leading dimensions of the output.

Option 2

  • If scale is a number, this applies to all but the last two dimensions (channel and batch) of the input. It may also be a tuple, to control dimensions individually.

  • mode: Set to :nearest, :bilinear or :trilinear

Currently supported upsampling modes and corresponding NNlib's methods are:

  • :nearest -> NNlib.upsample_nearest

  • :bilinear -> NNlib.upsample_bilinear

  • :trilinear -> NNlib.upsample_trilinear

Inputs

  • x: For the input dimensions look into the documentation for the corresponding NNlib function

    • As a rule of thumb, :nearest should work with arrays of arbitrary dimensions

    • :bilinear works with 4D Arrays

    • :trilinear works with 5D Arrays

Returns

  • Upsampled Input of size size or of size (I_1 x scale[1], ..., I_N x scale[N], C, N)

  • Empty NamedTuple()

source


+ + + + \ No newline at end of file diff --git a/v0.5.30/api/Lux/switching_frameworks.html b/v0.5.30/api/Lux/switching_frameworks.html new file mode 100644 index 000000000..569352fa0 --- /dev/null +++ b/v0.5.30/api/Lux/switching_frameworks.html @@ -0,0 +1,48 @@ + + + + + + Switching between Deep Learning Frameworks | Lux.jl Documentation + + + + + + + + + + + + + +
Lux.jl Documentation

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Switching between Deep Learning Frameworks ​

Flux Models to Lux Models ​

Flux.jl has been around in the Julia ecosystem for a long time and has a large userbase, hence we provide a way to convert Flux models to Lux models.

Tip

Accessing these functions require manually loading Flux, i.e., using Flux must be present somewhere in the code for these to be used.

# Adapt.adapt — Method.
julia
Adapt.adapt(from::FromFluxAdaptor, L)

Adapt a Flux model L to Lux model. See FromFluxAdaptor for more details.

source


# Lux.FromFluxAdaptor — Type.
julia
FromFluxAdaptor(preserve_ps_st::Bool=false, force_preserve::Bool=false)

Convert a Flux Model to Lux Model.

Warning

This always ingores the active field of some of the Flux layers. This is almost never going to be supported.

Keyword Arguments

  • preserve_ps_st: Set to true to preserve the states and parameters of the layer. This attempts the best possible way to preserve the original model. But it might fail. If you need to override possible failures, set force_preserve to true.

  • force_preserve: Some of the transformations with state and parameters preservation haven't been implemented yet, in these cases, if force_transform is false a warning will be printed and a core Lux layer will be returned. Else, it will create a FluxLayer.

Example

julia
import Flux
+using Adapt, Lux, Metalhead, Random
+
+m = ResNet(18)
+m2 = adapt(FromFluxAdaptor(), m.layers) # or FromFluxAdaptor()(m.layers)
+
+x = randn(Float32, 224, 224, 3, 1);
+
+ps, st = Lux.setup(Random.default_rng(), m2);
+
+m2(x, ps, st)

source


# Lux.FluxLayer — Type.
julia
FluxLayer(layer)

Serves as a compatibility layer between Flux and Lux. This uses Optimisers.destructure API internally.

Warning

Lux was written to overcome the limitations of destructure + Flux. It is recommended to rewrite your l in Lux instead of using this layer.

Warning

Introducing this Layer in your model will lead to type instabilities, given the way Optimisers.destructure works.

Arguments

  • layer: Flux layer

Parameters

  • p: Flattened parameters of the layer

source


Lux Models to Simple Chains ​

SimpleChains.jl provides a way to train Small Neural Networks really fast on CPUs. See this blog post for more details. This section describes how to convert Lux models to SimpleChains models while preserving the layer interface.

Tip

Accessing these functions require manually loading SimpleChains, i.e., using SimpleChains must be present somewhere in the code for these to be used.

# Adapt.adapt — Method.
julia
Adapt.adapt(from::ToSimpleChainsAdaptor, L::AbstractExplicitLayer)

Adapt a Flux model to Lux model. See ToSimpleChainsAdaptor for more details.

source


# Lux.ToSimpleChainsAdaptor — Type.
julia
ToSimpleChainsAdaptor()

Adaptor for converting a Lux Model to SimpleChains. The returned model is still a Lux model, and satisfies the AbstractExplicitLayer interfacem but all internal calculations are performed using SimpleChains.

Warning

There is no way to preserve trained parameters and states when converting to SimpleChains.jl.

Warning

Any kind of initialization function is not preserved when converting to SimpleChains.jl.

Arguments

  • input_dims: Tuple of input dimensions excluding the batch dimension. These must be of static type as SimpleChains expects.

Example

julia
import SimpleChains: static
+using Adapt, Lux, Random
+
+lux_model = Chain(Conv((5, 5), 1 => 6, relu), MaxPool((2, 2)),
+    Conv((5, 5), 6 => 16, relu), MaxPool((2, 2)), FlattenLayer(3),
+    Chain(Dense(256 => 128, relu), Dense(128 => 84, relu), Dense(84 => 10)))
+
+adaptor = ToSimpleChainsAdaptor((static(28), static(28), static(1)))
+
+simple_chains_model = adapt(adaptor, lux_model) # or adaptor(lux_model)
+
+ps, st = Lux.setup(Random.default_rng(), simple_chains_model)
+x = randn(Float32, 28, 28, 1, 1)
+
+simple_chains_model(x, ps, st)

source


# Lux.SimpleChainsLayer — Type.
julia
SimpleChainsLayer(layer)

Wraps a SimpleChains layer into a Lux layer. All operations are performed using SimpleChains but the layer satisfies the AbstractExplicitLayer interface.

Arguments

  • layer: SimpleChains layer

source


+ + + + \ No newline at end of file diff --git a/v0.5.30/api/Lux/utilities.html b/v0.5.30/api/Lux/utilities.html new file mode 100644 index 000000000..e1d55373f --- /dev/null +++ b/v0.5.30/api/Lux/utilities.html @@ -0,0 +1,26 @@ + + + + + + Utilities | Lux.jl Documentation + + + + + + + + + + + + + +
Lux.jl Documentation

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Trusted by

Scientific Computing

SciML.ai

Machine Learning

Structure Preserving

GeometricML.jl

Machine Learning

Physical Systems

MeshGraphNets.jl

Graph Neural Nets

Utilities ​

Index ​

Device Management / Data Transfer ​

# Lux.cpu — Function.
julia
cpu(x)

Transfer x to CPU.

Warning

This function has been deprecated. Use cpu_device instead.

source


# Lux.gpu — Function.
julia
gpu(x)

Transfer x to GPU determined by the backend set using Lux.gpu_backend!.

Warning

This function has been deprecated. Use gpu_device instead. Using this function inside performance critical code will cause massive slowdowns due to type inference failure.

source


Warning

For detailed API documentation on Data Transfer check out the LuxDeviceUtils.jl

Weight Initialization ​

Warning

For API documentation on Initialization check out the WeightInitializers.jl

Miscellaneous Utilities ​

# Lux.foldl_init — Function.
julia
foldl_init(op, x)
+foldl_init(op, x, init)

Exactly same as foldl(op, x; init) in the forward pass. But, gives gradients wrt init in the backward pass.

source


# Lux.istraining — Function.
julia
istraining(::Val{training})
+istraining(st::NamedTuple)

Returns true if training is true or if st contains a training field with value true. Else returns false.

Method undefined if st.training is not of type Val.

source


# Lux.multigate — Function.
julia
multigate(x::AbstractArray, ::Val{N})

Split up x into N equally sized chunks (along dimension 1).

source


Updating Floating Point Precision ​

By default, Lux uses Float32 for all parameters and states. To update the precision simply pass the parameters / states / arrays into one of the following functions.

# Lux.f16 — Function.
julia
f16(m)

Converts the eltype of m floating point values to Float16. Recurses into structs marked with Functors.@functor.

source


# Lux.f32 — Function.
julia
f32(m)

Converts the eltype of m floating point values to Float32. Recurses into structs marked with Functors.@functor.

source


# Lux.f64 — Function.
julia
f64(m)

Converts the eltype of m floating point values to Float64. Recurses into structs marked with Functors.@functor.

source


Stateful Layer ​

# Lux.StatefulLuxLayer — Type.
julia
StatefulLuxLayer(model, ps, st; st_fixed_type = Val(true))

Warning

This is not a Lux.AbstractExplicitLayer

A convenience wrapper over Lux layers which stores the parameters and states internally. Most users should not be using this version. This comes handy when Lux internally uses the @compact to construct models and in SciML codebases where propagating state might involving Boxing.

For a motivating example, see the Neural ODE tutorial.

Arguments

  • model: A Lux layer

  • ps: The parameters of the layer. This can be set to nothing, if the user provides the parameters on function call

  • st: The state of the layer

Keyword Arguments

  • st_fixed_type: If Val(true), then the type of the state is fixed, i.e., typeof(last(model(x, ps, st))) == st. If this is not the case, then st_fixed_type must be set to Val(false). If st_fixed_type is set to Val(false), then type stability is not guaranteed.

Inputs

  • x: The input to the layer

  • ps: The parameters of the layer. Optional, defaults to s.ps

Outputs

  • y: The output of the layer

source


Truncated Stacktraces ​

# Lux.disable_stacktrace_truncation! — Function.
julia
disable_stacktrace_truncation!(; disable::Bool=true)

An easy way to update TruncatedStacktraces.VERBOSE without having to load it manually.

Effectively does TruncatedStacktraces.VERBOSE[] = disable

source


+ + + + \ No newline at end of file diff --git a/v0.5.30/api/Testing_Functionality/LuxTestUtils.html b/v0.5.30/api/Testing_Functionality/LuxTestUtils.html new file mode 100644 index 000000000..93ffc1484 --- /dev/null +++ b/v0.5.30/api/Testing_Functionality/LuxTestUtils.html @@ -0,0 +1,41 @@ + + + + + + LuxTestUtils | Lux.jl Documentation + + + + + + + + + + + + + +
Lux.jl Documentation

Appearance


Trusted by

Scientific Computing

SciML.ai

Machine Learning

Structure Preserving

GeometricML.jl

Machine Learning

Physical Systems

MeshGraphNets.jl

Graph Neural Nets

LuxTestUtils ​

Warning

This is a testing package. Hence, we don't use features like weak dependencies to reduce load times. It is recommended that you exclusively use this package for testing and not add a dependency to it in your main package Project.toml.

Implements utilities for testing gradient correctness and dynamic dispatch of Lux.jl models.

Index ​

Testing using JET.jl ​

# LuxTestUtils.@jet — Macro.
julia
@jet f(args...) call_broken=false opt_broken=false

Run JET tests on the function f with the arguments args.... If JET fails to compile or julia version is < 1.7, then the macro will be a no-op.

Keyword Arguments

  • call_broken: Marks the test_call as broken.

  • opt_broken: Marks the test_opt as broken.

All additional arguments will be forwarded to @JET.test_call and @JET.test_opt.

TIP

Instead of specifying target_modules with every call, you can set preferences for target_modules using Preferences.jl. For example, to set target_modules to (Lux, LuxLib) we can run:

julia
using Preferences
+
+set_preferences!(Base.UUID("ac9de150-d08f-4546-94fb-7472b5760531"),
+    "target_modules" => ["Lux", "LuxLib"])

Example

julia
using LuxTestUtils
+
+@testset "Showcase JET Testing" begin
+    @jet sum([1, 2, 3]) target_modules=(Base, Core)
+
+    @jet sum(1, 1) target_modules=(Base, Core) opt_broken=true
+end

source


Gradient Correctness ​

# LuxTestUtils.@test_gradients — Macro.
julia
@test_gradients f args... [kwargs...]

Compare the gradients computed by Zygote.jl (Reverse Mode AD) against:

  • Tracker.jl (Reverse Mode AD)

  • ReverseDiff.jl (Reverse Mode AD)

  • ForwardDiff.jl (Forward Mode AD)

  • FiniteDifferences.jl (Finite Differences)

TIP

This function is completely compatible with Test.jl

Arguments

  • f: The function to test.

  • args...: Inputs to f wrt which the gradients are computed.

Keyword Arguments

  • gpu_testing: Disables ForwardDiff, ReverseDiff and FiniteDifferences tests. (Default: false)

  • soft_fail: If true, the test will not fail if any of the gradients are incorrect, instead it will show up as broken. (Default: false)

  • skip_(tracker|reverse_diff|forward_diff|finite_differences): Skip the corresponding gradient computation and check. (Default: false)

  • large_arrays_skip_(forward_diff|finite_differences): Skip the corresponding gradient computation and check for large arrays. (Forward Mode and Finite Differences are not efficient for large arrays.) (Default: true)

  • large_array_length: The length of the array above which the gradient computation is considered large. (Default: 25)

  • max_total_array_size: Treat as large array if the total size of all arrays is greater than this value. (Default: 100)

  • (tracker|reverse_diff|forward_diff|finite_differences)_broken: Mark the corresponding gradient test as broken. (Default: false)

Keyword Arguments for check_approx

  • atol: Absolute tolerance for gradient comparisons. (Default: 0.0)

  • rtol: Relative tolerance for gradient comparisons. (Default: atol > 0 ? 0.0 : √eps(typeof(atol)))

  • nans: Whether or not NaNs are considered equal. (Default: false)

Example

julia
using LuxTestUtils
+
+x = randn(10)
+
+@testset "Showcase Gradient Testing" begin
+    @test_gradients sum abs2 x
+
+    @test_gradients prod x
+end

source


+ + + + \ No newline at end of file diff --git a/v0.5.30/assets/api_Accelerator_Support_LuxAMDGPU.md.qoeTbLKY.js b/v0.5.30/assets/api_Accelerator_Support_LuxAMDGPU.md.qoeTbLKY.js new file mode 100644 index 000000000..e4b9da11a --- /dev/null +++ b/v0.5.30/assets/api_Accelerator_Support_LuxAMDGPU.md.qoeTbLKY.js @@ -0,0 +1 @@ +import{_ as e,c as a,o as t,a4 as o}from"./chunks/framework.BfjuC5t1.js";const P=JSON.parse('{"title":"LuxAMDGPU","description":"","frontmatter":{},"headers":[],"relativePath":"api/Accelerator_Support/LuxAMDGPU.md","filePath":"api/Accelerator_Support/LuxAMDGPU.md","lastUpdated":null}'),i={name:"api/Accelerator_Support/LuxAMDGPU.md"},r=o('

LuxAMDGPU ​

LuxAMDGPU is meant to be used as a trigger package for all AMDGPU dependencies in Lux. Users requiring AMDGPU support should install LuxAMDGPU and load it alongside Lux.

Index ​

API ​

# LuxAMDGPU.functional — Method.
julia
functional()

Check if LuxAMDGPU is functional.

source


',7),l=[r];function s(d,n,c,u,p,h){return t(),a("div",null,l)}const A=e(i,[["render",s]]);export{P as __pageData,A as default}; diff --git a/v0.5.30/assets/api_Accelerator_Support_LuxAMDGPU.md.qoeTbLKY.lean.js b/v0.5.30/assets/api_Accelerator_Support_LuxAMDGPU.md.qoeTbLKY.lean.js new file mode 100644 index 000000000..bccbb055e --- /dev/null +++ b/v0.5.30/assets/api_Accelerator_Support_LuxAMDGPU.md.qoeTbLKY.lean.js @@ -0,0 +1 @@ +import{_ as e,c as a,o as t,a4 as o}from"./chunks/framework.BfjuC5t1.js";const P=JSON.parse('{"title":"LuxAMDGPU","description":"","frontmatter":{},"headers":[],"relativePath":"api/Accelerator_Support/LuxAMDGPU.md","filePath":"api/Accelerator_Support/LuxAMDGPU.md","lastUpdated":null}'),i={name:"api/Accelerator_Support/LuxAMDGPU.md"},r=o("",7),l=[r];function s(d,n,c,u,p,h){return t(),a("div",null,l)}const A=e(i,[["render",s]]);export{P as __pageData,A as default}; diff --git a/v0.5.30/assets/api_Accelerator_Support_LuxCUDA.md.D46lK8Gh.js b/v0.5.30/assets/api_Accelerator_Support_LuxCUDA.md.D46lK8Gh.js new file mode 100644 index 000000000..8382e2991 --- /dev/null +++ b/v0.5.30/assets/api_Accelerator_Support_LuxCUDA.md.D46lK8Gh.js @@ -0,0 +1 @@ +import{_ as e,c as a,o as t,a4 as o}from"./chunks/framework.BfjuC5t1.js";const A=JSON.parse('{"title":"LuxCUDA","description":"","frontmatter":{},"headers":[],"relativePath":"api/Accelerator_Support/LuxCUDA.md","filePath":"api/Accelerator_Support/LuxCUDA.md","lastUpdated":null}'),i={name:"api/Accelerator_Support/LuxCUDA.md"},r=o('

LuxCUDA ​

LuxCUDA is meant to be used as a trigger package for all CUDA dependencies in Lux. Users requiring CUDA support should install LuxCUDA and load it alongside Lux.

Index ​

API Reference ​

# LuxCUDA.functional — Method.
julia
functional()

Check if LuxCUDA is functional.

source


',7),n=[r];function l(s,c,d,u,p,h){return t(),a("div",null,n)}const _=e(i,[["render",l]]);export{A as __pageData,_ as default}; diff --git a/v0.5.30/assets/api_Accelerator_Support_LuxCUDA.md.D46lK8Gh.lean.js b/v0.5.30/assets/api_Accelerator_Support_LuxCUDA.md.D46lK8Gh.lean.js new file mode 100644 index 000000000..cf7e412b8 --- /dev/null +++ b/v0.5.30/assets/api_Accelerator_Support_LuxCUDA.md.D46lK8Gh.lean.js @@ -0,0 +1 @@ +import{_ as e,c as a,o as t,a4 as o}from"./chunks/framework.BfjuC5t1.js";const A=JSON.parse('{"title":"LuxCUDA","description":"","frontmatter":{},"headers":[],"relativePath":"api/Accelerator_Support/LuxCUDA.md","filePath":"api/Accelerator_Support/LuxCUDA.md","lastUpdated":null}'),i={name:"api/Accelerator_Support/LuxCUDA.md"},r=o("",7),n=[r];function l(s,c,d,u,p,h){return t(),a("div",null,n)}const _=e(i,[["render",l]]);export{A as __pageData,_ as default}; diff --git a/v0.5.30/assets/api_Accelerator_Support_LuxDeviceUtils.md.BXWwkWYm.js b/v0.5.30/assets/api_Accelerator_Support_LuxDeviceUtils.md.BXWwkWYm.js new file mode 100644 index 000000000..077e3fdcd --- /dev/null +++ b/v0.5.30/assets/api_Accelerator_Support_LuxDeviceUtils.md.BXWwkWYm.js @@ -0,0 +1,5 @@ +import{_ as e,c as i,o as s,a4 as a}from"./chunks/framework.BfjuC5t1.js";const g=JSON.parse('{"title":"LuxDeviceUtils","description":"","frontmatter":{},"headers":[],"relativePath":"api/Accelerator_Support/LuxDeviceUtils.md","filePath":"api/Accelerator_Support/LuxDeviceUtils.md","lastUpdated":null}'),t={name:"api/Accelerator_Support/LuxDeviceUtils.md"},l=a(`

LuxDeviceUtils ​

LuxDeviceUtils.jl is a lightweight package defining rules for transferring data across devices. Most users should directly use Lux.jl instead.

Index ​

Preferences ​

# LuxDeviceUtils.gpu_backend! — Function.
julia
gpu_backend!() = gpu_backend!("")
+gpu_backend!(backend) = gpu_backend!(string(backend))
+gpu_backend!(backend::AbstractLuxGPUDevice)
+gpu_backend!(backend::String)

Creates a LocalPreferences.toml file with the desired GPU backend.

If backend == "", then the gpu_backend preference is deleted. Otherwise, backend is validated to be one of the possible backends and the preference is set to backend.

If a new backend is successfully set, then the Julia session must be restarted for the change to take effect.

source


Data Transfer ​

# LuxDeviceUtils.cpu_device — Function.
julia
cpu_device() -> LuxCPUDevice()

Return a LuxCPUDevice object which can be used to transfer data to CPU.

source


# LuxDeviceUtils.gpu_device — Function.
julia
gpu_device(device_id::Union{Nothing, Int}=nothing;
+    force_gpu_usage::Bool=false) -> AbstractLuxDevice()

Selects GPU device based on the following criteria:

  1. If gpu_backend preference is set and the backend is functional on the system, then that device is selected.

  2. Otherwise, an automatic selection algorithm is used. We go over possible device backends in the order specified by supported_gpu_backends() and select the first functional backend.

  3. If no GPU device is functional and force_gpu_usage is false, then cpu_device() is invoked.

  4. If nothing works, an error is thrown.

Arguments

Warning

device_id is only applicable for CUDA and AMDGPU backends. For Metal and CPU backends, device_id is ignored and a warning is printed.

Keyword Arguments

source


Miscellaneous ​

# LuxDeviceUtils.reset_gpu_device! — Function.
julia
reset_gpu_device!()

Resets the selected GPU device. This is useful when automatic GPU selection needs to be run again.

source


# LuxDeviceUtils.supported_gpu_backends — Function.
julia
supported_gpu_backends() -> Tuple{String, ...}

Return a tuple of supported GPU backends.

Warning

This is not the list of functional backends on the system, but rather backends which Lux.jl supports.

Danger

Metal.jl support is extremely experimental and most things are not expected to work.

source


# LuxDeviceUtils.default_device_rng — Function.
julia
default_device_rng(::AbstractLuxDevice)

Returns the default RNG for the device. This can be used to directly generate parameters and states on the device using WeightInitializers.jl.

source


# LuxDeviceUtils.get_device — Function.
julia
get_device(x::AbstractArray) -> AbstractLuxDevice

Returns the device of the array x. Trigger Packages must be loaded for this to return the correct device.

source


`,21),d=[l];function n(c,r,o,p,h,u){return s(),i("div",null,d)}const v=e(t,[["render",n]]);export{g as __pageData,v as default}; diff --git a/v0.5.30/assets/api_Accelerator_Support_LuxDeviceUtils.md.BXWwkWYm.lean.js b/v0.5.30/assets/api_Accelerator_Support_LuxDeviceUtils.md.BXWwkWYm.lean.js new file mode 100644 index 000000000..091c09472 --- /dev/null +++ b/v0.5.30/assets/api_Accelerator_Support_LuxDeviceUtils.md.BXWwkWYm.lean.js @@ -0,0 +1 @@ +import{_ as e,c as i,o as s,a4 as a}from"./chunks/framework.BfjuC5t1.js";const g=JSON.parse('{"title":"LuxDeviceUtils","description":"","frontmatter":{},"headers":[],"relativePath":"api/Accelerator_Support/LuxDeviceUtils.md","filePath":"api/Accelerator_Support/LuxDeviceUtils.md","lastUpdated":null}'),t={name:"api/Accelerator_Support/LuxDeviceUtils.md"},l=a("",21),d=[l];function n(c,r,o,p,h,u){return s(),i("div",null,d)}const v=e(t,[["render",n]]);export{g as __pageData,v as default}; diff --git a/v0.5.30/assets/api_Building_Blocks_LuxCore.md.CXlTipX8.js b/v0.5.30/assets/api_Building_Blocks_LuxCore.md.CXlTipX8.js new file mode 100644 index 000000000..b3b836c6d --- /dev/null +++ b/v0.5.30/assets/api_Building_Blocks_LuxCore.md.CXlTipX8.js @@ -0,0 +1,2 @@ +import{_ as e,c as a,o as i,a4 as s}from"./chunks/framework.BfjuC5t1.js";const k=JSON.parse('{"title":"LuxCore","description":"","frontmatter":{},"headers":[],"relativePath":"api/Building_Blocks/LuxCore.md","filePath":"api/Building_Blocks/LuxCore.md","lastUpdated":null}'),t={name:"api/Building_Blocks/LuxCore.md"},r=s(`

LuxCore ​

LuxCore.jl defines the abstract layers for Lux. Allows users to be compatible with the entirely of Lux.jl without having such a heavy dependency. If you are depending on Lux.jl directly, you do not need to depend on LuxCore.jl (all the functionality is exported via Lux.jl).

Index ​

Abstract Types ​

# LuxCore.AbstractExplicitLayer — Type.
julia
abstract type AbstractExplicitLayer

Abstract Type for all Lux Layers

Users implementing their custom layer, must implement

Optionally:

See also AbstractExplicitContainerLayer

source


# LuxCore.AbstractExplicitContainerLayer — Type.
julia
abstract type AbstractExplicitContainerLayer{layers} <: AbstractExplicitLayer

Abstract Container Type for certain Lux Layers. layers is a tuple containing fieldnames for the layer, and constructs the parameters and states using those.

Users implementing their custom layer can extend the same functions as in AbstractExplicitLayer.

Tip

Advanced structure manipulation of these layers post construction is possible via Functors.fmap. For a more flexible interface, we recommend using Lux.Experimental.@layer_map.

source


General ​

# LuxCore.apply — Function.
julia
apply(model, x, ps, st)

In most cases this function simply calls model(x, ps, st). However, it is still recommended to call apply instead of model(x, ps, st) directly. Some of the reasons for this include:

  1. For certain types of inputs x, we might want to perform preprocessing before calling model. For eg, if x is an Array of ReverseDiff.TrackedReals this can cause significant regressions in model(x, ps, st) (since it won't hit any of the BLAS dispatches). In those cases, we would automatically convert x to a ReverseDiff.TrackedArray.

  2. Certain user defined inputs need to be applied to specific layers but we want the datatype of propagate through all the layers (even unsupported ones). In these cases, we can unpack the input in apply and pass it to the appropriate layer and then repack it before returning. See the Lux manual on Custom Input Types for a motivating example.

source


# LuxCore.stateless_apply — Function.
julia
stateless_apply(model, x, ps)

Calls apply and only returns the first argument. This function requires that model has an empty state of NamedTuple(). Behavior of other kinds of models are undefined and it is the responsibility of the user to ensure that the model has an empty state.

source


# LuxCore.check_fmap_condition — Function.
julia
check_fmap_condition(cond, tmatch, x) -> Bool

fmaps into the structure x and see if cond is statisfied for any of the leaf elements.

Arguments

Returns

A Boolean Value

source


# LuxCore.contains_lux_layer — Function.
julia
contains_lux_layer(l) -> Bool

Check if the structure l is a Lux AbstractExplicitLayer or a container of such a layer.

source


# LuxCore.display_name — Function.
julia
display_name(layer::AbstractExplicitLayer)

Printed Name of the layer. If the layer has a field name that is used, else the type name is used.

source


# LuxCore.replicate — Function.
julia
replicate(rng::AbstractRNG)

Creates a copy of the rng state depending on its type.

source


# LuxCore.setup — Function.
julia
setup(rng::AbstractRNG, layer)

Shorthand for getting the parameters and states of the layer l. Is equivalent to (initialparameters(rng, l), initialstates(rng, l)).

Warning

This function is not pure, it mutates rng.

source


Parameters ​

# LuxCore.initialparameters — Function.
julia
initialparameters(rng::AbstractRNG, layer)

Generate the initial parameters of the layer l.

source


# LuxCore.parameterlength — Function.
julia
parameterlength(layer)

Return the total number of parameters of the layer l.

source


States ​

# LuxCore.initialstates — Function.
julia
initialstates(rng::AbstractRNG, layer)

Generate the initial states of the layer l.

source


# LuxCore.statelength — Function.
julia
statelength(layer)

Return the total number of states of the layer l.

source


# LuxCore.testmode — Function.
julia
testmode(st::NamedTuple)

Make all occurances of training in state st – Val(false).

source


# LuxCore.trainmode — Function.
julia
trainmode(st::NamedTuple)

Make all occurances of training in state st – Val(true).

source


# LuxCore.update_state — Function.
julia
update_state(st::NamedTuple, key::Symbol, value;
+    layer_check=_default_layer_check(key))

Recursively update all occurances of the key in the state st with the value.

source


Layer size ​

Warning

These specifications have been added very recently and most layers currently do not implement them.

# LuxCore.inputsize — Function.
julia
inputsize(layer)

Return the input size of the layer.

source


# LuxCore.outputsize — Function.
julia
outputsize(layer, x, rng)

Return the output size of the layer. If outputsize(layer) is defined, that method takes precedence, else we compute the layer output to determine the final size.

The fallback implementation of this function assumes the inputs were batched, i.e., if any of the outputs are Arrays, with ndims(A) > 1, it will return size(A)[1:(end - 1)]. If this behavior is undesirable, provide a custom outputsize(layer, x, rng) implementation).

source


`,46),o=[r];function l(d,n,p,c,h,u){return i(),a("div",null,o)}const g=e(t,[["render",l]]);export{k as __pageData,g as default}; diff --git a/v0.5.30/assets/api_Building_Blocks_LuxCore.md.CXlTipX8.lean.js b/v0.5.30/assets/api_Building_Blocks_LuxCore.md.CXlTipX8.lean.js new file mode 100644 index 000000000..3cf28564a --- /dev/null +++ b/v0.5.30/assets/api_Building_Blocks_LuxCore.md.CXlTipX8.lean.js @@ -0,0 +1 @@ +import{_ as e,c as a,o as i,a4 as s}from"./chunks/framework.BfjuC5t1.js";const k=JSON.parse('{"title":"LuxCore","description":"","frontmatter":{},"headers":[],"relativePath":"api/Building_Blocks/LuxCore.md","filePath":"api/Building_Blocks/LuxCore.md","lastUpdated":null}'),t={name:"api/Building_Blocks/LuxCore.md"},r=s("",46),o=[r];function l(d,n,p,c,h,u){return i(),a("div",null,o)}const g=e(t,[["render",l]]);export{k as __pageData,g as default}; diff --git a/v0.5.30/assets/api_Building_Blocks_LuxLib.md.B6OT9gA7.js b/v0.5.30/assets/api_Building_Blocks_LuxLib.md.B6OT9gA7.js new file mode 100644 index 000000000..b84be3131 --- /dev/null +++ b/v0.5.30/assets/api_Building_Blocks_LuxLib.md.B6OT9gA7.js @@ -0,0 +1,4 @@ +import{_ as n,c as o,m as t,a as e,a4 as a,o as s}from"./chunks/framework.BfjuC5t1.js";const j3=JSON.parse('{"title":"LuxLib","description":"","frontmatter":{},"headers":[],"relativePath":"api/Building_Blocks/LuxLib.md","filePath":"api/Building_Blocks/LuxLib.md","lastUpdated":null}'),i={name:"api/Building_Blocks/LuxLib.md"},l=a(`

LuxLib ​

Backend for Lux.jl

Index ​

Dropout ​

# LuxLib.alpha_dropout — Function.
julia
alpha_dropout(rng::AbstractRNG, x, p, ::Val{training})
+alpha_dropout(rng::AbstractRNG, x, p, ::Val{training}, α, A, B)

Alpha Dropout: Dropout ensuring that the mean and variance of the output remains same as the input. For details see [1]. Use the second call signature to avoid recomputing the constants for a fixed dropout probability.

Arguments

Returns

References

[1] Klambauer, Günter, et al. "Self-normalizing neural networks." Advances in neural information processing systems 30 (2017).

source


`,7),r={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},d=t("a",{id:"LuxLib.dropout",href:"#LuxLib.dropout"},"#",-1),Q=t("b",null,[t("u",null,"LuxLib.dropout")],-1),p=t("i",null,"Function",-1),h=a(`
julia
dropout(rng::AbstractRNG, x, p, ::Val{training}, invp; dims)
+dropout(rng::AbstractRNG, x, mask, p, ::Val{training}, ::Val{update_mask}, invp;
+        dims)

Dropout: Simple Way to prevent Neural Networks for Overfitting. For details see [1].

Arguments

Keyword Arguments

`,5),c=t("li",null,[t("p",null,[t("code",null,"dims"),e(": Dimensions along which dropout is applied")])],-1),T=t("code",null,"invp",-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},u={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.091ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.8ex",height:"3.048ex",role:"img",focusable:"false",viewBox:"0 -864.9 795.7 1347.1","aria-hidden":"true"},g=a('',1),_=[g],x=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mfrac",null,[t("mn",null,"1"),t("mi",null,"p")])])],-1),b=a('

Returns

References

[1] Srivastava, Nitish, et al. "Dropout: a simple way to prevent neural networks from overfitting." The journal of machine learning research 15.1 (2014): 1929-1958.

source

',5),k=t("br",null,null,-1),w=t("h2",{id:"Normalization",tabindex:"-1"},[e("Normalization "),t("a",{class:"header-anchor",href:"#Normalization","aria-label":'Permalink to "Normalization {#Normalization}"'},"​")],-1),L={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},f=t("a",{id:"LuxLib.batchnorm",href:"#LuxLib.batchnorm"},"#",-1),y=t("b",null,[t("u",null,"LuxLib.batchnorm")],-1),v=t("i",null,"Function",-1),H=a('
julia
batchnorm(x, scale, bias, running_mean, running_var; momentum, epsilon, training)

Batch Normalization. For details see [1].

',2),V={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},M={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.471ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.07ex",height:"2.016ex",role:"img",focusable:"false",viewBox:"0 -683 11080.9 891","aria-hidden":"true"},C=a('',1),D=[C],E=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"D"),t("mn",null,"1")]),t("mo",null,"×"),t("mo",null,"."),t("mo",null,"."),t("mo",null,"."),t("mo",null,"×"),t("msub",null,[t("mi",null,"D"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"N"),t("mo",null,"−"),t("mn",null,"2")])]),t("mo",null,"×"),t("mn",null,"1"),t("mo",null,"×"),t("msub",null,[t("mi",null,"D"),t("mi",null,"N")])])],-1),A=t("p",null,[t("strong",null,"Arguments")],-1),Z=t("li",null,[t("p",null,[t("code",null,"x"),e(": Input to be Normalized")])],-1),S=t("code",null,"scale",-1),j={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.489ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.229ex",height:"1.486ex",role:"img",focusable:"false",viewBox:"0 -441 543 657","aria-hidden":"true"},I=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D6FE",d:"M31 249Q11 249 11 258Q11 275 26 304T66 365T129 418T206 441Q233 441 239 440Q287 429 318 386T371 255Q385 195 385 170Q385 166 386 166L398 193Q418 244 443 300T486 391T508 430Q510 431 524 431H537Q543 425 543 422Q543 418 522 378T463 251T391 71Q385 55 378 6T357 -100Q341 -165 330 -190T303 -216Q286 -216 286 -188Q286 -138 340 32L346 51L347 69Q348 79 348 100Q348 257 291 317Q251 355 196 355Q148 355 108 329T51 260Q49 251 47 251Q45 249 31 249Z",style:{"stroke-width":"3"}})])])],-1),B=[I],N=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"γ")])],-1),z=t("code",null,"nothing",-1),R=t("code",null,"bias",-1),P={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},q={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.281ex",height:"2.034ex",role:"img",focusable:"false",viewBox:"0 -705 566 899","aria-hidden":"true"},G=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D6FD",d:"M29 -194Q23 -188 23 -186Q23 -183 102 134T186 465Q208 533 243 584T309 658Q365 705 429 705H431Q493 705 533 667T573 570Q573 465 469 396L482 383Q533 332 533 252Q533 139 448 65T257 -10Q227 -10 203 -2T165 17T143 40T131 59T126 65L62 -188Q60 -194 42 -194H29ZM353 431Q392 431 427 419L432 422Q436 426 439 429T449 439T461 453T472 471T484 495T493 524T501 560Q503 569 503 593Q503 611 502 616Q487 667 426 667Q384 667 347 643T286 582T247 514T224 455Q219 439 186 308T152 168Q151 163 151 147Q151 99 173 68Q204 26 260 26Q302 26 349 51T425 137Q441 171 449 214T457 279Q457 337 422 372Q380 358 347 358H337Q258 358 258 389Q258 396 261 403Q275 431 353 431Z",style:{"stroke-width":"3"}})])])],-1),J=[G],O=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"β")])],-1),K=t("code",null,"nothing",-1),X=t("li",null,[t("p",null,[t("code",null,"running_mean"),e(": Running mean (can be "),t("code",null,"nothing"),e(")")])],-1),U=t("li",null,[t("p",null,[t("code",null,"running_var"),e(": Running variance (can be "),t("code",null,"nothing"),e(")")])],-1),$=a('

Keyword Arguments

Returns

Normalized Array of same size as x. And a Named Tuple containing the updated running mean and variance.

Performance Considerations

If the input array is 2D, 4D, or 5D CuArray with element types Float16, Float32 and Float64, then the CUDNN code path will be used. In all other cases, a broadcasting fallback is used which is not highly optimized.

References

[1] Ioffe, Sergey, and Christian Szegedy. "Batch normalization: Accelerating deep network training by reducing internal covariate shift." International conference on machine learning. PMLR, 2015.

source

',9),W=t("br",null,null,-1),Y={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},t1=t("a",{id:"LuxLib.groupnorm",href:"#LuxLib.groupnorm"},"#",-1),e1=t("b",null,[t("u",null,"LuxLib.groupnorm")],-1),a1=t("i",null,"Function",-1),o1=a('
julia
groupnorm(x, scale, bias; groups, epsilon)

Group Normalization. For details see [1].

This op is similar to batch normalization, but statistics are shared across equally-sized groups of channels and not shared across batch dimension. Thus, group normalization does not depend on the batch composition and does not require maintaining internal state for storing statistics.

Arguments

',4),s1=t("li",null,[t("p",null,[t("code",null,"x"),e(": Input to be Normalized")])],-1),n1=t("code",null,"scale",-1),i1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},l1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.489ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.229ex",height:"1.486ex",role:"img",focusable:"false",viewBox:"0 -441 543 657","aria-hidden":"true"},r1=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D6FE",d:"M31 249Q11 249 11 258Q11 275 26 304T66 365T129 418T206 441Q233 441 239 440Q287 429 318 386T371 255Q385 195 385 170Q385 166 386 166L398 193Q418 244 443 300T486 391T508 430Q510 431 524 431H537Q543 425 543 422Q543 418 522 378T463 251T391 71Q385 55 378 6T357 -100Q341 -165 330 -190T303 -216Q286 -216 286 -188Q286 -138 340 32L346 51L347 69Q348 79 348 100Q348 257 291 317Q251 355 196 355Q148 355 108 329T51 260Q49 251 47 251Q45 249 31 249Z",style:{"stroke-width":"3"}})])])],-1),d1=[r1],Q1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"γ")])],-1),p1=t("code",null,"nothing",-1),h1=t("code",null,"bias",-1),c1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},T1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.281ex",height:"2.034ex",role:"img",focusable:"false",viewBox:"0 -705 566 899","aria-hidden":"true"},m1=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D6FD",d:"M29 -194Q23 -188 23 -186Q23 -183 102 134T186 465Q208 533 243 584T309 658Q365 705 429 705H431Q493 705 533 667T573 570Q573 465 469 396L482 383Q533 332 533 252Q533 139 448 65T257 -10Q227 -10 203 -2T165 17T143 40T131 59T126 65L62 -188Q60 -194 42 -194H29ZM353 431Q392 431 427 419L432 422Q436 426 439 429T449 439T461 453T472 471T484 495T493 524T501 560Q503 569 503 593Q503 611 502 616Q487 667 426 667Q384 667 347 643T286 582T247 514T224 455Q219 439 186 308T152 168Q151 163 151 147Q151 99 173 68Q204 26 260 26Q302 26 349 51T425 137Q441 171 449 214T457 279Q457 337 422 372Q380 358 347 358H337Q258 358 258 389Q258 396 261 403Q275 431 353 431Z",style:{"stroke-width":"3"}})])])],-1),u1=[m1],g1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"β")])],-1),_1=t("code",null,"nothing",-1),x1=a('

Keyword Arguments

Returns

The normalized array is returned.

Performance Considerations

The most common case of this Op – x is a 4D array – is optimized using KernelAbstractions and has a fast custom backwards pass implemented. All other cases have a fallback implementation which is not especially optimized.

We have tested the code path for Float16 and it works, but gradient accumulation is extremely fragile. Hence, for Float16 inputs, it uses the fallback implementation.

If the batch size is small (< 16), then the fallback implementation will be faster than the KA version. However, this customization is not possible using the direct groupnorm interface.

References

[1] Wu, Yuxin, and Kaiming He. "Group normalization." Proceedings of the European conference on computer vision (ECCV). 2018.

source

',11),b1=t("br",null,null,-1),k1={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},w1=t("a",{id:"LuxLib.instancenorm",href:"#LuxLib.instancenorm"},"#",-1),L1=t("b",null,[t("u",null,"LuxLib.instancenorm")],-1),f1=t("i",null,"Function",-1),y1=a('
julia
instancenorm(x, scale, bias; epsilon, training)

Instance Normalization. For details see [1].

',2),v1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},H1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.471ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.72ex",height:"2.016ex",role:"img",focusable:"false",viewBox:"0 -683 10042 891","aria-hidden":"true"},V1=a('',1),M1=[V1],C1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"D"),t("mn",null,"1")]),t("mo",null,"×"),t("mo",null,"."),t("mo",null,"."),t("mo",null,"."),t("mo",null,"×"),t("msub",null,[t("mi",null,"D"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"N"),t("mo",null,"−"),t("mn",null,"2")])]),t("mo",null,"×"),t("mn",null,"1"),t("mo",null,"×"),t("mn",null,"1")])],-1),D1=t("p",null,[t("strong",null,"Arguments")],-1),E1=t("li",null,[t("p",null,[t("code",null,"x"),e(": Input to be Normalized (must be atleast 3D)")])],-1),A1=t("code",null,"scale",-1),Z1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},S1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.489ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.229ex",height:"1.486ex",role:"img",focusable:"false",viewBox:"0 -441 543 657","aria-hidden":"true"},j1=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D6FE",d:"M31 249Q11 249 11 258Q11 275 26 304T66 365T129 418T206 441Q233 441 239 440Q287 429 318 386T371 255Q385 195 385 170Q385 166 386 166L398 193Q418 244 443 300T486 391T508 430Q510 431 524 431H537Q543 425 543 422Q543 418 522 378T463 251T391 71Q385 55 378 6T357 -100Q341 -165 330 -190T303 -216Q286 -216 286 -188Q286 -138 340 32L346 51L347 69Q348 79 348 100Q348 257 291 317Q251 355 196 355Q148 355 108 329T51 260Q49 251 47 251Q45 249 31 249Z",style:{"stroke-width":"3"}})])])],-1),F1=[j1],I1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"γ")])],-1),B1=t("code",null,"nothing",-1),N1=t("code",null,"bias",-1),z1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},R1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.281ex",height:"2.034ex",role:"img",focusable:"false",viewBox:"0 -705 566 899","aria-hidden":"true"},P1=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D6FD",d:"M29 -194Q23 -188 23 -186Q23 -183 102 134T186 465Q208 533 243 584T309 658Q365 705 429 705H431Q493 705 533 667T573 570Q573 465 469 396L482 383Q533 332 533 252Q533 139 448 65T257 -10Q227 -10 203 -2T165 17T143 40T131 59T126 65L62 -188Q60 -194 42 -194H29ZM353 431Q392 431 427 419L432 422Q436 426 439 429T449 439T461 453T472 471T484 495T493 524T501 560Q503 569 503 593Q503 611 502 616Q487 667 426 667Q384 667 347 643T286 582T247 514T224 455Q219 439 186 308T152 168Q151 163 151 147Q151 99 173 68Q204 26 260 26Q302 26 349 51T425 137Q441 171 449 214T457 279Q457 337 422 372Q380 358 347 358H337Q258 358 258 389Q258 396 261 403Q275 431 353 431Z",style:{"stroke-width":"3"}})])])],-1),q1=[P1],G1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"β")])],-1),J1=t("code",null,"nothing",-1),O1=a('

Keyword Arguments

Returns

Normalized Array of same size as x. And a Named Tuple containing the updated running mean and variance.

References

[1] Ulyanov, Dmitry, Andrea Vedaldi, and Victor Lempitsky. "Instance normalization: The missing ingredient for fast stylization." arXiv preprint arXiv:1607.08022 (2016).

source

',7),K1=t("br",null,null,-1),X1={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},U1=t("a",{id:"LuxLib.layernorm",href:"#LuxLib.layernorm"},"#",-1),$1=t("b",null,[t("u",null,"LuxLib.layernorm")],-1),W1=t("i",null,"Function",-1),Y1=a('
julia
layernorm(x, scale, bias; dims, epsilon)

Layer Normalization. For details see [1].

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Keyword Arguments

Returns

Normalized Array of same size as x.

References

[1] Ba, Jimmy Lei, Jamie Ryan Kiros, and Geoffrey E. Hinton. "Layer normalization." arXiv preprint arXiv:1607.06450 (2016).

source

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WeightInitializers ​

This package is a light dependency providing common weight initialization schemes for deep learning models.

Index ​

API Reference ​

Main Functions ​

# WeightInitializers.glorot_normal — Function.
julia
glorot_normal([::AbstractRNG=_default_rng()], [T=Float32], size...;
+    gain = 1) -> AbstractArray{T, length(size)}

Return an AbstractArray{T} of the given size containing random numbers drawn from a normal distribution with standard deviation gain * sqrt(2 / (fan_in + fan_out)). This method is described in [1] and also known as Xavier initialization.

References

[1] Glorot, Xavier, and Yoshua Bengio. "Understanding the difficulty of training deep feedforward neural networks." Proceedings of the thirteenth international conference on artificial intelligence and statistics. 2010.

source


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julia
glorot_uniform([::AbstractRNG=_default_rng()], [T=Float32], size...;
+    gain = 1) -> AbstractArray{T, length(size)}
`,1),g=i("code",null,"AbstractArray{T}",-1),c=i("code",null,"size",-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.612ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2922.7 1000","aria-hidden":"true"},u=a('',1),b=[u],F=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mo",{stretchy:"false"},"["),i("mo",null,"−"),i("mi",null,"x"),i("mo",null,","),i("mi",null,"x"),i("mo",{stretchy:"false"},"]")])],-1),C=i("code",null,"x = gain * sqrt(6 / (fan_in + fan_out))",-1),m=i("p",null,[i("strong",null,"References")],-1),A=i("p",null,[s('[1] Glorot, Xavier, and Yoshua Bengio. "Understanding the difficulty of training deep feedforward neural networks." '),i("em",null,"Proceedings of the thirteenth international conference on artificial intelligence and statistics"),s(". 2010.")],-1),z=i("p",null,[i("a",{href:"https://github.com/LuxDL/WeightInitializers.jl/blob/v0.1.7/src/initializers.jl#L22-L36",target:"_blank",rel:"noreferrer"},"source")],-1),f=a(`
# WeightInitializers.identity_init — Function.
julia
identity_init([::AbstractRNG=_default_rng()], [T=Float32], size...; gain::Number=1,
+    shift::Union{Integer, Tuple{Integer, Integer}}=0) -> AbstractArray{T}

Constructs an array that aims to provide an identity mapping when used as parameters in most layers of a neural network. The identity mapping is scaled by the gain parameter.

Behavior

Caveats

Arguments

Returns

Examples

julia
using Random
+
+# Identity matrix for fully connected layer
+identity_matrix = identity_init(MersenneTwister(123), Float32, 5, 5)
+
+# Identity tensor for convolutional layer
+identity_tensor = identity_init(MersenneTwister(123),
+    Float32,        # Bias initialization
+    3,
+    3,
+    5,        # Matrix multiplication
+    5;
+    gain=1.5,
+    shift=(1, 0))

source


# WeightInitializers.kaiming_normal — Function.
julia
kaiming_normal([::AbstractRNG=_default_rng()], [T=Float32], size...;
+    gain = √T(2)) -> AbstractArray{T, length(size)}

Return an AbstractArray{T} of the given size containing random numbers taken from a normal distribution standard deviation gain / sqrt(fan_in)

References

[1] He, Kaiming, et al. "Delving deep into rectifiers: Surpassing human-level performance on imagenet classification." Proceedings of the IEEE international conference on computer vision. 2015.

source


# WeightInitializers.kaiming_uniform — Function.
julia
kaiming_uniform([::AbstractRNG=_default_rng()], [T=Float32], size...;
+    gain = √T(2)) -> AbstractArray{T, length(size)}

Return an AbstractArray{T} of the given size containing random numbers drawn from a uniform distribution on the interval [-x, x], where x = gain * sqrt(3/fan_in).

References

[1] He, Kaiming, et al. "Delving deep into rectifiers: Surpassing human-level performance on imagenet classification." Proceedings of the IEEE international conference on computer vision. 2015.

source


# WeightInitializers.sparse_init — Function.
julia
sparse_init([::AbstractRNG=_default_rng()], [T=Float32], dims::Integer...;
+    sparsity::Number, std::Number=0.01) -> AbstractArray{T}

Creates a sparsely initialized weight matrix with a specified proportion of zeroed elements, using random numbers drawn from a normal distribution for the non-zero elements. This method is introduced in [^Martens2010]. Note: The sparsity parameter controls the proportion of the matrix that will be zeroed. For example, a sparsity of 0.3 means that approximately 30% of the elements will be set to zero. The non-zero elements are distributed according to a normal distribution, scaled by the std parameter.

Arguments

Returns

Examples

julia
using Random
+
+# Initialize a 5x5 sparsely initialized matrix with 30% sparsity
+rng = MersenneTwister(123)
+matrix = sparse_init(rng, Float32, 5, 5; sparsity=0.3, std=0.01)
5×5 Matrix{Float64}:
+  0.0          0.00273815    0.00592403   0.0          0.0
+  0.00459416  -0.000754831  -0.00888936  -0.0077507    0.0
+  0.0         -0.00194229    0.0          0.0         -0.00468489
+  0.0114265    0.0           0.0         -0.00734886   0.00277726
+ -0.00396679   0.0           0.00327215  -0.0071741   -0.00880897

References

[^Martens2010] Martens, J, "Deep learning via Hessian-free optimization" Proceedings of the 27th International Conference on International Conference on Machine Learning. 2010.

source


# WeightInitializers.truncated_normal — Function.
julia
truncated_normal([::AbstractRNG=_default_rng()], [T=Float32], size...; mean = 0,
+    std = 1, lo = -2, hi = 2) -> AbstractArray{T, length(size)}

Return an AbstractArray{T} of the given size where each element is drawn from a truncated normal distribution. The numbers are distributed like filter(x -> lo ≤ x ≤ hi, mean .+ std .* randn(100)).

source


# WeightInitializers.orthogonal — Function.
julia
orthogonal([::AbstractRNG=_default_rng()], [T=Float32], dims::Integer...;
+    gain = 1)  -> AbstractArray{T, length(dims)}

Return an AbstractArray{T} of the given dimensions (dims) which is a (semi) orthogonal matrix, as described in [^Saxe14]

The function constructs an orthogonal or semi-orthogonal matrix depending on the specified dimensions. For two dimensions, it returns a matrix where dims = (rows, cols). For more than two dimensions, it computes an orthogonal matrix of size prod(dims[1:(end - 1)]) by dims[end] before reshaping it to the original dimensions.

Cannot construct a vector, i.e., length(dims) == 1 is forbidden.

Arguments

References

[^Saxe14] Saxe, McClelland, Ganguli. "Exact solutions to the nonlinear dynamics of learning in deep linear neural networks", ICLR 2014, https://arxiv.org/abs/1312.6120

source


Commonly Used Wrappers ​

# WeightInitializers.zeros16 — Function.
julia
zeros16([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float16, length(size)}

Return an AbstractArray{Float16} of the given size containing an AbstractArray of zeros.

source


# WeightInitializers.ones16 — Function.
julia
ones16([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float16, length(size)}

Return an AbstractArray{Float16} of the given size containing an AbstractArray of ones.

source


# WeightInitializers.rand16 — Function.
julia
rand16([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float16, length(size)}

Return an AbstractArray{Float16} of the given size containing random numbers from a uniform distribution.

source


# WeightInitializers.randn16 — Function.
julia
randn16([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float16, length(size)}

Return an AbstractArray{Float16} of the given size containing random numbers from a standard normal distribution.

source


# WeightInitializers.zeros32 — Function.
julia
zeros32([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float32, length(size)}

Return an AbstractArray{Float32} of the given size containing an AbstractArray of zeros.

source


# WeightInitializers.ones32 — Function.
julia
ones32([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float32, length(size)}

Return an AbstractArray{Float32} of the given size containing an AbstractArray of ones.

source


# WeightInitializers.rand32 — Function.
julia
rand32([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float32, length(size)}

Return an AbstractArray{Float32} of the given size containing random numbers from a uniform distribution.

source


# WeightInitializers.randn32 — Function.
julia
randn32([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float32, length(size)}

Return an AbstractArray{Float32} of the given size containing random numbers from a standard normal distribution.

source


# WeightInitializers.zeros64 — Function.
julia
zeros64([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float64, length(size)}

Return an AbstractArray{Float64} of the given size containing an AbstractArray of zeros.

source


# WeightInitializers.ones64 — Function.
julia
ones64([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float64, length(size)}

Return an AbstractArray{Float64} of the given size containing an AbstractArray of ones.

source


# WeightInitializers.rand64 — Function.
julia
rand64([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float64, length(size)}

Return an AbstractArray{Float64} of the given size containing random numbers from a uniform distribution.

source


# WeightInitializers.randn64 — Function.
julia
randn64([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{Float64, length(size)}

Return an AbstractArray{Float64} of the given size containing random numbers from a standard normal distribution.

source


# WeightInitializers.zerosC16 — Function.
julia
zerosC16([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF16, length(size)}

Return an AbstractArray{ComplexF16} of the given size containing an AbstractArray of zeros.

source


# WeightInitializers.onesC16 — Function.
julia
onesC16([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF16, length(size)}

Return an AbstractArray{ComplexF16} of the given size containing an AbstractArray of ones.

source


# WeightInitializers.randC16 — Function.
julia
randC16([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF16, length(size)}

Return an AbstractArray{ComplexF16} of the given size containing random numbers from a uniform distribution.

source


# WeightInitializers.randnC16 — Function.
julia
randnC16([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF16, length(size)}

Return an AbstractArray{ComplexF16} of the given size containing random numbers from a standard normal distribution.

source


# WeightInitializers.zerosC32 — Function.
julia
zerosC32([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF32, length(size)}

Return an AbstractArray{ComplexF32} of the given size containing an AbstractArray of zeros.

source


# WeightInitializers.onesC32 — Function.
julia
onesC32([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF32, length(size)}

Return an AbstractArray{ComplexF32} of the given size containing an AbstractArray of ones.

source


# WeightInitializers.randC32 — Function.
julia
randC32([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF32, length(size)}

Return an AbstractArray{ComplexF32} of the given size containing random numbers from a uniform distribution.

source


# WeightInitializers.randnC32 — Function.
julia
randnC32([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF32, length(size)}

Return an AbstractArray{ComplexF32} of the given size containing random numbers from a standard normal distribution.

source


# WeightInitializers.zerosC64 — Function.
julia
zerosC64([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF64, length(size)}

Return an AbstractArray{ComplexF64} of the given size containing an AbstractArray of zeros.

source


# WeightInitializers.onesC64 — Function.
julia
onesC64([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF64, length(size)}

Return an AbstractArray{ComplexF64} of the given size containing an AbstractArray of ones.

source


# WeightInitializers.randC64 — Function.
julia
randC64([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF64, length(size)}

Return an AbstractArray{ComplexF64} of the given size containing random numbers from a uniform distribution.

source


# WeightInitializers.randnC64 — Function.
julia
randnC64([::AbstractRNG=_default_rng()], size...;
+    kwargs...) -> AbstractArray{ComplexF64, length(size)}

Return an AbstractArray{ComplexF64} of the given size containing random numbers from a standard normal distribution.

source


`,62);function v(_,D,I,W,x,B){return e(),t("div",null,[h,i("div",r,[p,s(" "),k,s(" — "),d,s(". "),o,i("p",null,[s("Return an "),g,s(" of the given "),c,s(" containing random numbers drawn from a uniform distribution on the interval "),i("mjx-container",E,[(e(),t("svg",y,b)),F]),s(", where "),C,s(". This method is described in [1] and also known as Xavier initialization.")]),m,A,z]),f])}const L=n(l,[["render",v]]);export{j as __pageData,L as default}; diff --git a/v0.5.30/assets/api_Building_Blocks_WeightInitializers.md.6GPvJ2xM.lean.js b/v0.5.30/assets/api_Building_Blocks_WeightInitializers.md.6GPvJ2xM.lean.js new file mode 100644 index 000000000..8974bf28e --- /dev/null +++ b/v0.5.30/assets/api_Building_Blocks_WeightInitializers.md.6GPvJ2xM.lean.js @@ -0,0 +1 @@ +import{_ as n,c as t,m as i,a as s,a4 as a,o as e}from"./chunks/framework.BfjuC5t1.js";const j=JSON.parse('{"title":"WeightInitializers","description":"","frontmatter":{},"headers":[],"relativePath":"api/Building_Blocks/WeightInitializers.md","filePath":"api/Building_Blocks/WeightInitializers.md","lastUpdated":null}'),l={name:"api/Building_Blocks/WeightInitializers.md"},h=a("",8),r={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},p=i("a",{id:"WeightInitializers.glorot_uniform",href:"#WeightInitializers.glorot_uniform"},"#",-1),k=i("b",null,[i("u",null,"WeightInitializers.glorot_uniform")],-1),d=i("i",null,"Function",-1),o=a("",1),g=i("code",null,"AbstractArray{T}",-1),c=i("code",null,"size",-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"6.612ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 2922.7 1000","aria-hidden":"true"},u=a("",1),b=[u],F=i("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[i("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[i("mo",{stretchy:"false"},"["),i("mo",null,"−"),i("mi",null,"x"),i("mo",null,","),i("mi",null,"x"),i("mo",{stretchy:"false"},"]")])],-1),C=i("code",null,"x = gain * sqrt(6 / (fan_in + fan_out))",-1),m=i("p",null,[i("strong",null,"References")],-1),A=i("p",null,[s('[1] Glorot, Xavier, and Yoshua Bengio. "Understanding the difficulty of training deep feedforward neural networks." '),i("em",null,"Proceedings of the thirteenth international conference on artificial intelligence and statistics"),s(". 2010.")],-1),z=i("p",null,[i("a",{href:"https://github.com/LuxDL/WeightInitializers.jl/blob/v0.1.7/src/initializers.jl#L22-L36",target:"_blank",rel:"noreferrer"},"source")],-1),f=a("",62);function v(_,D,I,W,x,B){return e(),t("div",null,[h,i("div",r,[p,s(" "),k,s(" — "),d,s(". "),o,i("p",null,[s("Return an "),g,s(" of the given "),c,s(" containing random numbers drawn from a uniform distribution on the interval "),i("mjx-container",E,[(e(),t("svg",y,b)),F]),s(", where "),C,s(". This method is described in [1] and also known as Xavier initialization.")]),m,A,z]),f])}const L=n(l,[["render",v]]);export{j as __pageData,L as default}; diff --git a/v0.5.30/assets/api_Domain_Specific_Modeling_Boltz.md.KvKJdetm.js b/v0.5.30/assets/api_Domain_Specific_Modeling_Boltz.md.KvKJdetm.js new file mode 100644 index 000000000..1df788554 --- /dev/null +++ b/v0.5.30/assets/api_Domain_Specific_Modeling_Boltz.md.KvKJdetm.js @@ -0,0 +1,4 @@ +import{_ as t,c as e,o as i,a4 as l}from"./chunks/framework.BfjuC5t1.js";const k=JSON.parse('{"title":"Boltz","description":"","frontmatter":{},"headers":[],"relativePath":"api/Domain_Specific_Modeling/Boltz.md","filePath":"api/Domain_Specific_Modeling/Boltz.md","lastUpdated":null}'),s={name:"api/Domain_Specific_Modeling/Boltz.md"},a=l(`

Boltz ​

Accelerate ⚡ your ML research using pre-built Deep Learning Models with Lux.

Index ​

Computer Vision Models ​

Classification Models: Native Lux Models ​

MODEL NAMEFUNCTIONNAMEPRETRAINEDTOP 1 ACCURACY (%)TOP 5 ACCURACY (%)
VGGvgg:vgg11✅67.3587.91
VGGvgg:vgg13✅68.4088.48
VGGvgg:vgg16✅70.2489.80
VGGvgg:vgg19✅71.0990.27
VGGvgg:vgg11_bn✅69.0988.94
VGGvgg:vgg13_bn✅69.6689.49
VGGvgg:vgg16_bn✅72.1191.02
VGGvgg:vgg19_bn✅72.9591.32
Vision Transformervision_transformer:tiny🚫
Vision Transformervision_transformer:small🚫
Vision Transformervision_transformer:base🚫
Vision Transformervision_transformer:large🚫
Vision Transformervision_transformer:huge🚫
Vision Transformervision_transformer:giant🚫
Vision Transformervision_transformer:gigantic🚫

Building Blocks ​

# Boltz.ClassTokens — Type.
julia
ClassTokens(dim; init=Lux.zeros32)

Appends class tokens to an input with embedding dimension dim for use in many vision transformer namels.

source


# Boltz.MultiHeadAttention — Type.
julia
MultiHeadAttention(in_planes::Int, number_heads::Int; qkv_bias::Bool=false,
+                   attention_dropout_rate::T=0.0f0,
+                   projection_dropout_rate::T=0.0f0) where {T}

Multi-head self-attention layer

source


# Boltz.ViPosEmbedding — Type.
julia
ViPosEmbedding(embedsize, npatches;
+               init = (rng, dims...) -> randn(rng, Float32, dims...))

Positional embedding layer used by many vision transformer-like namels.

source


# Boltz.transformer_encoder — Function.
julia
transformer_encoder(in_planes, depth, number_heads; mlp_ratio = 4.0f0, dropout = 0.0f0)

Transformer as used in the base ViT architecture. (reference).

Arguments

source


# Boltz.vgg — Function.
julia
vgg(imsize; config, inchannels, batchnorm = false, nclasses, fcsize, dropout)

Create a VGG model (reference).

Arguments

source


Non-Public API ​

# Boltz._seconddimmean — Function.
julia
_seconddimmean(x)

Computes the mean of x along dimension 2

source


# Boltz._fast_chunk — Function.
julia
_fast_chunk(x::AbstractArray, ::Val{n}, ::Val{dim})

Type-stable and faster version of MLUtils.chunk

source


# Boltz._flatten_spatial — Function.
julia
_flatten_spatial(x::AbstractArray{T, 4})

Flattens the first 2 dimensions of x, and permutes the remaining dimensions to (2, 1, 3)

source


# Boltz._vgg_block — Function.
julia
_vgg_block(input_filters, output_filters, depth, batchnorm)

A VGG block of convolution layers (reference).

Arguments

source


# Boltz._vgg_classifier_layers — Function.
julia
_vgg_classifier_layers(imsize, nclasses, fcsize, dropout)

Create VGG classifier (fully connected) layers (reference).

Arguments

source


# Boltz._vgg_convolutional_layers — Function.
julia
_vgg_convolutional_layers(config, batchnorm, inchannels)

Create VGG convolution layers (reference).

Arguments

source


Classification Models: Imported from Metalhead.jl ​

Tip

You need to load Flux and Metalhead before using these models.

MODEL NAMEFUNCTIONNAMEPRETRAINEDTOP 1 ACCURACY (%)TOP 5 ACCURACY (%)
AlexNetalexnet:alexnet✅54.4877.72
ResNetresnet:resnet18🚫68.0888.44
ResNetresnet:resnet34🚫72.1390.91
ResNetresnet:resnet50🚫74.5592.36
ResNetresnet:resnet101🚫74.8192.36
ResNetresnet:resnet152🚫77.6393.84
ConvMixerconvmixer:small🚫
ConvMixerconvmixer:base🚫
ConvMixerconvmixer:large🚫
DenseNetdensenet:densenet121🚫
DenseNetdensenet:densenet161🚫
DenseNetdensenet:densenet169🚫
DenseNetdensenet:densenet201🚫
GoogleNetgooglenet:googlenet🚫
MobileNetmobilenet:mobilenet_v1🚫
MobileNetmobilenet:mobilenet_v2🚫
MobileNetmobilenet:mobilenet_v3_small🚫
MobileNetmobilenet:mobilenet_v3_large🚫
ResNeXTresnext:resnext50🚫
ResNeXTresnext:resnext101🚫
ResNeXTresnext:resnext152🚫

These models can be created using <FUNCTION>(<NAME>; pretrained = <PRETRAINED>)

Preprocessing ​

All the pretrained models require that the images be normalized with the parameters mean = [0.485f0, 0.456f0, 0.406f0] and std = [0.229f0, 0.224f0, 0.225f0].

`,37),d=[a];function n(r,o,c,g,h,p){return i(),e("div",null,d)}const u=t(s,[["render",n]]);export{k as __pageData,u as default}; diff --git a/v0.5.30/assets/api_Domain_Specific_Modeling_Boltz.md.KvKJdetm.lean.js b/v0.5.30/assets/api_Domain_Specific_Modeling_Boltz.md.KvKJdetm.lean.js new file mode 100644 index 000000000..5dd614bbb --- /dev/null +++ b/v0.5.30/assets/api_Domain_Specific_Modeling_Boltz.md.KvKJdetm.lean.js @@ -0,0 +1 @@ +import{_ as t,c as e,o as i,a4 as l}from"./chunks/framework.BfjuC5t1.js";const k=JSON.parse('{"title":"Boltz","description":"","frontmatter":{},"headers":[],"relativePath":"api/Domain_Specific_Modeling/Boltz.md","filePath":"api/Domain_Specific_Modeling/Boltz.md","lastUpdated":null}'),s={name:"api/Domain_Specific_Modeling/Boltz.md"},a=l("",37),d=[a];function n(r,o,c,g,h,p){return i(),e("div",null,d)}const u=t(s,[["render",n]]);export{k as __pageData,u as default}; diff --git a/v0.5.30/assets/api_Lux_contrib.md.DdRrnWLR.js b/v0.5.30/assets/api_Lux_contrib.md.DdRrnWLR.js new file mode 100644 index 000000000..783116932 --- /dev/null +++ b/v0.5.30/assets/api_Lux_contrib.md.DdRrnWLR.js @@ -0,0 +1,102 @@ +import{_ as s,c as i,o as a,a4 as e}from"./chunks/framework.BfjuC5t1.js";const c=JSON.parse('{"title":"Experimental Features","description":"","frontmatter":{},"headers":[],"relativePath":"api/Lux/contrib.md","filePath":"api/Lux/contrib.md","lastUpdated":null}'),t={name:"api/Lux/contrib.md"},n=e(`

Experimental Features ​

All features listed on this page are experimental which means:

  1. No SemVer Guarantees. We use code here to iterate fast and most users should wait for these features to be marked non-experimental.

  2. Expect edge-cases and report them. It will help us move these features out of experimental sooner.

  3. None of the features are exported.

Warning

Starting v"0.5.2" all Experimental features need to be accessed via Lux.Experimental.<feature>. Direct access via Lux.<feature> will be removed in v"0.6".

Index ​

Training ​

Helper Functions making it easier to train Lux.jl models.

Lux.Training is meant to be simple and provide extremely basic functionality. We provide basic building blocks which can be seamlessly composed to create complex training pipelines.

# Lux.Experimental.TrainState — Type.
julia
TrainState

Training State containing:

source


# Lux.Experimental.compute_gradients — Function.
julia
compute_gradients(ad::ADTypes.AbstractADType, objective_function::Function, data,
+    ts::TrainState)

Compute the gradients of the objective function wrt parameters stored in ts.

Arguments

Return

A 4-Tuple containing:

source


# Lux.Experimental.apply_gradients — Function.
julia
apply_gradients(ts::TrainState, grads)

Update the parameters stored in ts using the gradients grads.

Arguments

Returns

Updated TrainState object.

source


Parameter Freezing ​

Info

In the long term, this will be supported via Optimisers.jl.

# Lux.Experimental.FrozenLayer — Type.
julia
FrozenLayer(l::AbstractExplicitLayer, which_params::Union{Tuple, Nothing})

Freeze the parameters with name which_params of the layer l.

Tip

It is always recommended to use the Lux.Experimental.freeze function instead of directly using the FrozenLayer constructor.

Warning

There are no checks for which_params. For example, if the original layer has parameters named (:weight, :bias), and which_paramsis set to(:myweight,) then none of the parameters are frozen and no error is thrown.

Arguments

Input

Returns

Parameters

States

Note on Internal Layer Implementation

The inner layer should work with NamedTuple parameters. In order to support custom parameter types, users need to implement Lux._merge(::CustomParamType, ::NamedTuple).

Example

julia
m = Lux.Experimental.FrozenLayer(Dense(2 => 2), (:weight,))

See also Lux.Experimental.freeze, Lux.Experimental.unfreeze.

source


# Lux.Experimental.freeze — Function.
julia
freeze(l::AbstractExplicitLayer, which_params::Union{Tuple, Nothing} = nothing)

Constructs a version of l with which_params frozen. If which_params is nothing, then all parameters are frozen.

source

julia
freeze(l::AbstractExplicitLayer, ps, st::NamedTuple,
+       which_params::Union{Tuple, Nothing} = nothing)

Construct a Lux.Experimental.FrozenLayer for l with the current parameters and states. If which_params is nothing, then all parameters are frozen.

source


# Lux.Experimental.unfreeze — Function.
julia
unfreeze(l::FrozenLayer)

Unfreezes the layer l.

source

julia
unfreeze(l::FrozenLayer, ps, st::NamedTuple)

Unwraps a Lux.Experimental.FrozenLayer l with the current parameters and states.

source


For detailed usage example look at the manual page.

Map over Layer ​

# Lux.Experimental.layer_map — Function.
julia
layer_map(f::Function, l::AbstractExplicitLayer, ps, st::NamedTuple,
+          name::String="model")

Map the function f over the model l, with the parameters ps and states st. This is different from Functors.fmap since it zips the layers, parameters, and states and invokes the function on all of them together.

Call Signature for f

Tip

We recommend using the macro Lux.@layer_map instead of this function. It automatically sets the name of the layer to be the variable name.

Example

julia
using Lux, Random, Setfield
+
+c = Parallel(+; chain=Chain(; dense_1=Dense(2 => 3), bn=BatchNorm(3),
+                              dense_2=Dense(3 => 5)),
+             dense_3=Dense(5 => 1))
+
+rng = Random.default_rng()
+ps, st = Lux.setup(rng, c)
+
+# Makes parameters of Dense Layers inside Chain zero
+function zero_dense_params(l, ps, st, name)
+    if l isa Dense
+        println("zeroing params of $name")
+        @set! ps.weight = zero.(ps.weight)
+        @set! ps.bias = zero.(ps.bias)
+    end
+    return l, ps, st
+end
+
+Lux.layer_map(zero_dense_params, c, ps, st)

source


# Lux.Experimental.@layer_map — Macro.
julia
@layer_map func layer ps st

See the documentation of Lux.Experimental.layer_map for more details. This macro eliminates the need to the set the layer name, and uses the variable name as the starting point.

Example

julia
using Lux, Random, Setfield
+
+c = Parallel(+; chain=Chain(; dense_1=Dense(2 => 3), bn=BatchNorm(3),
+                              dense_2=Dense(3 => 5)),
+             dense_3=Dense(5 => 1))
+
+rng = Random.default_rng()
+ps, st = Lux.setup(rng, c)
+
+# Makes parameters of Dense Layers inside Chain zero
+function zero_dense_params(l, ps, st, name)
+    if l isa Dense
+        println("zeroing params of $name")
+        @set! ps.weight = zero.(ps.weight)
+        @set! ps.bias = zero.(ps.bias)
+    end
+    return l, ps, st
+end
+
+Lux.@layer_map zero_dense_params c ps st

source


Debugging Functionality ​

Model not working properly! Here are some functionalities to help you debug you Lux model.

# Lux.Experimental.@debug_mode — Macro.
julia
@debug_mode layer kwargs...

Recurses into the layer and replaces the inner most non Container Layers with a Lux.Experimental.DebugLayer.

See Lux.Experimental.DebugLayer for details about the Keyword Arguments.

source


# Lux.Experimental.DebugLayer — Type.
julia
DebugLayer(layer::AbstractExplicitLayer; nan_check::Symbol=:both,
+    error_check::Bool=true, location::String="")

Danger

This layer is only meant to be used for debugging. If used for actual training or inference, will lead to extremely bad performance.

A wrapper over Lux layers that adds checks for NaNs and errors. This is useful for debugging.

Arguments

Keyword Arguments

Inputs

Outputs

If nan_check is enabled and NaNs are detected then a DomainError is thrown. If error_check is enabled, then any errors in the layer are thrown with useful information to track where the error originates.

Warning

nan_check for the backward mode only works with ChainRules Compatible Reverse Mode AD Tools currently.

See Lux.Experimental.@debug_mode to construct this layer.

source


Tied Parameters ​

# Lux.Experimental.share_parameters — Function.
julia
share_parameters(ps, sharing)
+share_parameters(ps, sharing, new_parameters)

Updates the parameters in ps with a common set of parameters new_parameters that are shared between each list in the nested list sharing. (That was kind of a mouthful, the example should make it clear).

Arguments

Returns

Updated Parameters having the same structure as ps.

Example

julia
model = Chain(; d1=Dense(2 => 4, tanh),
+    d3=Chain(; l1=Dense(4 => 2), l2=Dense(2 => 4)), d2=Dense(4 => 2))
+
+ps, st = Lux.setup(Xoshiro(0), model)
+
+# share parameters of (d1 and d3.l1) and (d3.l2 and d2)
+ps = Lux.share_parameters(ps, (("d3.l2", "d1"), ("d2", "d3.l1")))

source


Compact Layer API ​

# Lux.Experimental.@compact — Macro.
julia
@compact(kw...) do x
+    ...
+end
+@compact(forward::Function; name=nothing, dispatch=nothing, parameters...)

Creates a layer by specifying some parameters, in the form of keywords, and (usually as a do block) a function for the forward pass. You may think of @compact as a specialized let block creating local variables that are trainable in Lux. Declared variable names may be used within the body of the forward function. Note that unlike typical Lux models, the forward function doesn't need to explicitly manage states.

Reserved Kwargs:

  1. name: The name of the layer.

  2. dispatch: The constructed layer has the type Lux.Experimental.CompactLuxLayer{dispatch} which can be used for custom dispatches.

Examples

Here is a linear model:

julia
using Lux, Random
+import Lux.Experimental: @compact
+
+r = @compact(w=rand(3)) do x
+    return w .* x
+end
+ps, st = Lux.setup(Xoshiro(0), r)
+r([1, 1, 1], ps, st)  # x is set to [1, 1, 1].

Here is a linear model with bias and activation:

julia
d_in = 5
+d_out = 7
+d = @compact(W=randn(d_out, d_in), b=zeros(d_out), act=relu) do x
+    y = W * x
+    return act.(y .+ b)
+end
+ps, st = Lux.setup(Xoshiro(0), d)
+d(ones(5, 10), ps, st) # 7×10 Matrix as output.
+
+ps_dense = (; weight=ps.W, bias=ps.b)
+first(d([1, 2, 3, 4, 5], ps, st)) ≈
+first(Dense(d_in => d_out, relu)([1, 2, 3, 4, 5], ps_dense, NamedTuple())) # Equivalent to a dense layer

Finally, here is a simple MLP:

julia
n_in = 1
+n_out = 1
+nlayers = 3
+
+model = @compact(w1=Dense(n_in, 128),
+    w2=[Dense(128, 128) for i in 1:nlayers], w3=Dense(128, n_out), act=relu) do x
+    embed = act(w1(x))
+    for w in w2
+        embed = act(w(embed))
+    end
+    out = w3(embed)
+    return out
+end
+
+ps, st = Lux.setup(Xoshiro(0), model)
+
+model(randn(n_in, 32), ps, st)  # 1×32 Matrix as output.

We can train this model just like any Lux model:

julia
using Optimisers, Zygote
+
+x_data = collect(-2.0f0:0.1f0:2.0f0)'
+y_data = 2 .* x_data .- x_data .^ 3
+optim = Optimisers.setup(Adam(), ps)
+
+for epoch in 1:1000
+    loss, gs = Zygote.withgradient(
+        ps -> sum(abs2, first(model(x_data, ps, st)) .- y_data), ps)
+    @show epoch, loss
+    Optimisers.update!(optim, ps, gs[1])
+end

You may also specify a name for the model, which will be used instead of the default printout, which gives a verbatim representation of the code used to construct the model:

julia
model = @compact(w=rand(3), name="Linear(3 => 1)") do x
+    return sum(w .* x)
+end
+
+println(model)  # "Linear(3 => 1)()"

This can be useful when using @compact to hierarchically construct complex models to be used inside a Chain.

Type Stability

If your input function f is type-stable but the generated model is not type stable, it should be treated as a bug. We will appreciate issues if you find such cases.

Parameter Count

Array Parameter don't print the number of parameters on the side. However, they do account for the total number of parameters printed at the bottom.

source


`,41),h=[n];function l(p,k,r,d,o,E){return a(),i("div",null,h)}const y=s(t,[["render",l]]);export{c as __pageData,y as default}; diff --git a/v0.5.30/assets/api_Lux_contrib.md.DdRrnWLR.lean.js b/v0.5.30/assets/api_Lux_contrib.md.DdRrnWLR.lean.js new file mode 100644 index 000000000..2411f1cb2 --- /dev/null +++ b/v0.5.30/assets/api_Lux_contrib.md.DdRrnWLR.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as e}from"./chunks/framework.BfjuC5t1.js";const c=JSON.parse('{"title":"Experimental Features","description":"","frontmatter":{},"headers":[],"relativePath":"api/Lux/contrib.md","filePath":"api/Lux/contrib.md","lastUpdated":null}'),t={name:"api/Lux/contrib.md"},n=e("",41),h=[n];function l(p,k,r,d,o,E){return a(),i("div",null,h)}const y=s(t,[["render",l]]);export{c as __pageData,y as default}; diff --git a/v0.5.30/assets/api_Lux_layers.md.BLLg0WBY.js b/v0.5.30/assets/api_Lux_layers.md.BLLg0WBY.js new file mode 100644 index 000000000..ade011358 --- /dev/null +++ b/v0.5.30/assets/api_Lux_layers.md.BLLg0WBY.js @@ -0,0 +1,57 @@ +import{_ as Q,c as s,m as t,a,a4 as e,o as i}from"./chunks/framework.BfjuC5t1.js";const q4=JSON.parse('{"title":"Built-In Layers","description":"","frontmatter":{},"headers":[],"relativePath":"api/Lux/layers.md","filePath":"api/Lux/layers.md","lastUpdated":null}'),l={name:"api/Lux/layers.md"},T=e(`

Built-In Layers ​

Index ​

Containers ​

# Lux.BranchLayer — Type.
julia
BranchLayer(layers...)
+BranchLayer(; name=nothing, layers...)

Takes an input x and passes it through all the layers and returns a tuple of the outputs.

Arguments

Keyword Arguments

Inputs

Returns

Parameters

States

Comparison with Parallel

This is slightly different from Parallel(nothing, layers...)

  • If the input is a tuple, Parallel will pass each element individually to each layer.

  • BranchLayer essentially assumes 1 input comes in and is branched out into N outputs.

Example

An easy way to replicate an input to an NTuple is to do

julia
l = BranchLayer(NoOpLayer(), NoOpLayer(), NoOpLayer())

source


# Lux.Chain — Type.
julia
Chain(layers...; name=nothing, disable_optimizations::Bool = false)
+Chain(; layers..., name=nothing, disable_optimizations::Bool = false)

Collects multiple layers / functions to be called in sequence on a given input.

Arguments

Keyword Arguments

Inputs

Input x is passed sequentially to each layer, and must conform to the input requirements of the internal layers.

Returns

Parameters

States

Optimizations

Performs a few optimizations to generate reasonable architectures. Can be disabled using keyword argument disable_optimizations.

Miscellaneous Properties

Example

julia
c = Chain(Dense(2, 3, relu), BatchNorm(3), Dense(3, 2))

source


# Lux.PairwiseFusion — Type.
julia
PairwiseFusion(connection, layers...; name=nothing)
+PairwiseFusion(connection; name=nothing, layers...)
x1 → layer1 → y1 ↘
+                  connection → layer2 → y2 ↘
+              x2 ↗                          connection → y3
+                                        x3 ↗

Arguments

Keyword Arguments

Inputs

Layer behaves differently based on input type:

  1. If the input x is a tuple of length N + 1, then the layers must be a tuple of length N. The computation is as follows
julia
y = x[1]
+for i in 1:N
+    y = connection(x[i + 1], layers[i](y))
+end
  1. Any other kind of input
julia
y = x
+for i in 1:N
+    y = connection(x, layers[i](y))
+end

Returns

Parameters

States

source


# Lux.Parallel — Type.
julia
Parallel(connection, layers...; name=nothing)
+Parallel(connection; name=nothing, layers...)

Create a layer which passes an input to each path in layers, before reducing the output with connection.

Arguments

Keyword Arguments

Inputs

Returns

Parameters

States

See also SkipConnection which is Parallel with one identity.

source


# Lux.SkipConnection — Type.
julia
SkipConnection(layer, connection; name=nothing)

Create a skip connection which consists of a layer or Chain of consecutive layers and a shortcut connection linking the block's input to the output through a user-supplied 2-argument callable. The first argument to the callable will be propagated through the given layer while the second is the unchanged, "skipped" input.

The simplest "ResNet"-type connection is just SkipConnection(layer, +).

Arguments

Keyword Arguments

Inputs

Returns

Parameters

States

See Parallel for a more general implementation.

source


# Lux.RepeatedLayer — Type.
julia
RepeatedLayer(model; repeats::Val = Val(10), input_injection::Val = Val(false))

Iteratively applies model for repeats number of times. The initial input is passed into the model repeatedly if input_injection = Val(true). This layer unrolls the computation, however, semantically this is same as:

  1. input_injection = Val(false)
julia
res = x
+for i in 1:repeats
+    res, st = model(res, ps, st)
+end
  1. input_injection = Val(true)
julia
res = x
+for i in 1:repeats
+    res, st = model((res, x), ps, st)
+end

It is expected that repeats will be a reasonable number below 20, beyond that compile times for gradients might be unreasonably high.

Arguments

Keyword Arguments

Inputs

Returns

Parameters

States

source


Convolutional Layers ​

`,17),o={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},n=t("a",{id:"Lux.Conv",href:"#Lux.Conv"},"#",-1),d=t("b",null,[t("u",null,"Lux.Conv")],-1),r=t("i",null,"Type",-1),p=e(`
julia
Conv(k::NTuple{N,Integer}, (in_chs => out_chs)::Pair{<:Integer,<:Integer},
+     activation=identity; init_weight=glorot_uniform, init_bias=zeros32, stride=1,
+     pad=0, dilation=1, groups=1, use_bias=true)

Standard convolutional layer.

Image data should be stored in WHCN order (width, height, channels, batch). In other words, a 100 x 100 RGB image would be a 100 x 100 x 3 x 1 array, and a batch of 50 would be a 100 x 100 x 3 x 50 array. This has N = 2 spatial dimensions, and needs a kernel size like (5, 5), a 2-tuple of integers. To take convolutions along N feature dimensions, this layer expects as input an array with ndims(x) == N + 2, where size(x, N + 1) == in_chs is the number of input channels, and size(x, ndims(x)) is the number of observations in a batch.

Warning

Frameworks like Pytorch perform cross-correlation in their convolution layers

Arguments

Keyword Arguments

Inputs

Returns

`,12),h={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},m={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.148ex"},xmlns:"http://www.w3.org/2000/svg",width:"45.995ex",height:"5.686ex",role:"img",focusable:"false",viewBox:"0 -1563.5 20329.9 2513","aria-hidden":"true"},c=e('',1),g=[c],u=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("msub",null,[t("mi",null,"O"),t("mi",null,"i")]),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"⌊"),t("mfrac",null,[t("mrow",null,[t("msub",null,[t("mi",null,"I"),t("mi",null,"i")]),t("mo",null,"+"),t("msub",null,[t("mi",null,"p"),t("mi",null,"i")]),t("mo",null,"+"),t("msub",null,[t("mi",null,"p"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",{stretchy:"false"},"("),t("mi",null,"i"),t("mo",null,"+"),t("mi",null,"N"),t("mo",{stretchy:"false"},")"),t("mi",{mathvariant:"normal"},"%"),t("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),t("mi",null,"p"),t("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),t("mo",null,"−"),t("msub",null,[t("mi",null,"d"),t("mi",null,"i")]),t("mo",null,"×"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"k"),t("mi",null,"i")]),t("mo",null,"−"),t("mn",null,"1"),t("mo",{stretchy:"false"},")")]),t("msub",null,[t("mi",null,"s"),t("mi",null,"i")])]),t("mo",null,"+"),t("mn",null,"1"),t("mo",{"data-mjx-texclass":"CLOSE"},"⌋")])])],-1),k=e('

Parameters

source

',4),y=e(`
# Lux.ConvTranspose — Type.
julia
ConvTranspose(k::NTuple{N,Integer}, (in_chs => out_chs)::Pair{<:Integer,<:Integer},
+              activation=identity; init_weight=glorot_uniform, init_bias=zeros32,
+              stride=1, pad=0, dilation=1, groups=1, use_bias=true)

Standard convolutional transpose layer.

Arguments

Keyword Arguments

Inputs

Returns

Parameters

source


`,3),f={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},L=t("a",{id:"Lux.CrossCor",href:"#Lux.CrossCor"},"#",-1),b=t("b",null,[t("u",null,"Lux.CrossCor")],-1),x=t("i",null,"Type",-1),_=e(`
julia
CrossCor(k::NTuple{N,Integer}, (in_chs => out_chs)::Pair{<:Integer,<:Integer},
+         activation=identity; init_weight=glorot_uniform, init_bias=zeros32, stride=1,
+         pad=0, dilation=1, use_bias=true)

Cross Correlation layer.

Image data should be stored in WHCN order (width, height, channels, batch). In other words, a 100 x 100 RGB image would be a 100 x 100 x 3 x 1 array, and a batch of 50 would be a 100 x 100 x 3 x 50 array. This has N = 2 spatial dimensions, and needs a kernel size like (5, 5), a 2-tuple of integers. To take convolutions along N feature dimensions, this layer expects as input an array with ndims(x) == N + 2, where size(x, N + 1) == in_chs is the number of input channels, and size(x, ndims(x)) is the number of observations in a batch.

Arguments

Keyword Arguments

Inputs

Returns

`,11),w={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},H={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.148ex"},xmlns:"http://www.w3.org/2000/svg",width:"45.995ex",height:"5.686ex",role:"img",focusable:"false",viewBox:"0 -1563.5 20329.9 2513","aria-hidden":"true"},E=e('',1),M=[E],C=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("msub",null,[t("mi",null,"O"),t("mi",null,"i")]),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"⌊"),t("mfrac",null,[t("mrow",null,[t("msub",null,[t("mi",null,"I"),t("mi",null,"i")]),t("mo",null,"+"),t("msub",null,[t("mi",null,"p"),t("mi",null,"i")]),t("mo",null,"+"),t("msub",null,[t("mi",null,"p"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",{stretchy:"false"},"("),t("mi",null,"i"),t("mo",null,"+"),t("mi",null,"N"),t("mo",{stretchy:"false"},")"),t("mi",{mathvariant:"normal"},"%"),t("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),t("mi",null,"p"),t("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),t("mo",null,"−"),t("msub",null,[t("mi",null,"d"),t("mi",null,"i")]),t("mo",null,"×"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"k"),t("mi",null,"i")]),t("mo",null,"−"),t("mn",null,"1"),t("mo",{stretchy:"false"},")")]),t("msub",null,[t("mi",null,"s"),t("mi",null,"i")])]),t("mo",null,"+"),t("mn",null,"1"),t("mo",{"data-mjx-texclass":"CLOSE"},"⌋")])])],-1),D=e('

Parameters

source

',4),v=e('

Dropout Layers ​

# Lux.AlphaDropout — Type.
julia
AlphaDropout(p::Real)

AlphaDropout layer.

Arguments

Inputs

Returns

States

Call Lux.testmode to switch to test mode.

See also Dropout, VariationalHiddenDropout

source


# Lux.Dropout — Type.
julia
Dropout(p; dims=:)

Dropout layer.

Arguments

Keyword Arguments

Inputs

Returns

States

Call Lux.testmode to switch to test mode.

See also AlphaDropout, VariationalHiddenDropout

source


# Lux.VariationalHiddenDropout — Type.
julia
VariationalHiddenDropout(p; dims=:)

VariationalHiddenDropout layer. The only difference from Dropout is that the mask is retained until Lux.update_state(l, :update_mask, Val(true)) is called.

Arguments

Keyword Arguments

Inputs

Returns

States

Call Lux.testmode to switch to test mode.

See also AlphaDropout, Dropout

source


Pooling Layers ​

# Lux.AdaptiveMaxPool — Type.
julia
AdaptiveMaxPool(out::NTuple)

Adaptive Max Pooling layer. Calculates the necessary window size such that its output has size(y)[1:N] == out.

Arguments

Inputs

Returns

See also MaxPool, AdaptiveMeanPool.

source


# Lux.AdaptiveMeanPool — Type.
julia
AdaptiveMeanPool(out::NTuple)

Adaptive Mean Pooling layer. Calculates the necessary window size such that its output has size(y)[1:N] == out.

Arguments

Inputs

Returns

See also MeanPool, AdaptiveMaxPool.

source


# Lux.GlobalMaxPool — Type.
julia
GlobalMaxPool()

Global Max Pooling layer. Transforms (w,h,c,b)-shaped input into (1,1,c,b)-shaped output, by performing max pooling on the complete (w,h)-shaped feature maps.

Inputs

Returns

See also MaxPool, AdaptiveMaxPool, GlobalMeanPool

source


# Lux.GlobalMeanPool — Type.
julia
GlobalMeanPool()

Global Mean Pooling layer. Transforms (w,h,c,b)-shaped input into (1,1,c,b)-shaped output, by performing mean pooling on the complete (w,h)-shaped feature maps.

Inputs

Returns

See also MeanPool, AdaptiveMeanPool, GlobalMaxPool

source


',17),Z={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},F=t("a",{id:"Lux.MaxPool",href:"#Lux.MaxPool"},"#",-1),A=t("b",null,[t("u",null,"Lux.MaxPool")],-1),V=t("i",null,"Type",-1),N=e('
julia
MaxPool(window::NTuple; pad=0, stride=window)

Max pooling layer, which replaces all pixels in a block of size window with the maximum value.

Arguments

Keyword Arguments

Inputs

Returns

',10),j={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},B={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.148ex"},xmlns:"http://www.w3.org/2000/svg",width:"45.995ex",height:"5.686ex",role:"img",focusable:"false",viewBox:"0 -1563.5 20329.9 2513","aria-hidden":"true"},S=e('',1),R=[S],I=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("msub",null,[t("mi",null,"O"),t("mi",null,"i")]),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"⌊"),t("mfrac",null,[t("mrow",null,[t("msub",null,[t("mi",null,"I"),t("mi",null,"i")]),t("mo",null,"+"),t("msub",null,[t("mi",null,"p"),t("mi",null,"i")]),t("mo",null,"+"),t("msub",null,[t("mi",null,"p"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",{stretchy:"false"},"("),t("mi",null,"i"),t("mo",null,"+"),t("mi",null,"N"),t("mo",{stretchy:"false"},")"),t("mi",{mathvariant:"normal"},"%"),t("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),t("mi",null,"p"),t("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),t("mo",null,"−"),t("msub",null,[t("mi",null,"d"),t("mi",null,"i")]),t("mo",null,"×"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"k"),t("mi",null,"i")]),t("mo",null,"−"),t("mn",null,"1"),t("mo",{stretchy:"false"},")")]),t("msub",null,[t("mi",null,"s"),t("mi",null,"i")])]),t("mo",null,"+"),t("mn",null,"1"),t("mo",{"data-mjx-texclass":"CLOSE"},"⌋")])])],-1),P=e('

See also Conv, MeanPool, GlobalMaxPool, AdaptiveMaxPool

source

',3),z=t("br",null,null,-1),O={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},G=t("a",{id:"Lux.MeanPool",href:"#Lux.MeanPool"},"#",-1),W=t("b",null,[t("u",null,"Lux.MeanPool")],-1),X=t("i",null,"Type",-1),U=e('
julia
MeanPool(window::NTuple; pad=0, stride=window)

Mean pooling layer, which replaces all pixels in a block of size window with the mean value.

Arguments

Keyword Arguments

Inputs

Returns

',10),q={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},J={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.148ex"},xmlns:"http://www.w3.org/2000/svg",width:"45.995ex",height:"5.686ex",role:"img",focusable:"false",viewBox:"0 -1563.5 20329.9 2513","aria-hidden":"true"},K=e('',1),$=[K],Y=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("msub",null,[t("mi",null,"O"),t("mi",null,"i")]),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"⌊"),t("mfrac",null,[t("mrow",null,[t("msub",null,[t("mi",null,"I"),t("mi",null,"i")]),t("mo",null,"+"),t("msub",null,[t("mi",null,"p"),t("mi",null,"i")]),t("mo",null,"+"),t("msub",null,[t("mi",null,"p"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mo",{stretchy:"false"},"("),t("mi",null,"i"),t("mo",null,"+"),t("mi",null,"N"),t("mo",{stretchy:"false"},")"),t("mi",{mathvariant:"normal"},"%"),t("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),t("mi",null,"p"),t("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),t("mo",null,"−"),t("msub",null,[t("mi",null,"d"),t("mi",null,"i")]),t("mo",null,"×"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"k"),t("mi",null,"i")]),t("mo",null,"−"),t("mn",null,"1"),t("mo",{stretchy:"false"},")")]),t("msub",null,[t("mi",null,"s"),t("mi",null,"i")])]),t("mo",null,"+"),t("mn",null,"1"),t("mo",{"data-mjx-texclass":"CLOSE"},"⌋")])])],-1),t1=e('

See also Conv, MaxPool, GlobalMeanPool, AdaptiveMeanPool

source

',3),a1=t("br",null,null,-1),e1=t("h2",{id:"Recurrent-Layers",tabindex:"-1"},[a("Recurrent Layers "),t("a",{class:"header-anchor",href:"#Recurrent-Layers","aria-label":'Permalink to "Recurrent Layers {#Recurrent-Layers}"'},"​")],-1),s1={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},i1=t("a",{id:"Lux.GRUCell",href:"#Lux.GRUCell"},"#",-1),Q1=t("b",null,[t("u",null,"Lux.GRUCell")],-1),l1=t("i",null,"Type",-1),T1=e(`
julia
GRUCell((in_dims, out_dims)::Pair{<:Int,<:Int}; use_bias=true, train_state::Bool=false,
+        init_weight::Tuple{Function,Function,Function}=(glorot_uniform, glorot_uniform,
+                                                        glorot_uniform),
+        init_bias::Tuple{Function,Function,Function}=(zeros32, zeros32, zeros32),
+        init_state::Function=zeros32)

Gated Recurrent Unit (GRU) Cell

`,2),o1={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},n1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-5.146ex"},xmlns:"http://www.w3.org/2000/svg",width:"51.473ex",height:"11.422ex",role:"img",focusable:"false",viewBox:"0 -2774.4 22750.9 5048.7","aria-hidden":"true"},d1=e('',1),r1=[d1],p1=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mtable",{displaystyle:"true",columnalign:"right left",columnspacing:"0em",rowspacing:"3pt"},[t("mtr",null,[t("mtd",null,[t("mi",null,"r")]),t("mtd",null,[t("mi"),t("mo",null,"="),t("mi",null,"σ"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"r")])]),t("mo",null,"×"),t("mi",null,"x"),t("mo",null,"+"),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"r")])]),t("mo",null,"×"),t("msub",null,[t("mi",null,"h"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"p"),t("mi",null,"r"),t("mi",null,"e"),t("mi",null,"v")])]),t("mo",null,"+"),t("msub",null,[t("mi",null,"b"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"r")])]),t("mo",{stretchy:"false"},")")])]),t("mtr",null,[t("mtd",null,[t("mi",null,"z")]),t("mtd",null,[t("mi"),t("mo",null,"="),t("mi",null,"σ"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"z")])]),t("mo",null,"×"),t("mi",null,"x"),t("mo",null,"+"),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"z")])]),t("mo",null,"×"),t("msub",null,[t("mi",null,"h"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"p"),t("mi",null,"r"),t("mi",null,"e"),t("mi",null,"v")])]),t("mo",null,"+"),t("msub",null,[t("mi",null,"b"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"z")])]),t("mo",{stretchy:"false"},")")])]),t("mtr",null,[t("mtd",null,[t("mi",null,"n")]),t("mtd",null,[t("mi"),t("mo",null,"="),t("mi",null,"tanh"),t("mo",{"data-mjx-texclass":"NONE"},"⁡"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"n")])]),t("mo",null,"×"),t("mi",null,"x"),t("mo",null,"+"),t("msub",null,[t("mi",null,"b"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"n")])]),t("mo",null,"+"),t("mi",null,"r"),t("mo",null,"⋅"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"n")])]),t("mo",null,"×"),t("msub",null,[t("mi",null,"h"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"p"),t("mi",null,"r"),t("mi",null,"e"),t("mi",null,"v")])]),t("mo",null,"+"),t("msub",null,[t("mi",null,"b"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"n")])]),t("mo",{stretchy:"false"},")"),t("mo",{stretchy:"false"},")")])]),t("mtr",null,[t("mtd",null,[t("msub",null,[t("mi",null,"h"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"n"),t("mi",null,"e"),t("mi",null,"w")])])]),t("mtd",null,[t("mi"),t("mo",null,"="),t("mo",{stretchy:"false"},"("),t("mn",null,"1"),t("mo",null,"−"),t("mi",null,"z"),t("mo",{stretchy:"false"},")"),t("mo",null,"⋅"),t("mi",null,"n"),t("mo",null,"+"),t("mi",null,"z"),t("mo",null,"⋅"),t("msub",null,[t("mi",null,"h"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"p"),t("mi",null,"r"),t("mi",null,"e"),t("mi",null,"v")])])])])])])],-1),h1=e("

Arguments

Inputs

Returns

",5),m1=t("p",null,"Tuple containing",-1),c1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.342ex",height:"1.927ex",role:"img",focusable:"false",viewBox:"0 -694 1919.1 851.8","aria-hidden":"true"},u1=e('',1),k1=[u1],y1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"h"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"n"),t("mi",null,"e"),t("mi",null,"w")])])])],-1),f1=t("code",null,"(out_dims, batch_size)",-1),L1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},b1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.342ex",height:"1.927ex",role:"img",focusable:"false",viewBox:"0 -694 1919.1 851.8","aria-hidden":"true"},x1=e('',1),_1=[x1],w1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"h"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"n"),t("mi",null,"e"),t("mi",null,"w")])])])],-1),H1=t("li",null,[t("p",null,"Updated model state")],-1),E1=t("p",null,[t("strong",null,"Parameters")],-1),M1=t("code",null,"weight_i",-1),C1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},D1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"15.326ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 6774.2 1000","aria-hidden":"true"},v1=e('',1),Z1=[v1],F1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{fence:"false",stretchy:"false"},"{"),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"r")])]),t("mo",null,","),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"z")])]),t("mo",null,","),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"n")])]),t("mo",{fence:"false",stretchy:"false"},"}")])],-1),A1=t("code",null,"weight_h",-1),V1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},N1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"16.435ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 7264.2 1000","aria-hidden":"true"},j1=e('',1),B1=[j1],S1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{fence:"false",stretchy:"false"},"{"),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"r")])]),t("mo",null,","),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"z")])]),t("mo",null,","),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"n")])]),t("mo",{fence:"false",stretchy:"false"},"}")])],-1),R1=t("code",null,"bias_i",-1),I1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},P1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.67ex",height:"1.927ex",role:"img",focusable:"false",viewBox:"0 -694 1180.2 851.8","aria-hidden":"true"},z1=e('',1),O1=[z1],G1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"b"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"n")])])])],-1),W1=t("code",null,"use_bias=false",-1),X1=t("code",null,"bias_h",-1),U1={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},q1={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"12.939ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 5719.2 1000","aria-hidden":"true"},J1=e('',1),K1=[J1],$1=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{fence:"false",stretchy:"false"},"{"),t("msub",null,[t("mi",null,"b"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"r")])]),t("mo",null,","),t("msub",null,[t("mi",null,"b"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"z")])]),t("mo",null,","),t("msub",null,[t("mi",null,"b"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"n")])]),t("mo",{fence:"false",stretchy:"false"},"}")])],-1),Y1=t("code",null,"use_bias=false",-1),t2=t("code",null,"hidden_state",-1),a2=t("code",null,"train_state=false",-1),e2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},s2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"12.939ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 5719.2 1000","aria-hidden":"true"},i2=e('',1),Q2=[i2],l2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{fence:"false",stretchy:"false"},"{"),t("msub",null,[t("mi",null,"b"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"r")])]),t("mo",null,","),t("msub",null,[t("mi",null,"b"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"z")])]),t("mo",null,","),t("msub",null,[t("mi",null,"b"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"n")])]),t("mo",{fence:"false",stretchy:"false"},"}")])],-1),T2=t("p",null,[t("strong",null,"States")],-1),o2=t("ul",null,[t("li",null,[t("code",null,"rng"),a(": Controls the randomness (if any) in the initial state generation")])],-1),n2=t("p",null,[t("a",{href:"https://github.com/LuxDL/Lux.jl/blob/b45e6037be239361965386d26ebb1d675fc1560b/src/layers/recurrent.jl#L494",target:"_blank",rel:"noreferrer"},"source")],-1),d2=t("br",null,null,-1),r2={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},p2=t("a",{id:"Lux.LSTMCell",href:"#Lux.LSTMCell"},"#",-1),h2=t("b",null,[t("u",null,"Lux.LSTMCell")],-1),m2=t("i",null,"Type",-1),c2=e(`
julia
LSTMCell(in_dims => out_dims; use_bias::Bool=true, train_state::Bool=false,
+         train_memory::Bool=false,
+         init_weight=(glorot_uniform, glorot_uniform, glorot_uniform, glorot_uniform),
+         init_bias=(zeros32, zeros32, ones32, zeros32), init_state=zeros32,
+         init_memory=zeros32)

Long Short-Term (LSTM) Cell

`,2),g2={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},u2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-8.146ex"},xmlns:"http://www.w3.org/2000/svg",width:"40.257ex",height:"17.424ex",role:"img",focusable:"false",viewBox:"0 -4100.7 17793.6 7701.4","aria-hidden":"true"},k2=e('',1),y2=[k2],f2=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mtable",{displaystyle:"true",columnalign:"right left",columnspacing:"0em",rowspacing:"3pt"},[t("mtr",null,[t("mtd",null,[t("mi",null,"i")]),t("mtd",null,[t("mi"),t("mo",null,"="),t("mi",null,"σ"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"i")])]),t("mo",null,"×"),t("mi",null,"x"),t("mo",null,"+"),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"i")])]),t("mo",null,"×"),t("msub",null,[t("mi",null,"h"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"p"),t("mi",null,"r"),t("mi",null,"e"),t("mi",null,"v")])]),t("mo",null,"+"),t("msub",null,[t("mi",null,"b"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i")])]),t("mo",{stretchy:"false"},")")])]),t("mtr",null,[t("mtd",null,[t("mi",null,"f")]),t("mtd",null,[t("mi"),t("mo",null,"="),t("mi",null,"σ"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"f")])]),t("mo",null,"×"),t("mi",null,"x"),t("mo",null,"+"),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"f")])]),t("mo",null,"×"),t("msub",null,[t("mi",null,"h"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"p"),t("mi",null,"r"),t("mi",null,"e"),t("mi",null,"v")])]),t("mo",null,"+"),t("msub",null,[t("mi",null,"b"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"f")])]),t("mo",{stretchy:"false"},")")])]),t("mtr",null,[t("mtd",null,[t("mi",null,"g")]),t("mtd",null,[t("mi"),t("mo",null,"="),t("mi",null,"t"),t("mi",null,"a"),t("mi",null,"n"),t("mi",null,"h"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"g")])]),t("mo",null,"×"),t("mi",null,"x"),t("mo",null,"+"),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"g")])]),t("mo",null,"×"),t("msub",null,[t("mi",null,"h"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"p"),t("mi",null,"r"),t("mi",null,"e"),t("mi",null,"v")])]),t("mo",null,"+"),t("msub",null,[t("mi",null,"b"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"g")])]),t("mo",{stretchy:"false"},")")])]),t("mtr",null,[t("mtd",null,[t("mi",null,"o")]),t("mtd",null,[t("mi"),t("mo",null,"="),t("mi",null,"σ"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"o")])]),t("mo",null,"×"),t("mi",null,"x"),t("mo",null,"+"),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"o")])]),t("mo",null,"×"),t("msub",null,[t("mi",null,"h"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"p"),t("mi",null,"r"),t("mi",null,"e"),t("mi",null,"v")])]),t("mo",null,"+"),t("msub",null,[t("mi",null,"b"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"o")])]),t("mo",{stretchy:"false"},")")])]),t("mtr",null,[t("mtd",null,[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"n"),t("mi",null,"e"),t("mi",null,"w")])])]),t("mtd",null,[t("mi"),t("mo",null,"="),t("mi",null,"f"),t("mo",null,"⋅"),t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"p"),t("mi",null,"r"),t("mi",null,"e"),t("mi",null,"v")])]),t("mo",null,"+"),t("mi",null,"i"),t("mo",null,"⋅"),t("mi",null,"g")])]),t("mtr",null,[t("mtd",null,[t("msub",null,[t("mi",null,"h"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"n"),t("mi",null,"e"),t("mi",null,"w")])])]),t("mtd",null,[t("mi"),t("mo",null,"="),t("mi",null,"o"),t("mo",null,"⋅"),t("mi",null,"t"),t("mi",null,"a"),t("mi",null,"n"),t("mi",null,"h"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"n"),t("mi",null,"e"),t("mi",null,"w")])]),t("mo",{stretchy:"false"},")")])])])])],-1),L2=e("

Arguments

Inputs

Returns

",5),b2=t("p",null,"Tuple Containing",-1),x2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},_2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.342ex",height:"1.927ex",role:"img",focusable:"false",viewBox:"0 -694 1919.1 851.8","aria-hidden":"true"},w2=e('',1),H2=[w2],E2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"h"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"n"),t("mi",null,"e"),t("mi",null,"w")])])])],-1),M2=t("code",null,"(out_dims, batch_size)",-1),C2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},D2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.342ex",height:"1.927ex",role:"img",focusable:"false",viewBox:"0 -694 1919.1 851.8","aria-hidden":"true"},v2=e('',1),Z2=[v2],F2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"h"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"n"),t("mi",null,"e"),t("mi",null,"w")])])])],-1),A2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.018ex",height:"1.357ex",role:"img",focusable:"false",viewBox:"0 -442 1776.1 599.8","aria-hidden":"true"},N2=e('',1),j2=[N2],B2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"c"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"n"),t("mi",null,"e"),t("mi",null,"w")])])])],-1),S2=t("li",null,[t("p",null,"Updated model state")],-1),R2=t("p",null,[t("strong",null,"Parameters")],-1),I2=t("code",null,"weight_i",-1),P2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},z2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.753ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 8730.9 1045","aria-hidden":"true"},O2=e('',1),G2=[O2],W2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{fence:"false",stretchy:"false"},"{"),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"i")])]),t("mo",null,","),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"f")])]),t("mo",null,","),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"g")])]),t("mo",null,","),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"o")])]),t("mo",{fence:"false",stretchy:"false"},"}")])],-1),X2=t("code",null,"weight_h",-1),U2={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},q2={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.231ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 9384.3 1045","aria-hidden":"true"},J2=e('',1),K2=[J2],$2=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{fence:"false",stretchy:"false"},"{"),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"i")])]),t("mo",null,","),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"f")])]),t("mo",null,","),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"g")])]),t("mo",null,","),t("msub",null,[t("mi",null,"W"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"o")])]),t("mo",{fence:"false",stretchy:"false"},"}")])],-1),Y2=e("

  • bias: Bias vector (not present if use_bias=false)

  • hidden_state: Initial hidden state vector (not present if train_state=false)

  • memory: Initial memory vector (not present if train_memory=false)

    • ",3),t3=t("p",null,[t("strong",null,"States")],-1),a3=t("ul",null,[t("li",null,[t("code",null,"rng"),a(": Controls the randomness (if any) in the initial state generation")])],-1),e3=t("p",null,[t("a",{href:"https://github.com/LuxDL/Lux.jl/blob/b45e6037be239361965386d26ebb1d675fc1560b/src/layers/recurrent.jl#L308",target:"_blank",rel:"noreferrer"},"source")],-1),s3=t("br",null,null,-1),i3={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},Q3=t("a",{id:"Lux.RNNCell",href:"#Lux.RNNCell"},"#",-1),l3=t("b",null,[t("u",null,"Lux.RNNCell")],-1),T3=t("i",null,"Type",-1),o3=e(`
    julia
    RNNCell(in_dims => out_dims, activation=tanh; bias::Bool=true,
+        train_state::Bool=false, init_bias=zeros32, init_weight=glorot_uniform,
+        init_state=ones32)

    An Elman RNNCell cell with activation (typically set to tanh or relu).

    `,2),n3={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d3={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.65ex"},xmlns:"http://www.w3.org/2000/svg",width:"57.143ex",height:"2.347ex",role:"img",focusable:"false",viewBox:"0 -750 25257.3 1037.2","aria-hidden":"true"},r3=e('',1),p3=[r3],h3=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"h"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"n"),t("mi",null,"e"),t("mi",null,"w")])]),t("mo",null,"="),t("mi",null,"a"),t("mi",null,"c"),t("mi",null,"t"),t("mi",null,"i"),t("mi",null,"v"),t("mi",null,"a"),t("mi",null,"t"),t("mi",null,"i"),t("mi",null,"o"),t("mi",null,"n"),t("mo",{stretchy:"false"},"("),t("mi",null,"w"),t("mi",null,"e"),t("mi",null,"i"),t("mi",null,"g"),t("mi",null,"h"),t("msub",null,[t("mi",null,"t"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"i"),t("mi",null,"h")])]),t("mo",null,"×"),t("mi",null,"x"),t("mo",null,"+"),t("mi",null,"w"),t("mi",null,"e"),t("mi",null,"i"),t("mi",null,"g"),t("mi",null,"h"),t("msub",null,[t("mi",null,"t"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"h"),t("mi",null,"h")])]),t("mo",null,"×"),t("msub",null,[t("mi",null,"h"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"p"),t("mi",null,"r"),t("mi",null,"e"),t("mi",null,"v")])]),t("mo",null,"+"),t("mi",null,"b"),t("mi",null,"i"),t("mi",null,"a"),t("mi",null,"s"),t("mo",{stretchy:"false"},")")])],-1),m3=e("

    Arguments

    Inputs

    Returns

    ",5),c3=t("p",null,"Tuple containing",-1),g3={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},u3={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.342ex",height:"1.927ex",role:"img",focusable:"false",viewBox:"0 -694 1919.1 851.8","aria-hidden":"true"},k3=e('',1),y3=[k3],f3=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"h"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"n"),t("mi",null,"e"),t("mi",null,"w")])])])],-1),L3=t("code",null,"(out_dims, batch_size)",-1),b3={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},x3={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.357ex"},xmlns:"http://www.w3.org/2000/svg",width:"4.342ex",height:"1.927ex",role:"img",focusable:"false",viewBox:"0 -694 1919.1 851.8","aria-hidden":"true"},_3=e('',1),w3=[_3],H3=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"h"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"n"),t("mi",null,"e"),t("mi",null,"w")])])])],-1),E3=t("li",null,[t("p",null,"Updated model state")],-1),M3=e('

    Parameters

    States

    source

    ',5),C3=e(`
    # Lux.Recurrence — Type.
    julia
    Recurrence(cell;
+    ordering::AbstractTimeSeriesDataBatchOrdering=BatchLastIndex(),
+    return_sequence::Bool=false)

    Wraps a recurrent cell (like RNNCell, LSTMCell, GRUCell) to automatically operate over a sequence of inputs.

    Warning

    This is completely distinct from Flux.Recur. It doesn't make the cell stateful, rather allows operating on an entire sequence of inputs at once. See StatefulRecurrentCell for functionality similar to Flux.Recur.

    Arguments

    Keyword Arguments

    Inputs

    Returns

    Parameters

    States

    Tip

    Frameworks like Tensorflow have special implementation of MultiRNNCell to handle sequentially composed RNN Cells. In Lux, one can simple stack multiple Recurrence blocks in a Chain to achieve the same.

    Chain(
+    Recurrence(RNNCell(inputsize => latentsize); return_sequence=true),
+    Recurrence(RNNCell(latentsize => latentsize); return_sequence=true),
+    :
+    x -> stack(x; dims=2)
+)

    For some discussion on this topic, see https://github.com/LuxDL/Lux.jl/issues/472.

    source


    # Lux.StatefulRecurrentCell — Type.
    julia
    StatefulRecurrentCell(cell)

    Wraps a recurrent cell (like RNNCell, LSTMCell, GRUCell) and makes it stateful.

    Tip

    This is very similar to Flux.Recur

    To avoid undefined behavior, once the processing of a single sequence of data is complete, update the state with Lux.update_state(st, :carry, nothing).

    Arguments

    Inputs

    Returns

    Parameters

    States

    source


    Linear Layers ​

    # Lux.Bilinear — Type.
    julia
    Bilinear((in1_dims, in2_dims) => out, activation=identity; init_weight=glorot_uniform,
+         init_bias=zeros32, use_bias::Bool=true, allow_fast_activation::Bool=true)
+Bilinear(in12_dims => out, activation=identity; init_weight=glorot_uniform,
+         init_bias=zeros32, use_bias::Bool=true, allow_fast_activation::Bool=true)

    Create a fully connected layer between two inputs and an output, and otherwise similar to Dense. Its output, given vectors x & y, is another vector z with, for all i in 1:out:

    z[i] = activation(x' * W[i, :, :] * y + bias[i])

    If x and y are matrices, then each column of the output z = B(x, y) is of this form, with B the Bilinear layer.

    Arguments

    Keyword Arguments

    Input

    Returns

    Parameters

    source


    # Lux.Dense — Type.
    julia
    Dense(in_dims => out_dims, activation=identity; init_weight=glorot_uniform,
+      init_bias=zeros32, use_bias::Bool=true, allow_fast_activation::Bool=true)

    Create a traditional fully connected layer, whose forward pass is given by: y = activation.(weight * x .+ bias)

    Arguments

    Keyword Arguments

    Input

    Returns

    Parameters

    source


    # Lux.Embedding — Type.
    julia
    Embedding(in_dims => out_dims; init_weight=randn32)

    A lookup table that stores embeddings of dimension out_dims for a vocabulary of size in_dims.

    This layer is often used to store word embeddings and retrieve them using indices.

    Warning

    Unlike Flux.Embedding, this layer does not support using OneHotArray as an input.

    Arguments

    Keyword Arguments

    Input

    Returns

    source


    # Lux.Scale — Type.
    julia
    Scale(dims, activation=identity; init_weight=ones32, init_bias=zeros32, bias::Bool=true)

    Create a Sparsely Connected Layer with a very specific structure (only Diagonal Elements are non-zero). The forward pass is given by: y = activation.(weight .* x .+ bias)

    Arguments

    Keyword Arguments

    Input

    Returns

    Parameters

    source


    Misc. Helper Layers ​

    # Lux.FlattenLayer — Type.
    julia
    FlattenLayer(N = nothing)

    Flattens the passed array into a matrix.

    Arguments

    Inputs

    Returns

    source


    # Lux.Maxout — Type.
    julia
    Maxout(layers...)
+Maxout(; layers...)
+Maxout(f::Function, n_alts::Int)

    This contains a number of internal layers, each of which receives the same input. Its output is the elementwise maximum of the the internal layers' outputs.

    Maxout over linear dense layers satisfies the univeral approximation theorem. See [1].

    See also Parallel to reduce with other operators.

    Arguments

    Inputs

    Returns

    Parameters

    States

    References

    [1] Goodfellow, Warde-Farley, Mirza, Courville & Bengio "Maxout Networks" https://arxiv.org/abs/1302.4389

    source


    # Lux.NoOpLayer — Type.
    julia
    NoOpLayer()

    As the name suggests does nothing but allows pretty printing of layers. Whatever input is passed is returned.

    source


    # Lux.ReshapeLayer — Type.
    julia
    ReshapeLayer(dims)

    Reshapes the passed array to have a size of (dims..., :)

    Arguments

    Inputs

    Returns

    source


    # Lux.SelectDim — Type.
    julia
    SelectDim(dim, i)

    Return a view of all the data of the input x where the index for dimension dim equals i. Equivalent to view(x,:,:,...,i,:,:,...) where i is in position d.

    Arguments

    Inputs

    Returns

    source


    # Lux.WrappedFunction — Type.
    julia
    WrappedFunction(f)

    Wraps a stateless and parameter less function. Might be used when a function is added to Chain. For example, Chain(x -> relu.(x)) would not work and the right thing to do would be Chain((x, ps, st) -> (relu.(x), st)). An easier thing to do would be Chain(WrappedFunction(Base.Fix1(broadcast, relu)))

    Arguments

    Inputs

    Returns

    source


    Normalization Layers ​

    `,28),D3={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},v3=t("a",{id:"Lux.BatchNorm",href:"#Lux.BatchNorm"},"#",-1),Z3=t("b",null,[t("u",null,"Lux.BatchNorm")],-1),F3=t("i",null,"Type",-1),A3=e(`
    julia
    BatchNorm(chs::Integer, activation=identity; init_bias=zeros32, init_scale=ones32,
+          affine=true, track_stats=true, epsilon=1f-5, momentum=0.1f0,
+          allow_fast_activation::Bool=true)

    Batch Normalization layer.

    `,2),V3=t("code",null,"BatchNorm",-1),N3={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j3={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.471ex"},xmlns:"http://www.w3.org/2000/svg",width:"23.059ex",height:"2.016ex",role:"img",focusable:"false",viewBox:"0 -683 10192.1 891","aria-hidden":"true"},B3=e('',1),S3=[B3],R3=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"D"),t("mn",null,"1")]),t("mi",null,"×"),t("mo",null,"."),t("mo",null,"."),t("mo",null,"."),t("mi",null,"×"),t("msub",null,[t("mi",null,"D"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"N"),t("mo",null,"−"),t("mn",null,"2")])]),t("mi",null,"×"),t("mn",null,"1"),t("mi",null,"×"),t("msub",null,[t("mi",null,"D"),t("mi",null,"N")])])],-1),I3=e('

    Arguments

    Keyword Arguments

    Inputs

    Returns

    Parameters

    States

    Use Lux.testmode during inference.

    Example

    julia
    m = Chain(Dense(784 => 64), BatchNorm(64, relu), Dense(64 => 10), BatchNorm(10))

    Warning

    Passing a batch size of 1, during training will result in NaNs.

    See also BatchNorm, InstanceNorm, LayerNorm, WeightNorm

    source

    ',18),P3=e(`
    # Lux.GroupNorm — Type.
    julia
    GroupNorm(chs::Integer, groups::Integer, activation=identity; init_bias=zeros32,
+          init_scale=ones32, affine=true, epsilon=1f-5,
+          allow_fast_activation::Bool=true)

    Group Normalization layer.

    Arguments

    Keyword Arguments

    Inputs

    Returns

    Parameters

    States

    Use Lux.testmode during inference.

    Example

    julia
    m = Chain(Dense(784 => 64), GroupNorm(64, 4, relu), Dense(64 => 10), GroupNorm(10, 5))

    See also GroupNorm, InstanceNorm, LayerNorm, WeightNorm

    source


    `,3),z3={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},O3=t("a",{id:"Lux.InstanceNorm",href:"#Lux.InstanceNorm"},"#",-1),G3=t("b",null,[t("u",null,"Lux.InstanceNorm")],-1),W3=t("i",null,"Type",-1),X3=e(`
    julia
    InstanceNorm(chs::Integer, activation=identity; init_bias=zeros32, init_scale=ones32,
+             affine=true, epsilon=1f-5, allow_fast_activation::Bool=true)

    Instance Normalization. For details see [1].

    `,2),U3={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},q3={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.471ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.72ex",height:"2.016ex",role:"img",focusable:"false",viewBox:"0 -683 10042 891","aria-hidden":"true"},J3=e('',1),K3=[J3],$3=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("msub",null,[t("mi",null,"D"),t("mn",null,"1")]),t("mo",null,"×"),t("mo",null,"."),t("mo",null,"."),t("mo",null,"."),t("mo",null,"×"),t("msub",null,[t("mi",null,"D"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",null,"N"),t("mo",null,"−"),t("mn",null,"2")])]),t("mo",null,"×"),t("mn",null,"1"),t("mo",null,"×"),t("mn",null,"1")])],-1),Y3=e('

    Arguments

    Keyword Arguments

    Inputs

    Returns

    Parameters

    States

    Use Lux.testmode during inference.

    Example

    julia
    m = Chain(Dense(784 => 64), InstanceNorm(64, relu), Dense(64 => 10), InstanceNorm(10, 5))

    References

    [1] Ulyanov, Dmitry, Andrea Vedaldi, and Victor Lempitsky. "Instance normalization: The missing ingredient for fast stylization." arXiv preprint arXiv:1607.08022 (2016).

    See also BatchNorm, GroupNorm, LayerNorm, WeightNorm

    source

    ',19),t4=t("br",null,null,-1),a4={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},e4=t("a",{id:"Lux.LayerNorm",href:"#Lux.LayerNorm"},"#",-1),s4=t("b",null,[t("u",null,"Lux.LayerNorm")],-1),i4=t("i",null,"Type",-1),Q4=e(`
    julia
    LayerNorm(shape::NTuple{N, Int}, activation=identity; epsilon=1f-5, dims=Colon(),
+          affine::Bool=true, init_bias=zeros32, init_scale=ones32,)

    Computes mean and standard deviation over the whole input array, and uses these to normalize the whole array. Optionally applies an elementwise affine transformation afterwards.

    `,2),l4={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},T4={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},o4=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D465",d:"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z",style:{"stroke-width":"3"}})])])],-1),n4=[o4],d4=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"x")])],-1),r4={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},p4={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.76ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.034ex",height:"6.063ex",role:"img",focusable:"false",viewBox:"0 -1460 11064.9 2680","aria-hidden":"true"},h4=e('',1),m4=[h4],c4=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mi",null,"y"),t("mo",null,"="),t("mfrac",null,[t("mrow",null,[t("mi",null,"x"),t("mo",null,"−"),t("mrow",{"data-mjx-texclass":"ORD"},[t("mi",{mathvariant:"double-struck"},"E")]),t("mo",{stretchy:"false"},"["),t("mi",null,"x"),t("mo",{stretchy:"false"},"]")]),t("msqrt",null,[t("mi",null,"V"),t("mi",null,"a"),t("mi",null,"r"),t("mo",{stretchy:"false"},"["),t("mi",null,"x"),t("mo",{stretchy:"false"},"]"),t("mo",null,"+"),t("mi",null,"ϵ")])]),t("mo",null,"∗"),t("mi",null,"γ"),t("mo",null,"+"),t("mi",null,"β")])],-1),g4={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},u4={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.489ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.229ex",height:"1.486ex",role:"img",focusable:"false",viewBox:"0 -441 543 657","aria-hidden":"true"},k4=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D6FE",d:"M31 249Q11 249 11 258Q11 275 26 304T66 365T129 418T206 441Q233 441 239 440Q287 429 318 386T371 255Q385 195 385 170Q385 166 386 166L398 193Q418 244 443 300T486 391T508 430Q510 431 524 431H537Q543 425 543 422Q543 418 522 378T463 251T391 71Q385 55 378 6T357 -100Q341 -165 330 -190T303 -216Q286 -216 286 -188Q286 -138 340 32L346 51L347 69Q348 79 348 100Q348 257 291 317Q251 355 196 355Q148 355 108 329T51 260Q49 251 47 251Q45 249 31 249Z",style:{"stroke-width":"3"}})])])],-1),y4=[k4],f4=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"γ")])],-1),L4={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},b4={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.439ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.281ex",height:"2.034ex",role:"img",focusable:"false",viewBox:"0 -705 566 899","aria-hidden":"true"},x4=t("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[t("g",{"data-mml-node":"math"},[t("g",{"data-mml-node":"mi"},[t("path",{"data-c":"1D6FD",d:"M29 -194Q23 -188 23 -186Q23 -183 102 134T186 465Q208 533 243 584T309 658Q365 705 429 705H431Q493 705 533 667T573 570Q573 465 469 396L482 383Q533 332 533 252Q533 139 448 65T257 -10Q227 -10 203 -2T165 17T143 40T131 59T126 65L62 -188Q60 -194 42 -194H29ZM353 431Q392 431 427 419L432 422Q436 426 439 429T449 439T461 453T472 471T484 495T493 524T501 560Q503 569 503 593Q503 611 502 616Q487 667 426 667Q384 667 347 643T286 582T247 514T224 455Q219 439 186 308T152 168Q151 163 151 147Q151 99 173 68Q204 26 260 26Q302 26 349 51T425 137Q441 171 449 214T457 279Q457 337 422 372Q380 358 347 358H337Q258 358 258 389Q258 396 261 403Q275 431 353 431Z",style:{"stroke-width":"3"}})])])],-1),_4=[x4],w4=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"β")])],-1),H4=t("code",null,"affine=true",-1),E4=e('

    Warning

    As of v0.5.0, the doc used to say affine::Bool=false, but the code actually had affine::Bool=true as the default. Now the doc reflects the code, so please check whether your assumptions about the default (if made) were invalid.

    Arguments

    Keyword Arguments

    Inputs

    Returns

    Parameters

    source

    ',12),M4=t("br",null,null,-1),C4={style:{"border-width":"1px","border-style":"solid","border-color":"black",padding:"1em","border-radius":"25px"}},D4=t("a",{id:"Lux.WeightNorm",href:"#Lux.WeightNorm"},"#",-1),v4=t("b",null,[t("u",null,"Lux.WeightNorm")],-1),Z4=t("i",null,"Type",-1),F4=e(`
    julia
    WeightNorm(layer::AbstractExplicitLayer, which_params::NTuple{N,Symbol},
+           dims::Union{Tuple,Nothing}=nothing)

    Applies weight normalization to a parameter in the given layer.

    `,2),A4={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},V4={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.172ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.071ex",height:"4.704ex",role:"img",focusable:"false",viewBox:"0 -1119 4451.6 2079","aria-hidden":"true"},N4=e('',1),j4=[N4],B4=t("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[t("mi",null,"w"),t("mo",null,"="),t("mi",null,"g"),t("mfrac",null,[t("mi",null,"v"),t("mrow",null,[t("mo",{"data-mjx-texclass":"ORD"},"∥"),t("mi",null,"v"),t("mo",{"data-mjx-texclass":"ORD"},"∥")])])])],-1),S4=e('

    Weight normalization is a reparameterization that decouples the magnitude of a weight tensor from its direction. This updates the parameters in which_params (e.g. weight) using two parameters: one specifying the magnitude (e.g. weight_g) and one specifying the direction (e.g. weight_v).

    Arguments

    Inputs

    Returns

    Parameters

    States

    source

    ',12),R4=e(`

    Upsampling ​

    # Lux.PixelShuffle — Function.
    julia
    PixelShuffle(r::Int)

    Pixel shuffling layer with upscale factor r. Usually used for generating higher resolution images while upscaling them.

    See NNlib.pixel_shuffle for more details.

    PixelShuffle is not a Layer, rather it returns a WrappedFunction with the function set to Base.Fix2(pixel_shuffle, r)

    Arguments

    Inputs

    Returns

    source


    # Lux.Upsample — Type.
    julia
    Upsample(mode = :nearest; [scale, size]) 
+Upsample(scale, mode = :nearest)

    Upsampling Layer.

    Layer Construction

    Option 1

    Exactly one of two keywords must be specified:

    Option 2

    Currently supported upsampling modes and corresponding NNlib's methods are:

    Inputs

    Returns

    source


    `,6);function I4(P4,z4,O4,G4,W4,X4){return i(),s("div",null,[T,t("div",o,[n,a(" "),d,a(" — "),r,a(". "),p,t("mjx-container",h,[(i(),s("svg",m,g)),u]),k]),y,t("div",f,[L,a(" "),b,a(" — "),x,a(". "),_,t("mjx-container",w,[(i(),s("svg",H,M)),C]),D]),v,t("div",Z,[F,a(" "),A,a(" — "),V,a(". "),N,t("mjx-container",j,[(i(),s("svg",B,R)),I]),P]),z,t("div",O,[G,a(" "),W,a(" — "),X,a(". "),U,t("mjx-container",q,[(i(),s("svg",J,$)),Y]),t1]),a1,e1,t("div",s1,[i1,a(" "),Q1,a(" — "),l1,a(". "),T1,t("mjx-container",o1,[(i(),s("svg",n1,r1)),p1]),h1,t("ul",null,[t("li",null,[m1,t("ul",null,[t("li",null,[t("p",null,[a("Output "),t("mjx-container",c1,[(i(),s("svg",g1,k1)),y1]),a(" of shape "),f1])]),t("li",null,[t("p",null,[a("Tuple containing new hidden state "),t("mjx-container",L1,[(i(),s("svg",b1,_1)),w1])])])])]),H1]),E1,t("ul",null,[t("li",null,[t("p",null,[M1,a(": Concatenated Weights to map from input space "),t("mjx-container",C1,[(i(),s("svg",D1,Z1)),F1]),a(".")])]),t("li",null,[t("p",null,[A1,a(": Concatenated Weights to map from hidden space "),t("mjx-container",V1,[(i(),s("svg",N1,B1)),S1]),a(".")])]),t("li",null,[t("p",null,[R1,a(": Bias vector ("),t("mjx-container",I1,[(i(),s("svg",P1,O1)),G1]),a("; not present if "),W1,a(").")])]),t("li",null,[t("p",null,[X1,a(": Concatenated Bias vector for the hidden space "),t("mjx-container",U1,[(i(),s("svg",q1,K1)),$1]),a(" (not present if "),Y1,a(").")])]),t("li",null,[t("p",null,[t2,a(": Initial hidden state vector (not present if "),a2,a(") "),t("mjx-container",e2,[(i(),s("svg",s2,Q2)),l2]),a(".")])])]),T2,o2,n2]),d2,t("div",r2,[p2,a(" "),h2,a(" — "),m2,a(". "),c2,t("mjx-container",g2,[(i(),s("svg",u2,y2)),f2]),L2,t("ul",null,[t("li",null,[b2,t("ul",null,[t("li",null,[t("p",null,[a("Output "),t("mjx-container",x2,[(i(),s("svg",_2,H2)),E2]),a(" of shape "),M2])]),t("li",null,[t("p",null,[a("Tuple containing new hidden state "),t("mjx-container",C2,[(i(),s("svg",D2,Z2)),F2]),a(" and new memory "),t("mjx-container",A2,[(i(),s("svg",V2,j2)),B2])])])])]),S2]),R2,t("ul",null,[t("li",null,[t("p",null,[I2,a(": Concatenated Weights to map from input space "),t("mjx-container",P2,[(i(),s("svg",z2,G2)),W2]),a(".")])]),t("li",null,[t("p",null,[X2,a(": Concatenated Weights to map from hidden space "),t("mjx-container",U2,[(i(),s("svg",q2,K2)),$2])])]),Y2]),t3,a3,e3]),s3,t("div",i3,[Q3,a(" "),l3,a(" — "),T3,a(". "),o3,t("p",null,[t("mjx-container",n3,[(i(),s("svg",d3,p3)),h3])]),m3,t("ul",null,[t("li",null,[c3,t("ul",null,[t("li",null,[t("p",null,[a("Output "),t("mjx-container",g3,[(i(),s("svg",u3,y3)),f3]),a(" of shape "),L3])]),t("li",null,[t("p",null,[a("Tuple containing new hidden state "),t("mjx-container",b3,[(i(),s("svg",x3,w3)),H3])])])])]),E3]),M3]),C3,t("div",D3,[v3,a(" "),Z3,a(" — "),F3,a(". "),A3,t("p",null,[V3,a(" computes the mean and variance for each "),t("mjx-container",N3,[(i(),s("svg",j3,S3)),R3]),a(" input slice and normalises the input accordingly.")]),I3]),P3,t("div",z3,[O3,a(" "),G3,a(" — "),W3,a(". "),X3,t("p",null,[a("Instance Normalization computes the mean and variance for each "),t("mjx-container",U3,[(i(),s("svg",q3,K3)),$3]),a("` input slice and normalises the input accordingly.")]),Y3]),t4,t("div",a4,[e4,a(" "),s4,a(" — "),i4,a(". 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    Switching between Deep Learning Frameworks ​

    Flux Models to Lux Models ​

    Flux.jl has been around in the Julia ecosystem for a long time and has a large userbase, hence we provide a way to convert Flux models to Lux models.

    Tip

    Accessing these functions require manually loading Flux, i.e., using Flux must be present somewhere in the code for these to be used.

    # Adapt.adapt — Method.
    julia
    Adapt.adapt(from::FromFluxAdaptor, L)

    Adapt a Flux model L to Lux model. See FromFluxAdaptor for more details.

    source


    # Lux.FromFluxAdaptor — Type.
    julia
    FromFluxAdaptor(preserve_ps_st::Bool=false, force_preserve::Bool=false)

    Convert a Flux Model to Lux Model.

    Warning

    This always ingores the active field of some of the Flux layers. This is almost never going to be supported.

    Keyword Arguments

    Example

    julia
    import Flux
+using Adapt, Lux, Metalhead, Random
+
+m = ResNet(18)
+m2 = adapt(FromFluxAdaptor(), m.layers) # or FromFluxAdaptor()(m.layers)
+
+x = randn(Float32, 224, 224, 3, 1);
+
+ps, st = Lux.setup(Random.default_rng(), m2);
+
+m2(x, ps, st)

    source


    # Lux.FluxLayer — Type.
    julia
    FluxLayer(layer)

    Serves as a compatibility layer between Flux and Lux. This uses Optimisers.destructure API internally.

    Warning

    Lux was written to overcome the limitations of destructure + Flux. It is recommended to rewrite your l in Lux instead of using this layer.

    Warning

    Introducing this Layer in your model will lead to type instabilities, given the way Optimisers.destructure works.

    Arguments

    Parameters

    source


    Lux Models to Simple Chains ​

    SimpleChains.jl provides a way to train Small Neural Networks really fast on CPUs. See this blog post for more details. This section describes how to convert Lux models to SimpleChains models while preserving the layer interface.

    Tip

    Accessing these functions require manually loading SimpleChains, i.e., using SimpleChains must be present somewhere in the code for these to be used.

    # Adapt.adapt — Method.
    julia
    Adapt.adapt(from::ToSimpleChainsAdaptor, L::AbstractExplicitLayer)

    Adapt a Flux model to Lux model. See ToSimpleChainsAdaptor for more details.

    source


    # Lux.ToSimpleChainsAdaptor — Type.
    julia
    ToSimpleChainsAdaptor()

    Adaptor for converting a Lux Model to SimpleChains. The returned model is still a Lux model, and satisfies the AbstractExplicitLayer interfacem but all internal calculations are performed using SimpleChains.

    Warning

    There is no way to preserve trained parameters and states when converting to SimpleChains.jl.

    Warning

    Any kind of initialization function is not preserved when converting to SimpleChains.jl.

    Arguments

    Example

    julia
    import SimpleChains: static
+using Adapt, Lux, Random
+
+lux_model = Chain(Conv((5, 5), 1 => 6, relu), MaxPool((2, 2)),
+    Conv((5, 5), 6 => 16, relu), MaxPool((2, 2)), FlattenLayer(3),
+    Chain(Dense(256 => 128, relu), Dense(128 => 84, relu), Dense(84 => 10)))
+
+adaptor = ToSimpleChainsAdaptor((static(28), static(28), static(1)))
+
+simple_chains_model = adapt(adaptor, lux_model) # or adaptor(lux_model)
+
+ps, st = Lux.setup(Random.default_rng(), simple_chains_model)
+x = randn(Float32, 28, 28, 1, 1)
+
+simple_chains_model(x, ps, st)

    source


    # Lux.SimpleChainsLayer — Type.
    julia
    SimpleChainsLayer(layer)

    Wraps a SimpleChains layer into a Lux layer. All operations are performed using SimpleChains but the layer satisfies the AbstractExplicitLayer interface.

    Arguments

    source


    `,19),n=[l];function p(h,r,k,d,o,c){return a(),i("div",null,n)}const u=s(t,[["render",p]]);export{E as __pageData,u as default}; diff --git a/v0.5.30/assets/api_Lux_switching_frameworks.md.D8TUetx8.lean.js b/v0.5.30/assets/api_Lux_switching_frameworks.md.D8TUetx8.lean.js new file mode 100644 index 000000000..43d3ef818 --- /dev/null +++ b/v0.5.30/assets/api_Lux_switching_frameworks.md.D8TUetx8.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as e}from"./chunks/framework.BfjuC5t1.js";const E=JSON.parse('{"title":"Switching between Deep Learning Frameworks","description":"","frontmatter":{},"headers":[],"relativePath":"api/Lux/switching_frameworks.md","filePath":"api/Lux/switching_frameworks.md","lastUpdated":null}'),t={name:"api/Lux/switching_frameworks.md"},l=e("",19),n=[l];function p(h,r,k,d,o,c){return a(),i("div",null,n)}const u=s(t,[["render",p]]);export{E as __pageData,u as default}; diff --git a/v0.5.30/assets/api_Lux_utilities.md.Dh0D4iq-.js b/v0.5.30/assets/api_Lux_utilities.md.Dh0D4iq-.js new file mode 100644 index 000000000..671034510 --- /dev/null +++ b/v0.5.30/assets/api_Lux_utilities.md.Dh0D4iq-.js @@ -0,0 +1,3 @@ +import{_ as e,c as i,o as a,a4 as t}from"./chunks/framework.BfjuC5t1.js";const k=JSON.parse('{"title":"Utilities","description":"","frontmatter":{},"headers":[],"relativePath":"api/Lux/utilities.md","filePath":"api/Lux/utilities.md","lastUpdated":null}'),s={name:"api/Lux/utilities.md"},l=t(`

    Utilities ​

    Index ​

    Device Management / Data Transfer ​

    # Lux.cpu — Function.
    julia
    cpu(x)

    Transfer x to CPU.

    Warning

    This function has been deprecated. Use cpu_device instead.

    source


    # Lux.gpu — Function.
    julia
    gpu(x)

    Transfer x to GPU determined by the backend set using Lux.gpu_backend!.

    Warning

    This function has been deprecated. Use gpu_device instead. Using this function inside performance critical code will cause massive slowdowns due to type inference failure.

    source


    Warning

    For detailed API documentation on Data Transfer check out the LuxDeviceUtils.jl

    Weight Initialization ​

    Warning

    For API documentation on Initialization check out the WeightInitializers.jl

    Miscellaneous Utilities ​

    # Lux.foldl_init — Function.
    julia
    foldl_init(op, x)
+foldl_init(op, x, init)

    Exactly same as foldl(op, x; init) in the forward pass. But, gives gradients wrt init in the backward pass.

    source


    # Lux.istraining — Function.
    julia
    istraining(::Val{training})
+istraining(st::NamedTuple)

    Returns true if training is true or if st contains a training field with value true. Else returns false.

    Method undefined if st.training is not of type Val.

    source


    # Lux.multigate — Function.
    julia
    multigate(x::AbstractArray, ::Val{N})

    Split up x into N equally sized chunks (along dimension 1).

    source


    Updating Floating Point Precision ​

    By default, Lux uses Float32 for all parameters and states. To update the precision simply pass the parameters / states / arrays into one of the following functions.

    # Lux.f16 — Function.
    julia
    f16(m)

    Converts the eltype of m floating point values to Float16. Recurses into structs marked with Functors.@functor.

    source


    # Lux.f32 — Function.
    julia
    f32(m)

    Converts the eltype of m floating point values to Float32. Recurses into structs marked with Functors.@functor.

    source


    # Lux.f64 — Function.
    julia
    f64(m)

    Converts the eltype of m floating point values to Float64. Recurses into structs marked with Functors.@functor.

    source


    Stateful Layer ​

    # Lux.StatefulLuxLayer — Type.
    julia
    StatefulLuxLayer(model, ps, st; st_fixed_type = Val(true))

    Warning

    This is not a Lux.AbstractExplicitLayer

    A convenience wrapper over Lux layers which stores the parameters and states internally. Most users should not be using this version. This comes handy when Lux internally uses the @compact to construct models and in SciML codebases where propagating state might involving Boxing.

    For a motivating example, see the Neural ODE tutorial.

    Arguments

    Keyword Arguments

    Inputs

    Outputs

    source


    Truncated Stacktraces ​

    # Lux.disable_stacktrace_truncation! — Function.
    julia
    disable_stacktrace_truncation!(; disable::Bool=true)

    An easy way to update TruncatedStacktraces.VERBOSE without having to load it manually.

    Effectively does TruncatedStacktraces.VERBOSE[] = disable

    source


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    LuxTestUtils ​

    Warning

    This is a testing package. Hence, we don't use features like weak dependencies to reduce load times. It is recommended that you exclusively use this package for testing and not add a dependency to it in your main package Project.toml.

    Implements utilities for testing gradient correctness and dynamic dispatch of Lux.jl models.

    Index ​

    Testing using JET.jl ​

    # LuxTestUtils.@jet — Macro.
    julia
    @jet f(args...) call_broken=false opt_broken=false

    Run JET tests on the function f with the arguments args.... If JET fails to compile or julia version is < 1.7, then the macro will be a no-op.

    Keyword Arguments

    All additional arguments will be forwarded to @JET.test_call and @JET.test_opt.

    TIP

    Instead of specifying target_modules with every call, you can set preferences for target_modules using Preferences.jl. For example, to set target_modules to (Lux, LuxLib) we can run:

    julia
    using Preferences
+
+set_preferences!(Base.UUID("ac9de150-d08f-4546-94fb-7472b5760531"),
+    "target_modules" => ["Lux", "LuxLib"])

    Example

    julia
    using LuxTestUtils
+
+@testset "Showcase JET Testing" begin
+    @jet sum([1, 2, 3]) target_modules=(Base, Core)
+
+    @jet sum(1, 1) target_modules=(Base, Core) opt_broken=true
+end

    source


    Gradient Correctness ​

    # LuxTestUtils.@test_gradients — Macro.
    julia
    @test_gradients f args... [kwargs...]

    Compare the gradients computed by Zygote.jl (Reverse Mode AD) against:

    TIP

    This function is completely compatible with Test.jl

    Arguments

    Keyword Arguments

    Keyword Arguments for check_approx

    Example

    julia
    using LuxTestUtils
+
+x = randn(10)
+
+@testset "Showcase Gradient Testing" begin
+    @test_gradients sum abs2 x
+
+    @test_gradients prod x
+end

    source


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t,r,n=this._options.autoVacuum;try{this._options.autoVacuum=!1;try{for(var a=D(e),i=a.next();!i.done;i=a.next()){var s=i.value;this.discard(s)}}catch(u){t={error:u}}finally{try{i&&!i.done&&(r=a.return)&&r.call(a)}finally{if(t)throw t.error}}}finally{this._options.autoVacuum=n}this.maybeAutoVacuum()},o.prototype.replace=function(e){var t=this._options,r=t.idField,n=t.extractField,a=n(e,r);this.discard(a),this.add(e)},o.prototype.vacuum=function(e){return e===void 0&&(e={}),this.conditionalVacuum(e)},o.prototype.conditionalVacuum=function(e,t){var r=this;return this._currentVacuum?(this._enqueuedVacuumConditions=this._enqueuedVacuumConditions&&t,this._enqueuedVacuum!=null?this._enqueuedVacuum:(this._enqueuedVacuum=this._currentVacuum.then(function(){var n=r._enqueuedVacuumConditions;return 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    Citation ​

    If you found this library to be useful in academic work, then please cite:

    bibtex
    @software{pal2023lux,
+  author    = {Pal, Avik},
+  title     = {{Lux: Explicit Parameterization of Deep Neural Networks in Julia}},
+  month     = {April},
+  year      = 2023,
+  note      = {If you use this software, please cite it as below.},
+  publisher = {Zenodo},
+  version   = {v0.5.0},
+  doi       = {10.5281/zenodo.7808904},
+  url       = {https://doi.org/10.5281/zenodo.7808904}
+}
    bibtex
    @thesis{pal2023efficient,
+  title     = {{On Efficient Training \\& Inference of Neural Differential Equations}},
+  author    = {Pal, Avik},
+  year      = {2023},
+  school    = {Massachusetts Institute of Technology}
+}
    `,4),k=[h];function l(p,e,E,r,d,F){return a(),i("div",null,k)}const o=s(t,[["render",l]]);export{y as __pageData,o as default}; diff --git a/v0.5.30/assets/introduction_citation.md.B4ZpJtEk.lean.js b/v0.5.30/assets/introduction_citation.md.B4ZpJtEk.lean.js new file mode 100644 index 000000000..f9c176f58 --- /dev/null +++ b/v0.5.30/assets/introduction_citation.md.B4ZpJtEk.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.BfjuC5t1.js";const y=JSON.parse('{"title":"Citation","description":"","frontmatter":{},"headers":[],"relativePath":"introduction/citation.md","filePath":"introduction/citation.md","lastUpdated":null}'),t={name:"introduction/citation.md"},h=n("",4),k=[h];function l(p,e,E,r,d,F){return a(),i("div",null,k)}const o=s(t,[["render",l]]);export{y as __pageData,o as default}; diff --git a/v0.5.30/assets/introduction_index.md.BGT8f-rY.js b/v0.5.30/assets/introduction_index.md.BGT8f-rY.js new file mode 100644 index 000000000..e86e23b95 --- /dev/null +++ b/v0.5.30/assets/introduction_index.md.BGT8f-rY.js @@ -0,0 +1,88 @@ +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.BfjuC5t1.js";const y=JSON.parse('{"title":"Getting Started","description":"","frontmatter":{},"headers":[],"relativePath":"introduction/index.md","filePath":"introduction/index.md","lastUpdated":null}'),p={name:"introduction/index.md"},t=n(`

    Getting Started ​

    Installation ​

    Install Julia v1.10 or above. Lux.jl is available through the Julia package manager. You can enter it by pressing ] in the REPL and then typing

    julia
    pkg> add Lux

    Alternatively, you can also do

    julia
    import Pkg; Pkg.add("Lux")

    Quickstart ​

    Pre-Requisites

    You need to install Optimisers and Zygote if not done already. Pkg.add(["Optimisers", "Zygote"])

    julia
    using Lux, Random, Optimisers, Zygote
+# using LuxCUDA, LuxAMDGPU, Metal # Optional packages for GPU support

    We take randomness very seriously

    julia
    # Seeding
+rng = Random.default_rng()
+Random.seed!(rng, 0)
    Random.TaskLocalRNG()

    Build the model

    julia
    # Construct the layer
+model = Chain(Dense(128, 256, tanh), Chain(Dense(256, 1, tanh), Dense(1, 10)))
    Chain(
+    layer_1 = Dense(128 => 256, tanh_fast),  # 33_024 parameters
+    layer_2 = Dense(256 => 1, tanh_fast),  # 257 parameters
+    layer_3 = Dense(1 => 10),           # 20 parameters
+)         # Total: 33_301 parameters,
+          #        plus 0 states.

    Models don't hold parameters and states so initialize them. From there on, we just use our standard AD and Optimisers API.

    julia
    # Get the device determined by Lux
+device = gpu_device()
+
+# Parameter and State Variables
+ps, st = Lux.setup(rng, model) .|> device
+
+# Dummy Input
+x = rand(rng, Float32, 128, 2) |> device
+
+# Run the model
+y, st = Lux.apply(model, x, ps, st)
+
+# Gradients
+## Pullback API to capture change in state
+(l, st_), pb = pullback(p -> Lux.apply(model, x, p, st), ps)
+gs = pb((one.(l), nothing))[1]
+
+# Optimization
+st_opt = Optimisers.setup(Adam(0.0001f0), ps)
+st_opt, ps = Optimisers.update(st_opt, ps, gs)
    ((layer_1 = (weight = Leaf(Adam(0.0001, (0.9, 0.999), 1.0e-8), (Float32[0.00313608 0.00806096 … 0.00476192 0.00732118; -0.00447309 -0.0119719 … -0.00822211 -0.0110335; … ; -0.00294453 -0.00749935 … -0.00426221 -0.00678769; 0.000750543 0.00195163 … 0.00120731 0.00178011], Float32[9.83485f-7 6.49782f-6 … 2.26756f-6 5.3599f-6; 2.00083f-6 1.43324f-5 … 6.76022f-6 1.21738f-5; … ; 8.67016f-7 5.62395f-6 … 1.81662f-6 4.60721f-6; 5.63307f-8 3.80882f-7 … 1.45758f-7 3.16876f-7], (0.81, 0.998001))), bias = Leaf(Adam(0.0001, (0.9, 0.999), 1.0e-8), (Float32[0.00954525; -0.0146331; … ; -0.00881351; 0.00233261;;], Float32[9.11106f-6; 2.14125f-5; … ; 7.76769f-6; 5.44098f-7;;], (0.81, 0.998001)))), layer_2 = (weight = Leaf(Adam(0.0001, (0.9, 0.999), 1.0e-8), (Float32[-0.0104967 0.0714637 … -0.0224641 0.108277], Float32[1.10179f-5 0.000510699 … 5.04628f-5 0.00117238], (0.81, 0.998001))), bias = Leaf(Adam(0.0001, (0.9, 0.999), 1.0e-8), (Float32[0.178909;;], Float32[0.0032008;;], (0.81, 0.998001)))), layer_3 = (weight = Leaf(Adam(0.0001, (0.9, 0.999), 1.0e-8), (Float32[-0.105128; -0.105128; … ; -0.105128; -0.105128;;], Float32[0.00110518; 0.00110518; … ; 0.00110518; 0.00110518;;], (0.81, 0.998001))), bias = Leaf(Adam(0.0001, (0.9, 0.999), 1.0e-8), (Float32[0.2; 0.2; … ; 0.2; 0.2;;], Float32[0.00399995; 0.00399995; … ; 0.00399995; 0.00399995;;], (0.81, 0.998001))))), (layer_1 = (weight = Float32[-0.11044693 0.10963185 … 0.097855344 -0.009167461; -0.0110904 0.07588978 … -0.03180492 0.088967875; … ; 0.01864451 -0.034903362 … -0.016194405 0.019176451; -0.09216565 -0.047490627 … -0.08869007 0.009417342], bias = Float32[-9.999999f-5; 9.999998f-5; … ; 9.999999f-5; -9.9999954f-5;;]), layer_2 = (weight = Float32[0.05391791 -0.103956826 … -0.050862882 0.020512676], bias = Float32[-0.0001;;]), layer_3 = (weight = Float32[-0.6546853; 0.6101978; … ; 0.41120994; 0.5494141;;], bias = Float32[-0.0001; -0.0001; … ; -0.0001; -0.0001;;])))

    Defining Custom Layers ​

    julia
    using Lux, Random, Optimisers, Zygote
+# using LuxCUDA, LuxAMDGPU, Metal # Optional packages for GPU support
+import Lux.Experimental: @compact

    We will define a custom MLP using the @compact macro. The macro takes in a list of parameters, layers and states, and a function defining the forward pass of the neural network.

    julia
    n_in = 1
+n_out = 1
+nlayers = 3
+
+model = @compact(w1=Dense(n_in, 128),
+    w2=[Dense(128, 128) for i in 1:nlayers],
+    w3=Dense(128, n_out),
+    act=relu) do x
+    embed = act(w1(x))
+    for w in w2
+        embed = act(w(embed))
+    end
+    out = w3(embed)
+    return out
+end
    @compact(
+    w1 = Dense(1 => 128),               # 256 parameters
+    w2 = NamedTuple(
+        1 = Dense(128 => 128),          # 16_512 parameters
+        2 = Dense(128 => 128),          # 16_512 parameters
+        3 = Dense(128 => 128),          # 16_512 parameters
+    ),
+    w3 = Dense(128 => 1),               # 129 parameters
+    act = relu,
+) do x 
+    embed = act(w1(x))
+    for w = w2
+        embed = act(w(embed))
+    end
+    out = w3(embed)
+    return out
+end       # Total: 49_921 parameters,
+          #        plus 1 states.

    We can initialize the model and train it with the same code as before!

    julia
    ps, st = Lux.setup(Xoshiro(0), model)
+
+model(randn(n_in, 32), ps, st)  # 1×32 Matrix as output.
+
+x_data = collect(-2.0f0:0.1f0:2.0f0)'
+y_data = 2 .* x_data .- x_data .^ 3
+st_opt = Optimisers.setup(Adam(), ps)
+
+for epoch in 1:1000
+    global st  # Put this in a function in real use-cases
+    (loss, st), pb = Zygote.pullback(ps) do p
+        y, st_ = model(x_data, p, st)
+        return sum(abs2, y .- y_data), st_
+    end
+    gs = only(pb((one(loss), nothing)))
+    epoch % 100 == 1 && println("Epoch: $(epoch) | Loss: $(loss)")
+    Optimisers.update!(st_opt, ps, gs)
+end
    Epoch: 1 | Loss: 84.32512
+Epoch: 101 | Loss: 0.08861052
+Epoch: 201 | Loss: 0.007037298
+Epoch: 301 | Loss: 0.005391656
+Epoch: 401 | Loss: 0.014058021
+Epoch: 501 | Loss: 0.0022117028
+Epoch: 601 | Loss: 0.0015865607
+Epoch: 701 | Loss: 0.21984956
+Epoch: 801 | Loss: 0.00019668281
+Epoch: 901 | Loss: 0.0018975141

    Additional Packages ​

    LuxDL hosts various packages that provide additional functionality for Lux.jl. All packages mentioned in this documentation are available via the Julia General Registry.

    You can install all those packages via import Pkg; Pkg.add(<package name>).

    GPU Support ​

    GPU Support for Lux.jl requires loading additional packages:

    `,32),l=[t];function h(e,k,d,r,E,g){return a(),i("div",null,l)}const c=s(p,[["render",h]]);export{y as __pageData,c as default}; diff --git a/v0.5.30/assets/introduction_index.md.BGT8f-rY.lean.js b/v0.5.30/assets/introduction_index.md.BGT8f-rY.lean.js new file mode 100644 index 000000000..38c798599 --- /dev/null +++ b/v0.5.30/assets/introduction_index.md.BGT8f-rY.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.BfjuC5t1.js";const y=JSON.parse('{"title":"Getting Started","description":"","frontmatter":{},"headers":[],"relativePath":"introduction/index.md","filePath":"introduction/index.md","lastUpdated":null}'),p={name:"introduction/index.md"},t=n("",32),l=[t];function h(e,k,d,r,E,g){return a(),i("div",null,l)}const c=s(p,[["render",h]]);export{y as __pageData,c as default}; diff --git a/v0.5.30/assets/introduction_overview.md.CYVQehqb.js b/v0.5.30/assets/introduction_overview.md.CYVQehqb.js new file mode 100644 index 000000000..aa2820014 --- /dev/null +++ b/v0.5.30/assets/introduction_overview.md.CYVQehqb.js @@ -0,0 +1 @@ +import{_ as e,c as t,o as r,a4 as a}from"./chunks/framework.BfjuC5t1.js";const g=JSON.parse('{"title":"Why we wrote Lux?","description":"","frontmatter":{},"headers":[],"relativePath":"introduction/overview.md","filePath":"introduction/overview.md","lastUpdated":null}'),s={name:"introduction/overview.md"},i=a('

    Why we wrote Lux? ​

    Julia already has quite a few well established Neural Network Frameworks – Flux & KNet. However, certain design elements – Coupled Model and Parameters & Internal Mutations – associated with these frameworks make them less compiler and user friendly. Making changes to address these problems in the respective frameworks would be too disruptive for users. Here comes in Lux: a neural network framework built completely using pure functions to make it both compiler and autodiff friendly.

    Design Principles ​

    • Layers must be immutable – cannot store any parameter/state but rather store the information to construct them

    • Layers are pure functions

    • Layers return a Tuple containing the result and the updated state

    • Given same inputs the outputs must be same – yes this must hold true even for stochastic functions. Randomness must be controlled using rngs passed in the state.

    • Easily extensible

    • Extensive Testing – All layers and features are tested across all supported AD backends across all supported hardware backends.

    Why use Lux over Flux? ​

    • Neural Networks for SciML: For SciML Applications (Neural ODEs, Deep Equilibrium Models) solvers typically expect a monolithic parameter vector. Flux enables this via its destructure mechanism, but destructure comes with various edge cases and limitations. Lux forces users to make an explicit distinction between state variables and parameter variables to avoid these issues. Also, it comes battery-included for distributed training.

    • Sensible display of Custom Layers – Ever wanted to see Pytorch like Network printouts or wondered how to extend the pretty printing of Flux's layers? Lux handles all of that by default.

    • Truly immutable models - No unexpected internal mutations since all layers are implemented as pure functions. All layers are also deterministic given the parameters and state: if a layer is supposed to be stochastic (say Dropout), the state must contain a seed which is then updated after the function call.

    • Easy Parameter Manipulation – By separating parameter data and layer structures, Lux makes implementing WeightNorm, SpectralNorm, etc. downright trivial. Without this separation, it is much harder to pass such parameters around without mutations which AD systems don't like.

    • Small Neural Networks on CPU – Lux is developed for training large neural networks. For smaller architectures, we recommend using SimpleChains.jl or even better use it in conjunction with Lux via ToSimpleChainsAdaptor.

    • Reliability – We have learned from the mistakes of the past with Flux and everything in our core framework is extensively tested, along with downstream CI to ensure that everything works as expected.

    Why not use Lux (and Julia for traditional Deep Learning in general) ? ​

    • Lack of Large Models Support – Classical deep learning is not Lux's primary focus. For these, python frameworks like PyTorch and Jax are better suited.

    • XLA Support – Lux doesn't compile to XLA which means no TPU support unfortunately.

    ',8),o=[i];function n(l,u,d,p,c,h){return r(),t("div",null,o)}const f=e(s,[["render",n]]);export{g as __pageData,f as default}; diff --git a/v0.5.30/assets/introduction_overview.md.CYVQehqb.lean.js b/v0.5.30/assets/introduction_overview.md.CYVQehqb.lean.js new file mode 100644 index 000000000..8205d2a6c --- /dev/null +++ b/v0.5.30/assets/introduction_overview.md.CYVQehqb.lean.js @@ -0,0 +1 @@ +import{_ as e,c as t,o as r,a4 as a}from"./chunks/framework.BfjuC5t1.js";const g=JSON.parse('{"title":"Why we wrote Lux?","description":"","frontmatter":{},"headers":[],"relativePath":"introduction/overview.md","filePath":"introduction/overview.md","lastUpdated":null}'),s={name:"introduction/overview.md"},i=a("",8),o=[i];function n(l,u,d,p,c,h){return r(),t("div",null,o)}const f=e(s,[["render",n]]);export{g as __pageData,f as default}; diff --git a/v0.5.30/assets/introduction_resources.md.jcqOsVfN.js b/v0.5.30/assets/introduction_resources.md.jcqOsVfN.js new file mode 100644 index 000000000..6d28bb016 --- /dev/null +++ b/v0.5.30/assets/introduction_resources.md.jcqOsVfN.js @@ -0,0 +1 @@ +import{_ as e,c as t,o as r,a4 as s}from"./chunks/framework.BfjuC5t1.js";const g=JSON.parse('{"title":"Resources to Get Started","description":"","frontmatter":{},"headers":[],"relativePath":"introduction/resources.md","filePath":"introduction/resources.md","lastUpdated":null}'),a={name:"introduction/resources.md"},o=s('

    Resources to Get Started ​

    • Go through the Quickstart Example.

    • Read the introductory tutorials on Julia and Lux.

    • Go through the examples sorted based on their complexity in the documentation.

    Have More Questions?

    For usage related questions, please use Github Discussions or JuliaLang Discourse (machine learning domain) which allows questions and answers to be indexed. To report bugs use github issues or even better send in a pull request.

    ',3),i=[o];function n(u,l,c,d,h,p){return r(),t("div",null,i)}const m=e(a,[["render",n]]);export{g as __pageData,m as default}; diff --git a/v0.5.30/assets/introduction_resources.md.jcqOsVfN.lean.js b/v0.5.30/assets/introduction_resources.md.jcqOsVfN.lean.js new file mode 100644 index 000000000..d17dd4d7c --- /dev/null +++ b/v0.5.30/assets/introduction_resources.md.jcqOsVfN.lean.js @@ -0,0 +1 @@ +import{_ as e,c as t,o as r,a4 as s}from"./chunks/framework.BfjuC5t1.js";const g=JSON.parse('{"title":"Resources to Get Started","description":"","frontmatter":{},"headers":[],"relativePath":"introduction/resources.md","filePath":"introduction/resources.md","lastUpdated":null}'),a={name:"introduction/resources.md"},o=s("",3),i=[o];function n(u,l,c,d,h,p){return r(),t("div",null,i)}const m=e(a,[["render",n]]);export{g as __pageData,m as default}; diff --git a/v0.5.30/assets/manual_debugging.md.Cng6aRvr.js b/v0.5.30/assets/manual_debugging.md.Cng6aRvr.js new file mode 100644 index 000000000..060d74ab4 --- /dev/null +++ b/v0.5.30/assets/manual_debugging.md.Cng6aRvr.js @@ -0,0 +1,121 @@ +import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.BfjuC5t1.js";const y=JSON.parse('{"title":"Debugging Lux Models","description":"","frontmatter":{},"headers":[],"relativePath":"manual/debugging.md","filePath":"manual/debugging.md","lastUpdated":null}'),e={name:"manual/debugging.md"},l=n(`

    Debugging Lux Models ​

    Debugging DNNs can be very painful. Especially with the gigantic stacktraces for Lux, it is even harder to pin-point to which particular layer errored out. This page describes some useful tools that ship with Lux, that can help you debug your models.

    TL;DR

    Simply wrap your model with Lux.Experimental.@debug!!

    Don't Forget

    Remember to use the non Debug mode model after you finish debugging. Debug mode models are way slower.

    Let us construct a model which has an obviously incorrect dimension. In this example, you will see how easy it is to pin-point the problematic layer.

    Incorrect Model Specification: Dimension Mismatch Problems ​

    julia
    using Lux, Random
+
+model = Chain(Dense(1 => 16, relu), Chain(Dense(16 => 3), Dense(1 => 1)),
+    BatchNorm(1); disable_optimizations=true)
+
+model_debug = Lux.Experimental.@debug_mode model
    Chain(
+    layer_1 = DebugLayer(
+        layer = Dense(1 => 16, relu),   # 32 parameters
+    ),
+    layer_2 = Chain(
+        layer_1 = DebugLayer(
+            layer = Dense(16 => 3),     # 51 parameters
+        ),
+        layer_2 = DebugLayer(
+            layer = Dense(1 => 1),      # 2 parameters
+        ),
+    ),
+    layer_3 = DebugLayer(
+        layer = BatchNorm(1, affine=true, track_stats=true),  # 2 parameters, plus 3
+    ),
+)         # Total: 87 parameters,
+          #        plus 3 states.

    Note that we can use the parameters and states for model itself in model_debug, no need to make any changes. If you ran the original model this is the kind of error you would see:

    julia
    rng = Xoshiro(0)
+
+ps, st = Lux.setup(rng, model)
+x = randn(rng, Float32, 1, 1)
+
+try
+    model(x, ps, st)
+catch e
+    println(e)
+end
    DimensionMismatch("A has dimensions (1,1) but B has dimensions (3,1)")

    Ofcourse, this error will come with a detailed stacktrace, but it is still not very useful. Now let's try using the debug mode model:

    julia
    try
+    model_debug(x, ps, st)
+catch e
+    println(e)
+end
    [ Info: Input Type: Matrix{Float32} | Input Structure: (1, 1)
+[ Info: Running Layer: Dense(1 => 16, relu) at location model.layers.layer_1!
+[ Info: Output Type: Matrix{Float32} | Output Structure: (16, 1)
+[ Info: Input Type: Matrix{Float32} | Input Structure: (16, 1)
+[ Info: Running Layer: Dense(16 => 3) at location model.layers.layer_2.layers.layer_1!
+[ Info: Output Type: Matrix{Float32} | Output Structure: (3, 1)
+[ Info: Input Type: Matrix{Float32} | Input Structure: (3, 1)
+[ Info: Running Layer: Dense(1 => 1) at location model.layers.layer_2.layers.layer_2!
+┌ Error: Layer Dense(1 => 1) failed!! This layer is present at location model.layers.layer_2.layers.layer_2
+└ @ Lux.Experimental /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/src/contrib/debug.jl:110
+DimensionMismatch("A has dimensions (1,1) but B has dimensions (3,1)")

    See now we know that model.layers.layer_2.layers.layer_2 is the problematic layer. Let us fix that layer and see what happens:

    julia
    model = Chain(Dense(1 => 16, relu),
+    Chain(Dense(16 => 3),  // [!code --]
+    Chain(Dense(16 => 1),  // [!code ++]
+        Dense(1 => 1)),
+    BatchNorm(1); disable_optimizations=true)
    julia
    model_fixed = Chain(Dense(1 => 16, relu), Chain(Dense(16 => 1), Dense(1 => 1)),
+    BatchNorm(1); disable_optimizations=true)
+
+ps, st = Lux.setup(rng, model_fixed)
+
+model_fixed(x, ps, st)
    (Float32[0.0;;], (layer_1 = NamedTuple(), layer_2 = (layer_1 = NamedTuple(), layer_2 = NamedTuple()), layer_3 = (running_mean = Float32[-0.01397949], running_var = Float32[NaN], training = Val{true}())))

    Voila!! We have tracked down and fixed the problem.

    Tracking down NaNs ​

    Have you encountered those pesky little NaNs in your training? They are very hard to track down. We will create an artificially simulate NaNs in our model and see how we can track the offending layer.

    We can set nan_check to :forward, :backward or :both to check for NaNs in the debug model. (or even disable it by setting it to :none)

    julia
    model = Chain(Dense(1 => 16, relu), Chain(Dense(16 => 1), Dense(1 => 1)),
+    BatchNorm(1); disable_optimizations=true)
+
+ps, st = Lux.setup(rng, model)
+
+model_debug = Lux.Experimental.@debug_mode model nan_check=:both
    Chain(
+    layer_1 = DebugLayer(
+        layer = Dense(1 => 16, relu),   # 32 parameters
+    ),
+    layer_2 = Chain(
+        layer_1 = DebugLayer(
+            layer = Dense(16 => 1),     # 17 parameters
+        ),
+        layer_2 = DebugLayer(
+            layer = Dense(1 => 1),      # 2 parameters
+        ),
+    ),
+    layer_3 = DebugLayer(
+        layer = BatchNorm(1, affine=true, track_stats=true),  # 2 parameters, plus 3
+    ),
+)         # Total: 53 parameters,
+          #        plus 3 states.

    Let us set a value in the parameter to NaN:

    julia
    ps.layer_2.layer_2.weight[1, 1] = NaN
    NaN

    Now let us run the model

    julia
    model(x, ps, st)
    (Float32[NaN;;], (layer_1 = NamedTuple(), layer_2 = (layer_1 = NamedTuple(), layer_2 = NamedTuple()), layer_3 = (running_mean = Float32[NaN], running_var = Float32[NaN], training = Val{true}())))

    Ah as expected our output is NaN. But is is not very clear how to track where the first NaN occurred. Let's run the debug model and check:

    julia
    try
+    model_debug(x, ps, st)
+catch e
+    println(e)
+end
    [ Info: Input Type: Matrix{Float32} | Input Structure: (1, 1)
+[ Info: Running Layer: Dense(1 => 16, relu) at location model.layers.layer_1!
+[ Info: Output Type: Matrix{Float32} | Output Structure: (16, 1)
+[ Info: Input Type: Matrix{Float32} | Input Structure: (16, 1)
+[ Info: Running Layer: Dense(16 => 1) at location model.layers.layer_2.layers.layer_1!
+[ Info: Output Type: Matrix{Float32} | Output Structure: (1, 1)
+[ Info: Input Type: Matrix{Float32} | Input Structure: (1, 1)
+[ Info: Running Layer: Dense(1 => 1) at location model.layers.layer_2.layers.layer_2!
+DomainError((weight = Float32[NaN;;], bias = Float32[0.0;;]), "NaNs detected in parameters of layer Dense(1 => 1) at location model.layers.layer_2.layers.layer_2")

    And we have figured it out! The first NaN occurred in the parameters of model.layers.layer_2.layers.layer_2! But what if NaN occurs in the reverse pass! Let us define a custom layer and introduce a fake NaN in the backward pass.

    julia
    using ChainRulesCore, Zygote
+
+const CRC = ChainRulesCore
+
+offending_layer(x) = 2 .* x
    offending_layer (generic function with 1 method)
    julia
    model = Chain(Dense(1 => 16, relu), Chain(Dense(16 => 1), offending_layer),
+    BatchNorm(1); disable_optimizations=true)
+
+ps, st = Lux.setup(rng, model)
+
+model(x, ps, st)
    (Float32[0.0;;], (layer_1 = NamedTuple(), layer_2 = (layer_1 = NamedTuple(), layer_2 = NamedTuple()), layer_3 = (running_mean = Float32[-0.092828535], running_var = Float32[NaN], training = Val{true}())))

    Let us define a custom backward pass to introduce some NaNs:

    julia
    function CRC.rrule(::typeof(offending_layer), x)
+    y = offending_layer(x)
+    function ∇offending_layer(Δ)
+        Δ[1] = NaN
+        return NoTangent(), Δ
+    end
+    return y, ∇offending_layer
+end

    Let us compute the gradient of the layer now:

    julia
    Zygote.gradient(ps -> sum(first(model(x, ps, st))), ps)
    ((layer_1 = (weight = Float32[0.0; NaN; … ; NaN; 0.0;;], bias = Float32[0.0; NaN; … ; NaN; 0.0;;]), layer_2 = (layer_1 = (weight = Float32[NaN NaN … NaN NaN], bias = Float32[NaN;;]), layer_2 = nothing), layer_3 = (scale = Float32[0.0], bias = Fill(1.0f0, 1))),)

    Oh no!! A NaN is present in the gradient of ps. Let us run the debug model and see where the NaN occurred:

    julia
    model_debug = Lux.Experimental.@debug_mode model nan_check=:both
+
+try
+    Zygote.gradient(ps -> sum(first(model_debug(x, ps, st))), ps)
+catch e
+    println(e)
+end
    [ Info: Input Type: Matrix{Float32} | Input Structure: (1, 1)
+[ Info: Running Layer: Dense(1 => 16, relu) at location model.layers.layer_1!
+[ Info: Output Type: Matrix{Float32} | Output Structure: (16, 1)
+[ Info: Input Type: Matrix{Float32} | Input Structure: (16, 1)
+[ Info: Running Layer: Dense(16 => 1) at location model.layers.layer_2.layers.layer_1!
+[ Info: Output Type: Matrix{Float32} | Output Structure: (1, 1)
+[ Info: Input Type: Matrix{Float32} | Input Structure: (1, 1)
+[ Info: Running Layer: WrappedFunction(offending_layer) at location model.layers.layer_2.layers.layer_2!
+[ Info: Output Type: Matrix{Float32} | Output Structure: (1, 1)
+[ Info: Input Type: Matrix{Float32} | Input Structure: (1, 1)
+[ Info: Running Layer: BatchNorm(1, affine=true, track_stats=true) at location model.layers.layer_3!
+[ Info: Output Type: Matrix{Float32} | Output Structure: (1, 1)
+DomainError(Float32[NaN;;], "NaNs detected in pullback output for WrappedFunction(offending_layer) at location model.layers.layer_2.layers.layer_2!")

    And there you go our debug layer prints that the problem is in WrappedFunction(offending_layer) at location model.layers.layer_2.layers.layer_2! Once we fix the pullback of the layer, we will fix the NaNs.

    Conclusion ​

    In this manual section, we have discussed tracking down errors in Lux models. We have covered tracking incorrect model specifications and NaNs in forward and backward passes. However, remember that this is an Experimental feature, and there might be edge cases that don't work correctly. If you find any such cases, please open an issue on GitHub!

    `,49),p=[l];function t(h,k,r,d,g,o){return i(),a("div",null,p)}const E=s(e,[["render",t]]);export{y as __pageData,E as default}; diff --git a/v0.5.30/assets/manual_debugging.md.Cng6aRvr.lean.js b/v0.5.30/assets/manual_debugging.md.Cng6aRvr.lean.js new file mode 100644 index 000000000..429859f08 --- /dev/null +++ b/v0.5.30/assets/manual_debugging.md.Cng6aRvr.lean.js @@ -0,0 +1 @@ +import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.BfjuC5t1.js";const y=JSON.parse('{"title":"Debugging Lux Models","description":"","frontmatter":{},"headers":[],"relativePath":"manual/debugging.md","filePath":"manual/debugging.md","lastUpdated":null}'),e={name:"manual/debugging.md"},l=n("",49),p=[l];function t(h,k,r,d,g,o){return i(),a("div",null,p)}const E=s(e,[["render",t]]);export{y as __pageData,E as default}; diff --git a/v0.5.30/assets/manual_dispatch_custom_input.md.Ln2h9dji.js b/v0.5.30/assets/manual_dispatch_custom_input.md.Ln2h9dji.js new file mode 100644 index 000000000..f6c943073 --- /dev/null +++ b/v0.5.30/assets/manual_dispatch_custom_input.md.Ln2h9dji.js @@ -0,0 +1,58 @@ +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.BfjuC5t1.js";const o=JSON.parse('{"title":"Dispatching on Custom Input Types","description":"","frontmatter":{},"headers":[],"relativePath":"manual/dispatch_custom_input.md","filePath":"manual/dispatch_custom_input.md","lastUpdated":null}'),h={name:"manual/dispatch_custom_input.md"},t=n(`

    Dispatching on Custom Input Types ​

    Which function should participate in dispatch? ​

    • Defining a dispatch on (::Layer)(x::MyInputType, ps, st::NamedTuple) is inconvenient, since it requires the user to define a new method for every layer type.

    • (::AbstractExplicitLayer)(x::MyInputType, ps, st::NamedTuple) doesn't work.

    • Instead, we need to define the dispatch on Lux.apply(::AbstractExplicitLayer, x::MyInputType, ps, st::NamedTuple).

    Concrete Example ​

    Consider Neural ODEs. In these models, often time we want to every iteration of the neural network to take the current time as input. Here, we won't go through implementing an entire Neural ODE model. Instead we will define a time dependent version of Chain.

    Time-Dependent Chain Implementation ​

    julia
    using Lux, Random
+
+struct TDChain{L <: NamedTuple} <: Lux.AbstractExplicitContainerLayer{(:layers,)}
+    layers::L
+end
+
+function (l::TDChain)((x, t)::Tuple, ps, st::NamedTuple)
+    # Concatenate along the 2nd last dimension
+    sz = ntuple(i -> i == ndims(x) - 1 ? 1 : size(x, i), ndims(x))
+    t_ = ones(eltype(x), sz) .* t  # Needs to be modified for GPU
+    for name in keys(l.layers)
+        x, st_ = Lux.apply(getfield(l.layers, name), cat(x, t_; dims=ndims(x) - 1),
+                           getfield(ps, name), getfield(st, name))
+        st = merge(st, NamedTuple{(name,)}((st_,)))
+    end
+    return x, st
+end
+
+model = Chain(Dense(3, 4), TDChain((; d1=Dense(5, 4), d2=Dense(5, 4))), Dense(4, 1))
    Chain(
+    layer_1 = Dense(3 => 4),            # 16 parameters
+    layer_2 = TDChain(
+        layers = NamedTuple(
+            d1 = Dense(5 => 4),         # 24 parameters
+            d2 = Dense(5 => 4),         # 24 parameters
+        ),
+    ),
+    layer_3 = Dense(4 => 1),            # 5 parameters
+)         # Total: 69 parameters,
+          #        plus 0 states.

    Running the TDChain ​

    julia
    rng = MersenneTwister(0)
+ps, st = Lux.setup(rng, model)
+x = randn(rng, Float32, 3, 2)
+
+try
+    model(x, ps, st)
+catch e
+    Base.showerror(stdout, e)
+end
    MethodError: no method matching (::Main.TDChain{@NamedTuple{d1::Dense{true, typeof(identity), typeof(glorot_uniform), typeof(zeros32)}, d2::Dense{true, typeof(identity), typeof(glorot_uniform), typeof(zeros32)}}})(::Matrix{Float32}, ::@NamedTuple{d1::@NamedTuple{weight::Matrix{Float32}, bias::Matrix{Float32}}, d2::@NamedTuple{weight::Matrix{Float32}, bias::Matrix{Float32}}}, ::@NamedTuple{d1::@NamedTuple{}, d2::@NamedTuple{}})
+
+Closest candidates are:
+  (::Main.TDChain)(!Matched::Tuple, ::Any, ::NamedTuple)
+   @ Main dispatch_custom_input.md:29

    Writing the Correct Dispatch Rules ​

    • Create a Custom Layer storing the time.
    julia
    struct ArrayAndTime{A <: AbstractArray, T <: Real}
+    array::A
+    time::T
+end
    • Define the dispatch on Lux.apply(::AbstractExplicitLayer, x::ArrayAndTime, ps, st::NamedTuple).
    julia
    function Lux.apply(layer::Lux.AbstractExplicitLayer, x::ArrayAndTime, ps, st::NamedTuple)
+    y, st = layer(x.array, ps, st)
+    return ArrayAndTime(y, x.time), st
+end
+
+function Lux.apply(layer::TDChain, x::ArrayAndTime, ps, st::NamedTuple)
+    y, st = layer((x.array, x.time), ps, st)
+    return ArrayAndTime(y, x.time), st
+end
    • Run the model.
    julia
    xt = ArrayAndTime(x, 10.0f0)
+
+model(xt, ps, st)[1]
    Main.ArrayAndTime{Matrix{Float32}, Float32}(Float32[4.8016562 5.174927], 10.0f0)

    Using the Same Input for Non-TD Models ​

    Writing proper dispatch means we can simply replace the TDChain with a Chain (of course with dimension corrections) and the pipeline still works.

    julia
    model = Chain(Dense(3, 4), Chain((; d1=Dense(4, 4), d2=Dense(4, 4))), Dense(4, 1))
+
+ps, st = Lux.setup(rng, model)
+
+model(xt, ps, st)[1]
    Main.ArrayAndTime{Matrix{Float32}, Float32}(Float32[-0.08124366 -1.1121564], 10.0f0)
    `,23),p=[t];function l(e,k,r,d,E,g){return a(),i("div",null,p)}const c=s(h,[["render",l]]);export{o as __pageData,c as default}; diff --git a/v0.5.30/assets/manual_dispatch_custom_input.md.Ln2h9dji.lean.js b/v0.5.30/assets/manual_dispatch_custom_input.md.Ln2h9dji.lean.js new file mode 100644 index 000000000..86aa9d0d1 --- /dev/null +++ b/v0.5.30/assets/manual_dispatch_custom_input.md.Ln2h9dji.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.BfjuC5t1.js";const o=JSON.parse('{"title":"Dispatching on Custom Input Types","description":"","frontmatter":{},"headers":[],"relativePath":"manual/dispatch_custom_input.md","filePath":"manual/dispatch_custom_input.md","lastUpdated":null}'),h={name:"manual/dispatch_custom_input.md"},t=n("",23),p=[t];function l(e,k,r,d,E,g){return a(),i("div",null,p)}const c=s(h,[["render",l]]);export{o as __pageData,c as default}; diff --git a/v0.5.30/assets/manual_freezing_model_parameters.md.B_lUuLCd.js b/v0.5.30/assets/manual_freezing_model_parameters.md.B_lUuLCd.js new file mode 100644 index 000000000..2337ec082 --- /dev/null +++ b/v0.5.30/assets/manual_freezing_model_parameters.md.B_lUuLCd.js @@ -0,0 +1,59 @@ +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.BfjuC5t1.js";const F=JSON.parse('{"title":"Freezing Model Parameters","description":"","frontmatter":{},"headers":[],"relativePath":"manual/freezing_model_parameters.md","filePath":"manual/freezing_model_parameters.md","lastUpdated":null}'),e={name:"manual/freezing_model_parameters.md"},h=n(`

    Freezing Model Parameters ​

    Warning

    API for freezing parameters should be considered experimental at this point.

    In this manual entry, we will go over how to freeze certain parameters in a model.

    Freezing Layers of a Particular Kind ​

    To freeze a particular kind of layer, let's say Dense in the following example. We can use Lux.Experimental.@layer_map and freeze layers if they are of type Dense.

    julia
    using Lux, Random
+
+rng = Random.default_rng()
+Random.seed!(rng, 0)
+
+model = Chain(Dense(3, 4), Chain(Dense(4, 4), Dropout(0.5f0), BatchNorm(4)),
+    Dense(4, 1); disable_optimizations=true)
+
+ps, st = Lux.setup(rng, model)
+
+x = randn(rng, Float32, 3, 2)
+
+model(x, ps, st)
+
+function freeze_dense(d::Lux.Dense, ps, st, ::String)
+    return Lux.freeze(d, ps, st, (:weight, :bias))
+end
+freeze_dense(l, ps, st, name) = (l, ps, st)
+
+model_frozen, ps_frozen, st_frozen = Lux.Experimental.@layer_map freeze_dense model ps st
+
+model_frozen(x, ps_frozen, st_frozen)
    (Float32[-0.53158027 0.53158027], (layer_1 = (frozen_params = (weight = Float32[-0.026350189 -0.5554656 -0.35653266; -0.17461072 0.6705545 0.29924855; -0.8935247 -0.42453378 -0.3020351; -0.7988979 -0.7666331 -0.7104237], bias = Float32[0.0; 0.0; 0.0; 0.0;;]), states = NamedTuple()), layer_2 = (layer_1 = (frozen_params = (weight = Float32[-0.47289538 -0.680748 0.1764085 0.34383082; 0.42747158 -0.13819042 -0.109261915 -0.6143286; -0.35790488 -0.20881107 0.70390546 0.48137343; 0.82561636 0.38187847 0.05779423 -0.35181466], bias = Float32[0.0; 0.0; 0.0; 0.0;;]), states = NamedTuple()), layer_2 = (rng = Random.Xoshiro(0x7c071df294e77583, 0xd36a58e0d4ae463e, 0x84df7ccd14e8a7b8, 0x727006748bb9e892, 0x22a21880af5dc689), training = Val{true}()), layer_3 = (running_mean = Float32[0.0, 0.021013658, -0.057823665, 0.0], running_var = Float32[0.9, 0.9088315, 0.9668715, 0.9], training = Val{true}())), layer_3 = (frozen_params = (weight = Float32[0.3981135 0.45468387 -0.07694905 0.8353388], bias = Float32[0.0;;]), states = NamedTuple())))

    Freezing by Layer Name ​

    When the function in layer_map is called, the 4th argument is the name of the layer. For example, if you want to freeze the 1st layer inside the inner Chain. The name for this would be <model>.layer_2.layer_1.

    julia
    
+function freeze_by_name(d, ps, st, name::String)
+    if name == "model.layer_2.layer_1"
+        return Lux.Experimental.freeze(d, ps, st, (:weight, :bias))
+    else
+        return d, ps, st
+    end
+end
    julia
    
+function freeze_dense(d::Dense, ps, st, ::String)
+    return Lux.Experimental.freeze(d, ps, st, (:weight, :bias))
+end
+freeze_dense(l, ps, st, _) = (l, ps, st)

    Freezing Part of the Parameters ​

    Instead of freezing all the parameters, we can simply specify (:weight,) to freeze only the weight parameter while training the bias parameter.

    julia
    
+function freeze_by_name(d, ps, st, name::String)
+    if name == "model.layer_2.layer_1"
+        return Lux.freeze(d, ps, st, (:weight,))
+    else
+        return d, ps, st
+    end
+end
    julia
    
+function freeze_by_name(d, ps, st, name::String)
+    if name == "model.layer_2.layer_1"
+        return Lux.freeze(d, ps, st, (:weight, :bias))
+    else
+        return d, ps, st
+    end
+end

    Freezing Part of a Chain ​

    Starting v0.4.22, we can directly index into a Chain. So freezing a part of a Chain, is extremely easy.

    julia
    using Lux, Random
+
+rng = Random.default_rng()
+Random.seed!(rng, 0)
+
+model = Chain(Dense(3, 4), Dense(4, 4), Dropout(0.5f0), BatchNorm(4), Dense(4, 1))
+
+model_frozen = Chain(model[1:2], Lux.freeze(model[3:4]), model[5])
+ps, st = Lux.setup(rng, model_frozen)
+
+x = randn(rng, Float32, 3, 2)
+
+model_frozen(x, ps, st)
    (Float32[-0.53158027 0.53158027], (layer_1 = NamedTuple(), layer_2 = NamedTuple(), layer_3 = (frozen_params = (layer_3 = NamedTuple(), layer_4 = (scale = Float32[1.0, 1.0, 1.0, 1.0], bias = Float32[0.0, 0.0, 0.0, 0.0])), states = (layer_3 = (rng = Random.Xoshiro(0x7c071df294e77583, 0xd36a58e0d4ae463e, 0x84df7ccd14e8a7b8, 0x727006748bb9e892, 0x22a21880af5dc689), training = Val{true}()), layer_4 = (running_mean = Float32[0.0, 0.021013658, -0.057823665, 0.0], running_var = Float32[0.9, 0.9088315, 0.9668715, 0.9], training = Val{true}()))), layer_4 = NamedTuple()))
    `,17),l=[h];function t(p,k,r,d,E,g){return a(),i("div",null,l)}const o=s(e,[["render",t]]);export{F as __pageData,o as default}; diff --git a/v0.5.30/assets/manual_freezing_model_parameters.md.B_lUuLCd.lean.js b/v0.5.30/assets/manual_freezing_model_parameters.md.B_lUuLCd.lean.js new file mode 100644 index 000000000..1d3d43572 --- /dev/null +++ b/v0.5.30/assets/manual_freezing_model_parameters.md.B_lUuLCd.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.BfjuC5t1.js";const F=JSON.parse('{"title":"Freezing Model Parameters","description":"","frontmatter":{},"headers":[],"relativePath":"manual/freezing_model_parameters.md","filePath":"manual/freezing_model_parameters.md","lastUpdated":null}'),e={name:"manual/freezing_model_parameters.md"},h=n("",17),l=[h];function t(p,k,r,d,E,g){return a(),i("div",null,l)}const o=s(e,[["render",t]]);export{F as __pageData,o as default}; diff --git a/v0.5.30/assets/manual_gpu_management.md.DUY-sneY.js b/v0.5.30/assets/manual_gpu_management.md.DUY-sneY.js new file mode 100644 index 000000000..6409e6244 --- /dev/null +++ b/v0.5.30/assets/manual_gpu_management.md.DUY-sneY.js @@ -0,0 +1,26 @@ +import{_ as s,c as a,o as i,a4 as e}from"./chunks/framework.BfjuC5t1.js";const u=JSON.parse('{"title":"GPU Management","description":"","frontmatter":{},"headers":[],"relativePath":"manual/gpu_management.md","filePath":"manual/gpu_management.md","lastUpdated":null}'),n={name:"manual/gpu_management.md"},t=e(`

    GPU Management ​

    Info

    Starting from v0.5, Lux has transitioned to a new GPU management system. The old system using cpu and gpu functions is still in place but will be removed in v0.6. Using the old functions might lead to performance regressions if used inside performance critical code.

    Lux.jl can handle multiple GPU backends. Currently, the following backends are supported:

    julia
    using Lux, LuxCUDA, LuxAMDGPU  # Important to load trigger packages
+
+supported_gpu_backends()
    ("CUDA", "AMDGPU", "Metal")

    Metal Support

    Support for Metal GPUs should be considered extremely experimental at this point.

    Automatic Backend Management (Recommended Approach) ​

    Automatic Backend Management is done by two simple functions: cpu_device and gpu_device.

    • cpu_device: This is a simple function and just returns a LuxCPUDevice object.
    julia
    cdev = cpu_device()
    (::LuxCPUDevice) (generic function with 5 methods)
    julia
    x_cpu = randn(Float32, 3, 2)
    3×2 Matrix{Float32}:
+  0.433884   0.229779
+ -0.459193  -1.95972
+ -0.541064  -1.40102
    • gpu_device: This function performs automatic GPU device selection and returns an object.

      1. If no GPU is available, it returns a LuxCPUDevice object.

      2. If a LocalPreferences file is present, then the backend specified in the file is used. To set a backend, use Lux.gpu_backend!(<backend_name>). (a) If the trigger package corresponding to the device is not loaded, then a warning is displayed. (b) If no LocalPreferences file is present, then the first working GPU with loaded trigger package is used.

    julia
    gdev = gpu_device()
+
+x_gpu = x_cpu |> gdev
    3×2 CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}:
+  0.433884   0.229779
+ -0.459193  -1.95972
+ -0.541064  -1.40102
    julia
    (x_gpu |> cdev) ≈ x_cpu
    true

    Manual Backend Management ​

    Automatic Device Selection can be circumvented by directly using LuxCPUDevice and AbstractLuxGPUDevice objects.

    julia
    cdev = LuxCPUDevice()
+
+x_cpu = randn(Float32, 3, 2)
+
+if LuxCUDA.functional()
+    gdev = LuxCUDADevice()
+    x_gpu = x_cpu |> gdev
+elseif LuxAMDGPU.functional()
+    gdev = LuxAMDGPUDevice()
+    x_gpu = x_cpu |> gdev
+else
+    @info "No GPU is available. Using CPU."
+    x_gpu = x_cpu
+end
+
+(x_gpu |> cdev) ≈ x_cpu
    true
    `,22),p=[t];function l(h,d,c,k,o,g){return i(),a("div",null,p)}const E=s(n,[["render",l]]);export{u as __pageData,E as default}; diff --git a/v0.5.30/assets/manual_gpu_management.md.DUY-sneY.lean.js b/v0.5.30/assets/manual_gpu_management.md.DUY-sneY.lean.js new file mode 100644 index 000000000..503b4e41d --- /dev/null +++ b/v0.5.30/assets/manual_gpu_management.md.DUY-sneY.lean.js @@ -0,0 +1 @@ +import{_ as s,c as a,o as i,a4 as e}from"./chunks/framework.BfjuC5t1.js";const u=JSON.parse('{"title":"GPU Management","description":"","frontmatter":{},"headers":[],"relativePath":"manual/gpu_management.md","filePath":"manual/gpu_management.md","lastUpdated":null}'),n={name:"manual/gpu_management.md"},t=e("",22),p=[t];function l(h,d,c,k,o,g){return i(),a("div",null,p)}const E=s(n,[["render",l]]);export{u as __pageData,E as default}; diff --git a/v0.5.30/assets/manual_interface.md.ypfbSQ9y.js b/v0.5.30/assets/manual_interface.md.ypfbSQ9y.js new file mode 100644 index 000000000..fd31ee847 --- /dev/null +++ b/v0.5.30/assets/manual_interface.md.ypfbSQ9y.js @@ -0,0 +1,92 @@ +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.BfjuC5t1.js";const y=JSON.parse('{"title":"Lux Interface","description":"","frontmatter":{},"headers":[],"relativePath":"manual/interface.md","filePath":"manual/interface.md","lastUpdated":null}'),t={name:"manual/interface.md"},e=n(`

    Lux Interface ​

    Tip

    If you just want to define compatibility with Lux without actually using any of the other functionality provided by Lux (like layers), it is recommended to depend on LuxCore.jl instead of Lux.jl. LuxCore.jl is a significantly lighter dependency.

    First let's set the expectations straight.

    • Do you have to follow the interface? No.

    • Should you follow it? Probably yes.

    • Why? It provides the ability for frameworks built on top of Lux to be cross compatible. Additionally, any new functionality built into Lux, will just work for your framework.

    Warning

    The interface is optional for frameworks being developed independent of Lux. All functionality in the core library (and officially supported ones) must adhere to the interface

    Layer Interface ​

    Singular Layer ​

    If the layer doesn't contain any other Lux layer, then it is a Singular Layer. This means it should optionally subtype Lux.AbstractExplicitLayer but mandatorily define all the necessary functions mentioned in the docstrings. Consider a simplified version of Dense called Linear.

    First, setup the architectural details for this layer. Note, that the architecture doesn't contain any mutable structure like arrays. When in doubt, remember, once constructed a model architecture cannot change.

    Tip

    For people coming from Flux.jl background this might be weird. We recommend checking out the Flux to Lux migration guide first before proceeding.

    julia
    using Lux, Random
+
+struct Linear{F1, F2} <: Lux.AbstractExplicitLayer
+    in_dims::Int
+    out_dims::Int
+    init_weight::F1
+    init_bias::F2
+end
+
+function Linear(in_dims::Int, out_dims::Int; init_weight=Lux.glorot_uniform,
+    init_bias=Lux.zeros32)
+    return Linear{typeof(init_weight), typeof(init_bias)}(in_dims, out_dims, init_weight,
+        init_bias)
+end
+
+l = Linear(2, 4)
    Linear()

    Next, we need to implement functions which return the parameters and states for the layer. In case of Linear, the parameters are weight and bias while the states are empty. States become important when defining layers like BatchNorm, WeightNorm, etc. The recommended data structure for returning parameters is a NamedTuple, though anything satisfying the Parameter Interface is valid.

    julia
    function Lux.initialparameters(rng::AbstractRNG, l::Linear)
+    return (weight=l.init_weight(rng, l.out_dims, l.in_dims),
+            bias=l.init_bias(rng, l.out_dims, 1))
+end
+
+Lux.initialstates(::AbstractRNG, ::Linear) = NamedTuple()

    You could also implement Lux.parameterlength and Lux.statelength to prevent wasteful reconstruction of the parameters and states.

    julia
    # This works
+println("Parameter Length: ", Lux.parameterlength(l), "; State Length: ",
+    Lux.statelength(l))
+
+# But still recommened to define these
+Lux.parameterlength(l::Linear) = l.out_dims * l.in_dims + l.out_dims
+
+Lux.statelength(::Linear) = 0
    Parameter Length: 12; State Length: 0

    Tip

    You might notice that we don't pass in a PRNG for these functions. If your parameter length and/or state length depend on a random number generator, you should think really hard about what you are trying to do and why.

    Now, we need to define how the layer works. For this you make your layer a function with exactly 3 arguments – x the input, ps the parameters, and st the states. This function must return two things – y the output, and st_new the updated state.

    julia
    function (l::Linear)(x::AbstractMatrix, ps, st::NamedTuple)
+    y = ps.weight * x .+ ps.bias
+    return y, st
+end

    Finally, let's run this layer. If you have made this far into the documentation, we don't feel you need a refresher on that.

    julia
    rng = Random.default_rng()
+Random.seed!(rng, 0)
+
+ps, st = Lux.setup(rng, l)
+
+println("Parameter Length: ", Lux.parameterlength(l), "; State Length: ",
+    Lux.statelength(l))
+
+x = randn(rng, Float32, 2, 1)
+
+Lux.apply(l, x, ps, st) # or \`l(x, ps, st)\`
    (Float32[-0.15276335; 0.45325348; 1.0207279; 0.78226817;;], NamedTuple())

    Container Layer ​

    If your layer comprises of other Lux layers, then it is a Container Layer. Note that you could treat it as a Singular Layer, and it is still fine. FWIW, if you cannot subtype your layer with Lux.AbstractExplicitContainerLayer then you should go down the Singular Layer route. But subtyping allows us to bypass some of these common definitions. Let us now define a layer, which is basically a composition of two linear layers.

    julia
    struct ComposedLinear{L1, L2} <: Lux.AbstractExplicitContainerLayer{(:linear_1, :linear_2)}
+    linear_1::L1
+    linear_2::L2
+end
+
+function (cl::ComposedLinear)(x::AbstractMatrix, ps, st::NamedTuple)
+    # To access the parameters and states for \`linear_1\` we do \`ps.linear_1\` and
+    # \`st.linear_1\`. Similarly for \`linear_2\`
+    y, st_l1 = cl.linear_1(x, ps.linear_1, st.linear_1)
+    y, st_l2 = cl.linear_2(y, ps.linear_2, st.linear_2)
+    # Finally, we need to return the new state which has the exact structure as \`st\`
+    return y, (linear_1 = st_l1, linear_2 = st_l2)
+end

    Here, you will notice we have passed (:linear_1, :linear_2) to the supertype. It essentially informs the type that, <obj>.linear_1 and <obj>.linear_2 are Lux layers and we need to construct parameters and states for those. Let's construct these and see:

    julia
    model = ComposedLinear(Linear(2, 4), Linear(4, 2))
+display(model)
+
+ps, st = Lux.setup(rng, model)
+
+println("Parameters: ", ps)
+println("States: ", st)
+
+println("Parameter Length: ", Lux.parameterlength(model), "; State Length: ",
+    Lux.statelength(model))
+
+x = randn(rng, Float32, 2, 1)
+
+Lux.apply(model, x, ps, st) # or \`model(x, ps, st)\`
    (Float32[1.3410565; 0.78000563;;], (linear_1 = NamedTuple(), linear_2 = NamedTuple()))

    Parameter Interface ​

    We accept any parameter type as long as we can fetch the parameters using getproperty(obj, :parameter_name). This allows us to simultaneously support NamedTuples and ComponentArrays. Let us go through a concrete example of what it means. Consider Dense which expects two parameters named weight and bias.

    Info

    If you are defining your own parameter type, it is your responsibility to make sure that it works with the AutoDiff System you are using.

    julia
    using Lux, Random
+
+d = Dense(2, 3)
+rng = Random.default_rng()
+Random.seed!(rng, 0)
+
+ps_default, st = Lux.setup(rng, d)
+
+x = randn(rng, Float32, 2, 1)
+
+println("Result with \`NamedTuple\` parameters: ", first(d(x, ps_default, st)))
    Result with \`NamedTuple\` parameters: Float32[1.135916; 0.7668784; -1.0876652;;]

    Let, us define a custom parameter type with fields myweight and mybias but if we try to access weight we get back myweight, similar for bias.

    Warning

    This is for demonstrative purposes, don't try this at home!

    julia
    struct DenseLayerParameters{W, B}
+    myweight::W
+    mybias::B
+end
+
+function Base.getproperty(ps::DenseLayerParameters, x::Symbol)
+    if x == :weight
+        return getfield(ps, :myweight)
+    elseif x == :bias
+        return getfield(ps, :mybias)
+    end
+    return getfield(ps, x)
+end
+
+ps = DenseLayerParameters(ps_default.weight, ps_default.bias)
+
+println("Result with \`DenseLayerParameters\` parameters: ", first(d(x, ps, st)))
    Result with \`DenseLayerParameters\` parameters: Float32[1.135916; 0.7668784; -1.0876652;;]

    The takeaway from this shouldn't be – lets define weird parameter types. Simply because you can do weird things like this doesn't mean you should, since it only leads to bugs.

    Instead this shows the flexibility you have for how your parameters can be structured.

    State Interface ​

    States are always type constrained to be NamedTuple. The structure of the input state must match that of the output state, i.e. keys(st_in) == keys(st_out). This doesn't imply that types of the input and output state match. To generate efficient code, we often do dispatch on the state, for example, Dropout, BatchNorm, etc.

    `,42),h=[e];function l(p,k,r,d,E,g){return a(),i("div",null,h)}const c=s(t,[["render",l]]);export{y as __pageData,c as default}; diff --git a/v0.5.30/assets/manual_interface.md.ypfbSQ9y.lean.js b/v0.5.30/assets/manual_interface.md.ypfbSQ9y.lean.js new file mode 100644 index 000000000..05f4fe60b --- /dev/null +++ b/v0.5.30/assets/manual_interface.md.ypfbSQ9y.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.BfjuC5t1.js";const y=JSON.parse('{"title":"Lux Interface","description":"","frontmatter":{},"headers":[],"relativePath":"manual/interface.md","filePath":"manual/interface.md","lastUpdated":null}'),t={name:"manual/interface.md"},e=n("",42),h=[e];function l(p,k,r,d,E,g){return a(),i("div",null,h)}const c=s(t,[["render",l]]);export{y as __pageData,c as default}; diff --git a/v0.5.30/assets/manual_migrate_from_flux.md.CGt97TpW.js b/v0.5.30/assets/manual_migrate_from_flux.md.CGt97TpW.js new file mode 100644 index 000000000..b1df676a6 --- /dev/null +++ b/v0.5.30/assets/manual_migrate_from_flux.md.CGt97TpW.js @@ -0,0 +1,75 @@ +import{_ as l,c as i,m as s,a,a4 as t,o as n}from"./chunks/framework.BfjuC5t1.js";const w=JSON.parse('{"title":"Migrating from Flux to Lux","description":"","frontmatter":{},"headers":[],"relativePath":"manual/migrate_from_flux.md","filePath":"manual/migrate_from_flux.md","lastUpdated":null}'),e={name:"manual/migrate_from_flux.md"},h=t(`

    Migrating from Flux to Lux ​

    For the core library layers like Dense, Conv, etc. we have intentionally kept the API very similar to Flux. In most cases, replacing using Flux with using Lux should be enough to get you started. We cover the additional changes that you will have to make in the following example.

    julia
    using Lux, Random, NNlib, Zygote
+
+model = Chain(Dense(2 => 4), BatchNorm(4, relu), Dense(4 => 2))
+rng = Random.default_rng()
+x = randn(rng, Float32, 2, 4)
+
+ps, st = Lux.setup(rng, model)
+
+model(x, ps, st)
+
+gradient(ps -> sum(first(model(x, ps, st))), ps)
    julia
    using Flux, Random, NNlib, Zygote
+
+model = Chain(Dense(2 => 4), BatchNorm(4, relu), Dense(4 => 2))
+rng = Random.default_rng()
+x = randn(rng, Float32, 2, 4)
+
+
+
+model(x)
+
+gradient(model -> sum(model(x)), model)

    Implementing Custom Layers ​

    Flux and Lux operate under extremely different design philosophies regarding how layers should be implemented. A summary of the differences would be:

    • Flux stores everything in a single struct and relies on Functors.@functor and Flux.trainable to distinguish between trainable and non-trainable parameters.

    • Lux relies on the user to define Lux.initialparameters and Lux.initialstates to distinguish between trainable parameters (called "parameters") and non-trainable parameters (called "states"). Additionally, Lux layers define the model architecture, hence device transfer utilities like gpu_device, cpu_device, etc. cannot be applied on Lux layers, instead they need to be applied on the parameters and states.

    `,6),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},k={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.24ex",height:"1.645ex",role:"img",focusable:"false",viewBox:"0 -716 4525.9 727","aria-hidden":"true"},r=t('',1),d=[r],E=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"A"),s("mo",null,"×"),s("mi",null,"B"),s("mo",null,"×"),s("mi",null,"x")])],-1),o={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.697ex",height:"1.62ex",role:"img",focusable:"false",viewBox:"0 -716 750 716","aria-hidden":"true"},c=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D434",d:"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z",style:{"stroke-width":"3"}})])])],-1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"A")])],-1),F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},m={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.717ex",height:"1.545ex",role:"img",focusable:"false",viewBox:"0 -683 759 683","aria-hidden":"true"},C=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D435",d:"M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z",style:{"stroke-width":"3"}})])])],-1),x=[C],Q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"B")])],-1),A=t(`
    julia
    using Lux, Random, NNlib, Zygote
+
+struct LuxLinear <: Lux.AbstractExplicitLayer
+    init_A
+    init_B
+end
+
+function LuxLinear(A::AbstractArray, B::AbstractArray)
+    # Storing Arrays or any mutable structure inside a Lux Layer is not recommended
+    # instead we will convert this to a function to perform lazy initialization
+    return LuxLinear(() -> copy(A), () -> copy(B))
+end
+
+# \`B\` is a parameter
+Lux.initialparameters(::AbstractRNG, layer::LuxLinear) = (B=layer.init_B(),)
+
+# \`A\` is a state
+Lux.initialstates(::AbstractRNG, layer::LuxLinear) = (A=layer.init_A(),)
+
+(l::LuxLinear)(x, ps, st) = st.A * ps.B * x, st
    julia
    using Flux, Random, NNlib, Zygote, Optimisers
+
+struct FluxLinear
+    A
+    B
+end
+
+
+
+
+
+
+
+# \`A\` is not trainable
+Optimisers.trainable(f::FluxLinear) = (B=f.B,)
+
+# Needed so that both \`A\` and \`B\` can be transfered between devices
+Flux.@functor FluxLinear
+
+(l::FluxLinear)(x) = l.A * l.B * x

    Now let us run the model.

    julia
    rng = Random.default_rng()
+model = LuxLinear(randn(rng, 2, 4), randn(rng, 4, 2))
+x = randn(rng, 2, 1)
+
+ps, st = Lux.setup(rng, model)
+
+model(x, ps, st)
+
+gradient(ps -> sum(first(model(x, ps, st))), ps)
    julia
    rng = Random.default_rng()
+model = FluxLinear(randn(rng, 2, 4), randn(rng, 4, 2))
+x = randn(rng, 2, 1)
+
+
+
+model(x)
+
+gradient(model -> sum(model(x)), model)

    To reiterate some important points:

    • Don't store mutables like Arrays inside a Lux Layer.

    • Parameters and States should be constructured inside the respective initial* functions.

    Certain Important Implementation Details ​

    Training/Inference Mode ​

    Flux supports a mode called :auto which automatically decides if the user is training the model or running inference. This is the default mode for Flux.BatchNorm, Flux.GroupNorm, Flux.Dropout, etc. Lux doesn't support this mode (specifically to keep code simple and do exactly what the user wants), hence our default mode is training. This can be changed using Lux.testmode.

    Can we still use Flux Layers? ​

    If you have Flux loaded in your code, you can use the function FromFluxAdaptor to automatically convert your model to Lux. Note that in case a native Lux counterpart isn't available, we fallback to using Optimisers.destructure.

    `,10);function b(v,D,B,L,T,f){return n(),i("div",null,[h,s("p",null,[a("Let's work through a concrete example to demonstrate this. We will implement a very simple layer that computes "),s("mjx-container",p,[(n(),i("svg",k,d)),E]),a(" where "),s("mjx-container",o,[(n(),i("svg",g,y)),u]),a(" is not trainable and "),s("mjx-container",F,[(n(),i("svg",m,x)),Q]),a(" is trainable.")]),A])}const M=l(e,[["render",b]]);export{w as __pageData,M as default}; diff --git a/v0.5.30/assets/manual_migrate_from_flux.md.CGt97TpW.lean.js b/v0.5.30/assets/manual_migrate_from_flux.md.CGt97TpW.lean.js new file mode 100644 index 000000000..6bc5d396c --- /dev/null +++ b/v0.5.30/assets/manual_migrate_from_flux.md.CGt97TpW.lean.js @@ -0,0 +1 @@ +import{_ as l,c as i,m as s,a,a4 as t,o as n}from"./chunks/framework.BfjuC5t1.js";const w=JSON.parse('{"title":"Migrating from Flux to Lux","description":"","frontmatter":{},"headers":[],"relativePath":"manual/migrate_from_flux.md","filePath":"manual/migrate_from_flux.md","lastUpdated":null}'),e={name:"manual/migrate_from_flux.md"},h=t("",6),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},k={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.24ex",height:"1.645ex",role:"img",focusable:"false",viewBox:"0 -716 4525.9 727","aria-hidden":"true"},r=t("",1),d=[r],E=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"A"),s("mo",null,"×"),s("mi",null,"B"),s("mo",null,"×"),s("mi",null,"x")])],-1),o={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.697ex",height:"1.62ex",role:"img",focusable:"false",viewBox:"0 -716 750 716","aria-hidden":"true"},c=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D434",d:"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z",style:{"stroke-width":"3"}})])])],-1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"A")])],-1),F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},m={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"0"},xmlns:"http://www.w3.org/2000/svg",width:"1.717ex",height:"1.545ex",role:"img",focusable:"false",viewBox:"0 -683 759 683","aria-hidden":"true"},C=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D435",d:"M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z",style:{"stroke-width":"3"}})])])],-1),x=[C],Q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"B")])],-1),A=t("",10);function b(v,D,B,L,T,f){return n(),i("div",null,[h,s("p",null,[a("Let's work through a concrete example to demonstrate this. We will implement a very simple layer that computes "),s("mjx-container",p,[(n(),i("svg",k,d)),E]),a(" where "),s("mjx-container",o,[(n(),i("svg",g,y)),u]),a(" is not trainable and "),s("mjx-container",F,[(n(),i("svg",m,x)),Q]),a(" is trainable.")]),A])}const M=l(e,[["render",b]]);export{w as __pageData,M as default}; diff --git a/v0.5.30/assets/manual_weight_initializers.md._StOXcgy.js b/v0.5.30/assets/manual_weight_initializers.md._StOXcgy.js new file mode 100644 index 000000000..1f9c5aee2 --- /dev/null +++ b/v0.5.30/assets/manual_weight_initializers.md._StOXcgy.js @@ -0,0 +1,30 @@ +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.BfjuC5t1.js";const o=JSON.parse('{"title":"Initializing Weights","description":"","frontmatter":{},"headers":[],"relativePath":"manual/weight_initializers.md","filePath":"manual/weight_initializers.md","lastUpdated":null}'),t={name:"manual/weight_initializers.md"},e=n(`

    Initializing Weights ​

    WeightInitializers.jl provides common weight initialization schemes for deep learning models.

    julia
    using WeightInitializers, Random
+
+# Fixing rng
+rng = Random.MersenneTwister(42)
    Random.MersenneTwister(42)
    julia
    # Explicit rng call
+weights = kaiming_normal(rng, 2, 5)
    2×5 Matrix{Float32}:
+ -0.351662   0.0171745   1.12442   -0.296372   -1.67094
+ -0.281053  -0.18941    -0.724099   0.0987538   0.634549
    julia
    # Default rng call
+weights = kaiming_normal(2, 5)
    2×5 Matrix{Float32}:
+ -0.227513  -0.265372   0.265788  1.29955  -0.192836
+  0.687611   0.454679  -0.433656  0.20548   0.292002
    julia
    # Passing kwargs (if needed) with explicit rng call
+weights_cl = kaiming_normal(rng; gain=1.0)
+weights = weights_cl(2, 5)
    2×5 Matrix{Float32}:
+ 0.484056   0.231723   0.164379   0.306147   0.18365
+ 0.0836414  0.666965  -0.396323  -0.711329  -0.382971
    julia
    # Passing kwargs (if needed) with default rng call
+weights_cl = kaiming_normal(; gain=1.0)
+weights = weights_cl(2, 5)
    2×5 Matrix{Float32}:
+ -0.160876  -0.187646   0.18794   0.918918  -0.136356
+  0.486214   0.321506  -0.306641  0.145296   0.206476

    To generate weights directly on GPU, pass in a CUDA.RNG. (Note that this is currently implemented only for NVIDIA GPUs)

    julia
    using LuxCUDA
+
+weights = kaiming_normal(CUDA.default_rng(), 2, 5)
    2×5 CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}:
+ -0.152879  0.151805  0.115322  0.0608437  -0.357408
+ -0.671014  0.283396  0.260171  0.425698   -0.701588

    You can also generate Complex Numbers:

    julia
    weights = kaiming_normal(CUDA.default_rng(), ComplexF32, 2, 5)
    2×5 CuArray{ComplexF32, 2, CUDA.Mem.DeviceBuffer}:
+ -0.239414-0.306575im  0.0877513-0.485896im  …  -0.328706-0.340686im
+ 0.0245199-0.04416im    0.252702-0.161867im       0.41303-0.533871im

    Quick examples ​

    The package is meant to be working with deep learning libraries such as (F)Lux. All the methods take as input the chosen rng type and the dimension for the array.

    julia
    weights = init(rng, dims...)

    The rng is optional, if not specified a default one will be used.

    julia
    weights = init(dims...)

    If there is the need to use keyword arguments the methods can be called with just the rng (optionally) and the keywords to get in return a function behaving like the two examples above.

    julia
    weights_init = init(rng; kwargs...)
+weights = weights_init(rng, dims...)
+
+# Or
+
+weights_init = init(; kwargs...)
+weights = weights_init(dims...)
    `,25),l=[e];function p(h,k,d,g,r,c){return a(),i("div",null,l)}const y=s(t,[["render",p]]);export{o as __pageData,y as default}; diff --git a/v0.5.30/assets/manual_weight_initializers.md._StOXcgy.lean.js b/v0.5.30/assets/manual_weight_initializers.md._StOXcgy.lean.js new file mode 100644 index 000000000..b4b45ccbf --- /dev/null +++ b/v0.5.30/assets/manual_weight_initializers.md._StOXcgy.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.BfjuC5t1.js";const o=JSON.parse('{"title":"Initializing Weights","description":"","frontmatter":{},"headers":[],"relativePath":"manual/weight_initializers.md","filePath":"manual/weight_initializers.md","lastUpdated":null}'),t={name:"manual/weight_initializers.md"},e=n("",25),l=[e];function p(h,k,d,g,r,c){return a(),i("div",null,l)}const y=s(t,[["render",p]]);export{o as __pageData,y as default}; diff --git a/v0.5.30/assets/results.Dao8ZugC.gif b/v0.5.30/assets/results.Dao8ZugC.gif new file mode 100644 index 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b/v0.5.30/assets/tutorials_advanced_1_GravitationalWaveForm.md.CwWPFlQf.js new file mode 100644 index 000000000..265dd7aa9 --- /dev/null +++ b/v0.5.30/assets/tutorials_advanced_1_GravitationalWaveForm.md.CwWPFlQf.js @@ -0,0 +1,303 @@ +import{_ as h,c as s,m as A,a,a4 as n,o as i}from"./chunks/framework.BfjuC5t1.js";const XA=JSON.parse('{"title":"Training a Neural ODE to Model Gravitational Waveforms","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/advanced/1_GravitationalWaveForm.md","filePath":"tutorials/advanced/1_GravitationalWaveForm.md","lastUpdated":null}'),t={name:"tutorials/advanced/1_GravitationalWaveForm.md"},e=n(`

      Training a Neural ODE to Model Gravitational Waveforms ​

      This code is adapted from Astroinformatics/ScientificMachineLearning

      The code has been minimally adapted from Keith et. al. 2021 which originally used Flux.jl

      Package Imports ​

      julia
      using Lux, ComponentArrays, LineSearches, LuxAMDGPU, LuxCUDA, OrdinaryDiffEq, Optimization,
+      OptimizationOptimJL, Printf, Random, SciMLSensitivity
+using CairoMakie
+
+CUDA.allowscalar(false)

      Define some Utility Functions ​

      Tip

      This section can be skipped. It defines functions to simulate the model, however, from a scientific machine learning perspective, isn't super relevant.

      `,7),l={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},p={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.819ex",height:"1.658ex",role:"img",focusable:"false",viewBox:"0 -583 4782.1 733","aria-hidden":"true"},k=n('',1),E=[k],r=A("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[A("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[A("mi",null,"r"),A("mo",null,"="),A("msub",null,[A("mi",null,"r"),A("mn",null,"1")]),A("mo",null,"−"),A("msub",null,[A("mi",null,"r"),A("mn",null,"2")])])],-1),d={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},Q={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.008ex",height:"1.339ex",role:"img",focusable:"false",viewBox:"0 -442 887.6 592","aria-hidden":"true"},C=n('',1),o=[C],g=A("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[A("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[A("msub",null,[A("mi",null,"r"),A("mn",null,"1")])])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},v={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.339ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.008ex",height:"1.339ex",role:"img",focusable:"false",viewBox:"0 -442 887.6 592","aria-hidden":"true"},y=n('',1),u=[y],I=A("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[A("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[A("msub",null,[A("mi",null,"r"),A("mn",null,"2")])])],-1),F=n(`
      julia
      function one2two(path, m₁, m₂)
+    M = m₁ + m₂
+    r₁ = m₂ / M .* path
+    r₂ = -m₁ / M .* path
+    return r₁, r₂
+end
      one2two (generic function with 1 method)
      `,2),c={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},q={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"24.527ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 10840.9 1000","aria-hidden":"true"},B=n('',1),T=[B],m=A("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[A("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[A("mo",{stretchy:"false"},"("),A("mi",null,"χ"),A("mo",{stretchy:"false"},"("),A("mi",null,"t"),A("mo",{stretchy:"false"},")"),A("mo",null,","),A("mi",null,"ϕ"),A("mo",{stretchy:"false"},"("),A("mi",null,"t"),A("mo",{stretchy:"false"},")"),A("mo",{stretchy:"false"},")"),A("mo",{stretchy:"false"},"↦"),A("mo",{stretchy:"false"},"("),A("mi",null,"x"),A("mo",{stretchy:"false"},"("),A("mi",null,"t"),A("mo",{stretchy:"false"},")"),A("mo",null,","),A("mi",null,"y"),A("mo",{stretchy:"false"},"("),A("mi",null,"t"),A("mo",{stretchy:"false"},")"),A("mo",{stretchy:"false"},")")])],-1),b=n(`
      julia
      @views function soln2orbit(soln, model_params=nothing)
+    @assert size(soln, 1) ∈ [2, 4] "size(soln,1) must be either 2 or 4"
+
+    if size(soln, 1) == 2
+        χ = soln[1, :]
+        ϕ = soln[2, :]
+
+        @assert length(model_params)==3 "model_params must have length 3 when size(soln,2) = 2"
+        p, M, e = model_params
+    else
+        χ = soln[1, :]
+        ϕ = soln[2, :]
+        p = soln[3, :]
+        e = soln[4, :]
+    end
+
+    r = p ./ (1 .+ e .* cos.(χ))
+    x = r .* cos.(ϕ)
+    y = r .* sin.(ϕ)
+
+    orbit = vcat(x', y')
+    return orbit
+end
      soln2orbit (generic function with 2 methods)

      This function uses second-order one-sided difference stencils at the endpoints; see https://doi.org/10.1090/S0025-5718-1988-0935077-0

      julia
      function d_dt(v::AbstractVector, dt)
+    a = -3 / 2 * v[1] + 2 * v[2] - 1 / 2 * v[3]
+    b = (v[3:end] .- v[1:(end - 2)]) / 2
+    c = 3 / 2 * v[end] - 2 * v[end - 1] + 1 / 2 * v[end - 2]
+    return [a; b; c] / dt
+end
      d_dt (generic function with 1 method)

      This function uses second-order one-sided difference stencils at the endpoints; see https://doi.org/10.1090/S0025-5718-1988-0935077-0

      julia
      function d2_dt2(v::AbstractVector, dt)
+    a = 2 * v[1] - 5 * v[2] + 4 * v[3] - v[4]
+    b = v[1:(end - 2)] .- 2 * v[2:(end - 1)] .+ v[3:end]
+    c = 2 * v[end] - 5 * v[end - 1] + 4 * v[end - 2] - v[end - 3]
+    return [a; b; c] / (dt^2)
+end
      d2_dt2 (generic function with 1 method)

      Now we define a function to compute the trace-free moment tensor from the orbit

      julia
      function orbit2tensor(orbit, component, mass=1)
+    x = orbit[1, :]
+    y = orbit[2, :]
+
+    Ixx = x .^ 2
+    Iyy = y .^ 2
+    Ixy = x .* y
+    trace = Ixx .+ Iyy
+
+    if component[1] == 1 && component[2] == 1
+        tmp = Ixx .- trace ./ 3
+    elseif component[1] == 2 && component[2] == 2
+        tmp = Iyy .- trace ./ 3
+    else
+        tmp = Ixy
+    end
+
+    return mass .* tmp
+end
+
+function h_22_quadrupole_components(dt, orbit, component, mass=1)
+    mtensor = orbit2tensor(orbit, component, mass)
+    mtensor_ddot = d2_dt2(mtensor, dt)
+    return 2 * mtensor_ddot
+end
+
+function h_22_quadrupole(dt, orbit, mass=1)
+    h11 = h_22_quadrupole_components(dt, orbit, (1, 1), mass)
+    h22 = h_22_quadrupole_components(dt, orbit, (2, 2), mass)
+    h12 = h_22_quadrupole_components(dt, orbit, (1, 2), mass)
+    return h11, h12, h22
+end
+
+function h_22_strain_one_body(dt::T, orbit) where {T}
+    h11, h12, h22 = h_22_quadrupole(dt, orbit)
+
+    h₊ = h11 - h22
+    hₓ = T(2) * h12
+
+    scaling_const = √(T(π) / 5)
+    return scaling_const * h₊, -scaling_const * hₓ
+end
+
+function h_22_quadrupole_two_body(dt, orbit1, mass1, orbit2, mass2)
+    h11_1, h12_1, h22_1 = h_22_quadrupole(dt, orbit1, mass1)
+    h11_2, h12_2, h22_2 = h_22_quadrupole(dt, orbit2, mass2)
+    h11 = h11_1 + h11_2
+    h12 = h12_1 + h12_2
+    h22 = h22_1 + h22_2
+    return h11, h12, h22
+end
+
+function h_22_strain_two_body(dt::T, orbit1, mass1, orbit2, mass2) where {T}
+    # compute (2,2) mode strain from orbits of BH 1 of mass1 and BH2 of mass 2
+
+    @assert abs(mass1 + mass2 - 1.0)<1e-12 "Masses do not sum to unity"
+
+    h11, h12, h22 = h_22_quadrupole_two_body(dt, orbit1, mass1, orbit2, mass2)
+
+    h₊ = h11 - h22
+    hₓ = T(2) * h12
+
+    scaling_const = √(T(π) / 5)
+    return scaling_const * h₊, -scaling_const * hₓ
+end
+
+function compute_waveform(dt::T, soln, mass_ratio, model_params=nothing) where {T}
+    @assert mass_ratio≤1 "mass_ratio must be <= 1"
+    @assert mass_ratio≥0 "mass_ratio must be non-negative"
+
+    orbit = soln2orbit(soln, model_params)
+    if mass_ratio > 0
+        m₂ = inv(T(1) + mass_ratio)
+        m₁ = mass_ratio * m₂
+
+        orbit₁, orbit₂ = one2two(orbit, m₁, m₂)
+        waveform = h_22_strain_two_body(dt, orbit1, mass1, orbit2, mass2)
+    else
+        waveform = h_22_strain_one_body(dt, orbit)
+    end
+    return waveform
+end
      compute_waveform (generic function with 2 methods)

      Simulating the True Model ​

      RelativisticOrbitModel defines system of odes which describes motion of point like particle in schwarzschild background, uses

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      julia
      function RelativisticOrbitModel(u, (p, M, e), t)
+    χ, ϕ = u
+
+    numer = (p - 2 - 2 * e * cos(χ)) * (1 + e * cos(χ))^2
+    denom = sqrt((p - 2)^2 - 4 * e^2)
+
+    χ̇ = numer * sqrt(p - 6 - 2 * e * cos(χ)) / (M * (p^2) * denom)
+    ϕ̇ = numer / (M * (p^(3 / 2)) * denom)
+
+    return [χ̇, ϕ̇]
+end
+
+mass_ratio = 0.0         # test particle
+u0 = Float64[π, 0.0]     # initial conditions
+datasize = 250
+tspan = (0.0f0, 6.0f4)   # timespace for GW waveform
+tsteps = range(tspan[1], tspan[2]; length=datasize)  # time at each timestep
+dt_data = tsteps[2] - tsteps[1]
+dt = 100.0
+const ode_model_params = [100.0, 1.0, 0.5]; # p, M, e

      Let's simulate the true model and plot the results using OrdinaryDiffEq.jl

      julia
      prob = ODEProblem(RelativisticOrbitModel, u0, tspan, ode_model_params)
+soln = Array(solve(prob, RK4(); saveat=tsteps, dt, adaptive=false))
+waveform = first(compute_waveform(dt_data, soln, mass_ratio, ode_model_params))
+
+begin
+    fig = Figure()
+    ax = CairoMakie.Axis(fig[1, 1]; xlabel="Time", ylabel="Waveform")
+
+    l = lines!(ax, tsteps, waveform; linewidth=2, alpha=0.75)
+    s = scatter!(ax, tsteps, waveform; markershape=:circle,
+        markersize=12, markeralpha=0.25, alpha=0.5)
+
+    axislegend(ax, [[l, s]], ["Waveform Data"])
+
+    fig
+end

      Defiing a Neural Network Model ​

      Next, we define the neural network model that takes 1 input (time) and has two outputs. We'll make a function ODE_model that takes the initial conditions, neural network parameters and a time as inputs and returns the derivatives.

      It is typically never recommended to use globals but incase you do use them, make sure to mark them as const.

      We will deviate from the standard Neural Network initialization and use WeightInitializers.jl,

      julia
      const nn = Chain(Base.Fix1(broadcast, cos),
+    Dense(1 => 32, cos; init_weight=truncated_normal(; std=1e-4)),
+    Dense(32 => 32, cos; init_weight=truncated_normal(; std=1e-4)),
+    Dense(32 => 2; init_weight=truncated_normal(; std=1e-4)))
+ps, st = Lux.setup(Xoshiro(), nn)
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      Similar to most DL frameworks, Lux defaults to using Float32, however, in this case we need Float64

      julia
      const params = ComponentArray{Float64}(ps)
+
+const nn_model = StatefulLuxLayer(nn, st)
      Lux.StatefulLuxLayer{true, Lux.Chain{@NamedTuple{layer_1::Lux.WrappedFunction{Base.Fix1{typeof(broadcast), typeof(cos)}}, layer_2::Lux.Dense{true, typeof(cos), PartialFunctions.PartialFunction{nothing, nothing, typeof(WeightInitializers.truncated_normal), Tuple{}, @NamedTuple{std::Float64}}, typeof(WeightInitializers.zeros32)}, layer_3::Lux.Dense{true, typeof(cos), PartialFunctions.PartialFunction{nothing, nothing, typeof(WeightInitializers.truncated_normal), Tuple{}, @NamedTuple{std::Float64}}, typeof(WeightInitializers.zeros32)}, layer_4::Lux.Dense{true, typeof(identity), PartialFunctions.PartialFunction{nothing, nothing, typeof(WeightInitializers.truncated_normal), Tuple{}, @NamedTuple{std::Float64}}, typeof(WeightInitializers.zeros32)}}, Nothing}, Nothing, @NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}, layer_3::@NamedTuple{}, layer_4::@NamedTuple{}}}(Chain(), nothing, (layer_1 = NamedTuple(), layer_2 = NamedTuple(), layer_3 = NamedTuple(), layer_4 = NamedTuple()), nothing)

      Now we define a system of odes which describes motion of point like particle with Newtonian physics, uses

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      julia
      function ODE_model(u, nn_params, t)
+    χ, ϕ = u
+    p, M, e = ode_model_params
+
+    # In this example we know that \`st\` is am empty NamedTuple hence we can safely ignore
+    # it, however, in general, we should use \`st\` to store the state of the neural network.
+    y = 1 .+ nn_model([first(u)], nn_params)
+
+    numer = (1 + e * cos(χ))^2
+    denom = M * (p^(3 / 2))
+
+    χ̇ = (numer / denom) * y[1]
+    ϕ̇ = (numer / denom) * y[2]
+
+    return [χ̇, ϕ̇]
+end
      ODE_model (generic function with 1 method)

      Let us now simulate the neural network model and plot the results. We'll use the untrained neural network parameters to simulate the model.

      julia
      prob_nn = ODEProblem(ODE_model, u0, tspan, params)
+soln_nn = Array(solve(prob_nn, RK4(); u0, p=params, saveat=tsteps, dt, adaptive=false))
+waveform_nn = first(compute_waveform(dt_data, soln_nn, mass_ratio, ode_model_params))
+
+begin
+    fig = Figure()
+    ax = CairoMakie.Axis(fig[1, 1]; xlabel="Time", ylabel="Waveform")
+
+    l1 = lines!(ax, tsteps, waveform; linewidth=2, alpha=0.75)
+    s1 = scatter!(ax, tsteps, waveform; markershape=:circle, markersize=12,
+        markeralpha=0.25, alpha=0.5, strokewidth=2)
+
+    l2 = lines!(ax, tsteps, waveform_nn; linewidth=2, alpha=0.75)
+    s2 = scatter!(ax, tsteps, waveform_nn; markershape=:circle,
+        markersize=12, markeralpha=0.25, alpha=0.5, strokewidth=2)
+
+    axislegend(ax, [[l1, s1], [l2, s2]],
+        ["Waveform Data", "Waveform Neural Net (Untrained)"]; position=:lb)
+
+    fig
+end

      Setting Up for Training the Neural Network ​

      Next, we define the objective (loss) function to be minimized when training the neural differential equations.

      julia
      function loss(θ)
+    pred = Array(solve(prob_nn, RK4(); u0, p=θ, saveat=tsteps, dt, adaptive=false))
+    pred_waveform = first(compute_waveform(dt_data, pred, mass_ratio, ode_model_params))
+    loss = sum(abs2, waveform .- pred_waveform)
+    return loss, pred_waveform
+end
      loss (generic function with 1 method)

      Warmup the loss function

      julia
      loss(params)
      (0.17215171721421207, [-0.024249801535431388, -0.02346585418572156, -0.022681906836011435, -0.021357317180048352, -0.019464416988440935, -0.016963046554685536, -0.013800484708468138, -0.00990849440296376, -0.00520559267126083, 0.0004032969641172105, 0.007017656891419924, 0.014720493495480241, 0.02353090231748062, 0.033276169354516875, 0.043314705833896336, 0.05188106697558526, 0.054700333055434175, 0.0427238357065267, 0.002423105357175596, -0.06575883215773011, -0.11027317642844461, -0.07678253350835433, -0.0072353830951188206, 0.03869619541269424, 0.054302679477350145, 0.053010890392771556, 0.044889237694299845, 0.034846679863281424, 0.024936638661368058, 0.015923083057834027, 0.008021668513541608, 0.0012311811425605268, -0.004529475034590188, -0.009361716233634384, -0.013364035775378412, -0.016620815901878253, -0.019203788197126054, -0.021169013129862177, -0.022559076807699988, -0.023404004269245684, -0.023722253289358303, -0.023521083092865745, -0.022797843963709284, 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0.01953487303756195, 0.02874787822057803, 0.03858428047507269, 0.047938884837366906, 0.05401544627420644, 0.05050337220632601, 0.0256911577239574, -0.030974995521538738, -0.09638900641676833, -0.102573566871294, -0.040619015798842875, 0.021284462092519427, 0.05040555779361737, 0.05546518394540094, 0.04946935076603893, 0.03970253564114501, 0.029377636383265602, 0.01975531095702029, 0.01123161885375543, 0.003879775858755852, -0.0023695397955581397, -0.00761096830444328, -0.011966053312152423, -0.015522255130645694, -0.018364387021327692, -0.020552878493211888, -0.022147379737285706, -0.02317926869799286, -0.02367518135491305, -0.023649303371970062, -0.02310461742752934, -0.02203298018800196, -0.020414371431591624, -0.018224930107454487, -0.015413676223328199, -0.011928852014086397, -0.007709193266232499, -0.0026602412566282306, 0.0032996827586000317, 0.010262587199066909, 0.018274577343534007, 0.027303342429091142, 0.03702853083260528, 0.0465057213069404, 0.05331917019944852, 0.051918238954459836, 0.03153306060791138, -0.019910122722075096, -0.08788362950254597, -0.10750094646131855, -0.05250722342833319, 0.013532854861997918, 0.0479619737149416, 0.055852146956217485, 0.050901076175073945, 0.04135375329743446, 0.03093541376814808, 0.02110756232480277, 0.01237125722871237, 0.004818557596569256, -0.0015962956792808102, -0.006991680144950654, -0.011469023119692376, -0.015132311698807245, -0.018060132121416765, -0.020332234338905318, -0.021995136036621243, -0.023091139245199024, -0.023646409526520064, -0.023679578179550936, -0.023193543086071973, -0.022182036958480172, -0.02063327847752358, -0.018513107066246644, -0.015785984296997794, -0.012396365770967076, -0.008287656846264849, -0.003368634740061504, 0.0024402092108903213, 0.00922922779343203, 0.017051490948011293, 0.02589298414209541, 0.03549058692942278, 0.04503937218323815, 0.05245167905094164, 0.05286401786344559, 0.0364818425938837, -0.009505948227704146, -0.07802438838691865, -0.11013670289983736, -0.06425595915170446, 0.004772010596095392, 0.04482024983889405, 0.055946769355377436, 0.05225496995452235, 0.04301460045508618, 0.03252435619257789, 0.022501895668115328, 0.013547176658980737, 0.0057907331212782714, -0.0008020753538423008, -0.006349674377069929, -0.01095520031828327, -0.014727439711552081, -0.017748123886680903, -0.02010087532816729, -0.021835155048116412, -0.0229959341098181, -0.023611652701661365, -0.02370339152416624, -0.023275956637742234, -0.022325259983575547, -0.020841440939984492, -0.018793020521969617, -0.016146637502150406, -0.012849766519993163, -0.008848805202157648, -0.004847843884322281])

      Now let us define a callback function to store the loss over time

      julia
      const losses = Float64[]
+
+function callback(θ, l, pred_waveform)
+    push!(losses, l)
+    @printf "Training %10s Iteration: %5d %10s Loss: %.10f\\n" "" length(losses) "" l
+    return false
+end
      callback (generic function with 1 method)

      Training the Neural Network ​

      Training uses the BFGS optimizers. This seems to give good results because the Newtonian model seems to give a very good initial guess

      julia
      adtype = Optimization.AutoZygote()
+optf = Optimization.OptimizationFunction((x, p) -> loss(x), adtype)
+optprob = Optimization.OptimizationProblem(optf, params)
+res = Optimization.solve(
+    optprob, BFGS(; initial_stepnorm=0.01, linesearch=LineSearches.BackTracking());
+    callback, maxiters=1000)
      retcode: Success
+u: ComponentVector{Float64}(layer_1 = Float64[], layer_2 = (weight = [-0.00011973267100973714; -6.019301872584702e-5; 9.096157009471292e-5; 4.266174801152644e-5; 9.349408855980382e-7; 0.00016044428048176378; -9.652911103319343e-6; -0.0001385483919874571; 9.681806659489127e-6; -2.8657123039017627e-5; 0.00017334803123936343; 2.4411341655644033e-5; 9.011603833644094e-5; 5.220362072567235e-5; 0.0002490672632118383; -2.4143722839640925e-5; 0.00012566449004216483; -4.847905802303613e-5; 4.074634125572134e-5; 1.0247664249599429e-5; -0.0001859721960498307; 3.735608697743877e-5; -7.656955858682703e-5; -1.2043876267849151e-5; -8.479990356138734e-5; -2.4505294277351263e-5; -7.95876258051809e-5; -0.00022258625540396467; -0.00017038380610754774; 2.2777765479984303e-5; 4.27112718170935e-5; 6.095390563132088e-5;;], bias = [-1.164825726562541e-16; 7.32997919745033e-18; 9.983766760539752e-17; 7.770460759065174e-17; 1.7788999500159933e-18; 1.4588208534933488e-16; -1.2507218408227132e-17; -1.251678622168931e-16; 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0.0001495518057810956 0.00020418711702514773 3.953914111772107e-5 -6.365618527335629e-6 6.240187704971275e-5 0.00015583859695763455 -9.599388666974163e-5 5.6562542714540895e-5 7.875502834504688e-5 -8.023809267608356e-6 -6.209254442072207e-5 3.4325022544369584e-5 6.87778787425581e-5 -8.38185465807251e-5 -9.155928509132557e-5 -2.6343574599006666e-5 -1.791681151079214e-5 -7.370268812227703e-5 3.1803815919564016e-5 -0.00022330733426205592 -8.918961237923293e-6 -0.00024460524090390393 0.0001476391748030524 7.990460054425742e-5 1.0085648146932791e-5 0.00013233675909869608 -0.00021251011875282548 -6.576830727569789e-5 -0.00010873914524270921 -2.6075373706400867e-5 -8.926604877050693e-5 -8.430424585530198e-5], bias = [1.921786307209035e-9; 8.789190050134396e-11; 1.2504148812771212e-9; 2.759638658565189e-9; -4.0864654563959214e-9; -1.5256145600285591e-9; -7.257926362306835e-10; -2.32442960482532e-9; 2.26637932249765e-9; 2.085537853776543e-9; -3.0927651263003428e-9; 1.1204678255460235e-9; 1.224877475321225e-9; 2.7271956201550424e-9; 1.020909304245852e-9; -6.646559494382461e-10; 3.899342734955543e-11; -8.234145849406738e-11; 1.581324318981226e-9; 1.3057169819360422e-9; 1.4432009549384312e-10; -3.935652982223644e-10; 1.2538523267575744e-9; 1.9956939078962535e-9; 2.55591752995915e-9; 4.101057123727002e-9; 2.329851411471181e-9; -1.8697572701351324e-9; 8.933663432767605e-10; -2.903453407028585e-9; -2.9091078170073337e-9; -9.91884728601028e-10;;]), layer_4 = (weight = [-0.0005572566820208557 -0.0007937026262524729 -0.0006027371350159636 -0.0008097167570915016 -0.0006632364353912129 -0.0007586931955229081 -0.0006962550015859167 -0.0007105567364154836 -0.0006658085334180905 -0.0006602566700924333 -0.0006626099449352349 -0.0007211122134551628 -0.0006367930196168518 -0.0007610696972092854 -0.0007117310752981213 -0.0005740901170262534 -0.0007709460867192456 -0.0006457321711362864 -0.0006559189228036226 -0.00071990248582105 -0.0007860558927556543 -0.00069686912726478 -0.0005244937356517977 -0.0009616786115207227 -0.0007539177071414011 -0.0006872892690566108 -0.0006167645875060232 -0.0006239984997886235 -0.0005674648472694767 -0.0006296852286443204 -0.0008124558416854573 -0.0007791480513692754; 0.00014216770893870395 5.398784074717275e-5 0.00023440740675234172 0.00018101927179873937 0.00038097963229907544 0.0004179167254411029 0.00016871553604570189 0.0002684071421866321 0.00029311844363497764 -4.684615903553573e-6 0.0001715444594282229 0.00015608806149225427 0.0002515337605158771 0.00022016138424090162 0.00030322691643611805 0.00015330975900653944 0.0002746350862441426 0.0002501048844999265 0.0003728965915869229 0.00032248962985238777 0.0003586351545196296 0.00018497025779880998 0.0003025448352555981 0.00021959541944993648 0.0003294169957206736 0.00028422808379670095 0.00020632328939831497 0.00032818817391118334 5.102628667107437e-5 0.00014884949250286642 0.00017417684072532018 0.00026142470856713477], bias = [-0.0006732848512731586; 0.00023393989498430928;;]))

      Visualizing the Results ​

      Let us now plot the loss over time

      julia
      begin
+    fig = Figure()
+    ax = CairoMakie.Axis(fig[1, 1]; xlabel="Iteration", ylabel="Loss")
+
+    lines!(ax, losses; linewidth=4, alpha=0.75)
+    scatter!(ax, 1:length(losses), losses; markershape=:circle,
+        markersize=12, markeralpha=0.25, strokewidth=2)
+
+    fig
+end

      Finally let us visualize the results

      julia
      prob_nn = ODEProblem(ODE_model, u0, tspan, res.u)
+soln_nn = Array(solve(prob_nn, RK4(); u0, p=res.u, saveat=tsteps, dt, adaptive=false))
+waveform_nn_trained = first(compute_waveform(
+    dt_data, soln_nn, mass_ratio, ode_model_params))
+
+begin
+    fig = Figure()
+    ax = CairoMakie.Axis(fig[1, 1]; xlabel="Time", ylabel="Waveform")
+
+    l1 = lines!(ax, tsteps, waveform; linewidth=2, alpha=0.75)
+    s1 = scatter!(ax, tsteps, waveform; markershape=:circle,
+        markeralpha=0.25, alpha=0.5, strokewidth=2, markersize=12)
+
+    l2 = lines!(ax, tsteps, waveform_nn; linewidth=2, alpha=0.75)
+    s2 = scatter!(ax, tsteps, waveform_nn; markershape=:circle,
+        markeralpha=0.25, alpha=0.5, strokewidth=2, markersize=12)
+
+    l3 = lines!(ax, tsteps, waveform_nn_trained; linewidth=2, alpha=0.75)
+    s3 = scatter!(ax, tsteps, waveform_nn_trained; markershape=:circle,
+        markeralpha=0.25, alpha=0.5, strokewidth=2, markersize=12)
+
+    axislegend(ax, [[l1, s1], [l2, s2], [l3, s3]],
+        ["Waveform Data", "Waveform Neural Net (Untrained)", "Waveform Neural Net"];
+        position=:lb)
+
+    fig
+end

      Appendix ​

      julia
      using InteractiveUtils
+InteractiveUtils.versioninfo()
+if @isdefined(LuxCUDA) && CUDA.functional(); println(); CUDA.versioninfo(); end
+if @isdefined(LuxAMDGPU) && LuxAMDGPU.functional(); println(); AMDGPU.versioninfo(); end
      Julia Version 1.10.2
+Commit bd47eca2c8a (2024-03-01 10:14 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 48 × AMD EPYC 7402 24-Core Processor
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
+Threads: 48 default, 0 interactive, 24 GC (on 2 virtual cores)
+Environment:
+  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
+  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6
+  JULIA_PROJECT = /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/docs
+  JULIA_AMDGPU_LOGGING_ENABLED = true
+  JULIA_DEBUG = Literate
+  JULIA_CPU_THREADS = 2
+  JULIA_NUM_THREADS = 48
+  JULIA_LOAD_PATH = @:@v#.#:@stdlib
+  JULIA_CUDA_HARD_MEMORY_LIMIT = 25%
+
+CUDA runtime 12.3, artifact installation
+CUDA driver 12.4
+NVIDIA driver 550.54.15
+
+CUDA libraries: 
+- CUBLAS: 12.3.4
+- CURAND: 10.3.4
+- CUFFT: 11.0.12
+- CUSOLVER: 11.5.4
+- CUSPARSE: 12.2.0
+- CUPTI: 21.0.0
+- NVML: 12.0.0+550.54.15
+
+Julia packages: 
+- CUDA: 5.2.0
+- CUDA_Driver_jll: 0.7.0+1
+- CUDA_Runtime_jll: 0.11.1+0
+
+Toolchain:
+- Julia: 1.10.2
+- LLVM: 15.0.7
+
+Environment:
+- JULIA_CUDA_HARD_MEMORY_LIMIT: 25%
+
+1 device:
+  0: NVIDIA A100-PCIE-40GB MIG 1g.5gb (sm_80, 4.600 GiB / 4.750 GiB available)
+┌ Warning: LuxAMDGPU is loaded but the AMDGPU is not functional.
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      Julia & Lux for the Uninitiated ​

      This is a quick intro to Lux loosely based on:

      1. PyTorch's tutorial.

      2. Flux's tutorial.

      3. Jax's tutorial.

      It introduces basic Julia programming, as well Zygote, a source-to-source automatic differentiation (AD) framework in Julia. We'll use these tools to build a very simple neural network. Let's start with importing Lux.jl

      julia
      using Lux, Random

      Now let us control the randomness in our code using proper Pseudo Random Number Generator (PRNG)

      julia
      rng = Random.default_rng()
+Random.seed!(rng, 0)
      Random.TaskLocalRNG()

      Arrays ​

      The starting point for all of our models is the Array (sometimes referred to as a Tensor in other frameworks). This is really just a list of numbers, which might be arranged into a shape like a square. Let's write down an array with three elements.

      julia
      x = [1, 2, 3]
      3-element Vector{Int64}:
+ 1
+ 2
+ 3

      Here's a matrix – a square array with four elements.

      julia
      x = [1 2; 3 4]
      2×2 Matrix{Int64}:
+ 1  2
+ 3  4

      We often work with arrays of thousands of elements, and don't usually write them down by hand. Here's how we can create an array of 5×3 = 15 elements, each a random number from zero to one.

      julia
      x = rand(rng, 5, 3)
      5×3 Matrix{Float64}:
+ 0.455238   0.746943   0.193291
+ 0.547642   0.746801   0.116989
+ 0.773354   0.97667    0.899766
+ 0.940585   0.0869468  0.422918
+ 0.0296477  0.351491   0.707534

      There's a few functions like this; try replacing rand with ones, zeros, or randn.

      By default, Julia works stores numbers is a high-precision format called Float64. In ML we often don't need all those digits, and can ask Julia to work with Float32 instead. We can even ask for more digits using BigFloat.

      julia
      x = rand(BigFloat, 5, 3)
      5×3 Matrix{BigFloat}:
+ 0.981339    0.793159  0.459019
+ 0.043883    0.624384  0.56055
+ 0.164786    0.524008  0.0355555
+ 0.414769    0.577181  0.621958
+ 0.00823197  0.30215   0.655881
      julia
      x = rand(Float32, 5, 3)
      5×3 Matrix{Float32}:
+ 0.567794   0.369178   0.342539
+ 0.0985227  0.201145   0.587206
+ 0.776598   0.148248   0.0851708
+ 0.723731   0.0770206  0.839303
+ 0.404728   0.230954   0.679087

      We can ask the array how many elements it has.

      julia
      length(x)
      15

      Or, more specifically, what size it has.

      julia
      size(x)
      (5, 3)

      We sometimes want to see some elements of the array on their own.

      julia
      x
      5×3 Matrix{Float32}:
+ 0.567794   0.369178   0.342539
+ 0.0985227  0.201145   0.587206
+ 0.776598   0.148248   0.0851708
+ 0.723731   0.0770206  0.839303
+ 0.404728   0.230954   0.679087
      julia
      x[2, 3]
      0.58720636f0

      This means get the second row and the third column. We can also get every row of the third column.

      julia
      x[:, 3]
      5-element Vector{Float32}:
+ 0.34253937
+ 0.58720636
+ 0.085170805
+ 0.8393034
+ 0.67908657

      We can add arrays, and subtract them, which adds or subtracts each element of the array.

      julia
      x + x
      5×3 Matrix{Float32}:
+ 1.13559   0.738356  0.685079
+ 0.197045  0.40229   1.17441
+ 1.5532    0.296496  0.170342
+ 1.44746   0.154041  1.67861
+ 0.809456  0.461908  1.35817
      julia
      x - x
      5×3 Matrix{Float32}:
+ 0.0  0.0  0.0
+ 0.0  0.0  0.0
+ 0.0  0.0  0.0
+ 0.0  0.0  0.0
+ 0.0  0.0  0.0

      Julia supports a feature called broadcasting, using the . syntax. This tiles small arrays (or single numbers) to fill bigger ones.

      julia
      x .+ 1
      5×3 Matrix{Float32}:
+ 1.56779  1.36918  1.34254
+ 1.09852  1.20114  1.58721
+ 1.7766   1.14825  1.08517
+ 1.72373  1.07702  1.8393
+ 1.40473  1.23095  1.67909

      We can see Julia tile the column vector 1:5 across all rows of the larger array.

      julia
      zeros(5, 5) .+ (1:5)
      5×5 Matrix{Float64}:
+ 1.0  1.0  1.0  1.0  1.0
+ 2.0  2.0  2.0  2.0  2.0
+ 3.0  3.0  3.0  3.0  3.0
+ 4.0  4.0  4.0  4.0  4.0
+ 5.0  5.0  5.0  5.0  5.0

      The x' syntax is used to transpose a column 1:5 into an equivalent row, and Julia will tile that across columns.

      julia
      zeros(5, 5) .+ (1:5)'
      5×5 Matrix{Float64}:
+ 1.0  2.0  3.0  4.0  5.0
+ 1.0  2.0  3.0  4.0  5.0
+ 1.0  2.0  3.0  4.0  5.0
+ 1.0  2.0  3.0  4.0  5.0
+ 1.0  2.0  3.0  4.0  5.0

      We can use this to make a times table.

      julia
      (1:5) .* (1:5)'
      5×5 Matrix{Int64}:
+ 1   2   3   4   5
+ 2   4   6   8  10
+ 3   6   9  12  15
+ 4   8  12  16  20
+ 5  10  15  20  25

      Finally, and importantly for machine learning, we can conveniently do things like matrix multiply.

      julia
      W = randn(5, 10)
+x = rand(10)
+W * x
      5-element Vector{Float64}:
+  1.2197981041108443
+ -2.62625877100596
+ -2.8573820474674845
+ -2.4319346874291314
+  1.0108668577150213

      Julia's arrays are very powerful, and you can learn more about what they can do here.

      CUDA Arrays ​

      CUDA functionality is provided separately by the CUDA.jl package. If you have a GPU and LuxCUDA is installed, Lux will provide CUDA capabilities. For additional details on backends see the manual section.

      You can manually add CUDA. Once CUDA is loaded you can move any array to the GPU with the cu function (or the gpu function exported by \`Lux\`\`), and it supports all of the above operations with the same syntax.

      julia
      using LuxCUDA, LuxAMDGPU
+
+if LuxCUDA.functional()
+    x_cu = cu(rand(5, 3))
+    @show x_cu
+elseif LuxAMDGPU.functional() # Similarly, for AMDGPU
+    x_amd = roc(rand(5, 3))
+    @show x_amd
+end
      5×3 CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}:
+ 0.857126  0.681728  0.73806
+ 0.191956  0.506485  0.622865
+ 0.857257  0.663036  0.239756
+ 0.54452   0.503186  0.27993
+ 0.833518  0.975649  0.967811

      (Im)mutability ​

      Lux as you might have read is Immutable by convention which means that the core library is built without any form of mutation and all functions are pure. However, we don't enforce it in any form. We do strongly recommend that users extending this framework for their respective applications don't mutate their arrays.

      julia
      x = reshape(1:8, 2, 4)
      2×4 reshape(::UnitRange{Int64}, 2, 4) with eltype Int64:
+ 1  3  5  7
+ 2  4  6  8

      To update this array, we should first copy the array.

      julia
      x_copy = copy(x)
+view(x_copy, :, 1) .= 0
+
+println("Original Array ", x)
+println("Mutated Array ", x_copy)
      Original Array [1 3 5 7; 2 4 6 8]
+Mutated Array [0 3 5 7; 0 4 6 8]

      Note that our current default AD engine (Zygote) is unable to differentiate through this mutation, however, for these specialized cases it is quite trivial to write custom backward passes. (This problem will be fixed once we move towards Enzyme.jl)

      Managing Randomness ​

      We rely on the Julia StdLib Random for managing the randomness in our execution. First, we create an PRNG (pseudorandom number generator) and seed it.

      julia
      rng = Xoshiro(0)     # Creates a Xoshiro PRNG with seed 0
      Random.Xoshiro(0xdb2fa90498613fdf, 0x48d73dc42d195740, 0x8c49bc52dc8a77ea, 0x1911b814c02405e8, 0x22a21880af5dc689)

      If we call any function that relies on rng and uses it via randn, rand, etc. rng will be mutated. As we have already established we care a lot about immutability, hence we should use Lux.replicate on PRNGs before using them.

      First, let us run a random number generator 3 times with the replicated rng.

      julia
      random_vectors = Vector{Vector{Float64}}(undef, 3)
+for i in 1:3
+    random_vectors[i] = rand(Lux.replicate(rng), 10)
+    println("Iteration $i ", random_vectors[i])
+end
+@assert random_vectors[1] ≈ random_vectors[2] ≈ random_vectors[3]
      Iteration 1 [0.4552384158732863, 0.5476424498276177, 0.7733535276924052, 0.9405848223512736, 0.02964765308691042, 0.74694291453392, 0.7468008914093891, 0.9766699015845924, 0.08694684883050086, 0.35149138733595564]
+Iteration 2 [0.4552384158732863, 0.5476424498276177, 0.7733535276924052, 0.9405848223512736, 0.02964765308691042, 0.74694291453392, 0.7468008914093891, 0.9766699015845924, 0.08694684883050086, 0.35149138733595564]
+Iteration 3 [0.4552384158732863, 0.5476424498276177, 0.7733535276924052, 0.9405848223512736, 0.02964765308691042, 0.74694291453392, 0.7468008914093891, 0.9766699015845924, 0.08694684883050086, 0.35149138733595564]

      As expected we get the same output. We can remove the replicate call and we will get different outputs.

      julia
      for i in 1:3
+    println("Iteration $i ", rand(rng, 10))
+end
      Iteration 1 [0.4552384158732863, 0.5476424498276177, 0.7733535276924052, 0.9405848223512736, 0.02964765308691042, 0.74694291453392, 0.7468008914093891, 0.9766699015845924, 0.08694684883050086, 0.35149138733595564]
+Iteration 2 [0.018743665453639813, 0.8601828553599953, 0.6556360448565952, 0.7746656838366666, 0.7817315740767116, 0.5553797706980106, 0.1261990389976131, 0.4488101521328277, 0.624383955429775, 0.05657739601024536]
+Iteration 3 [0.19597391412112541, 0.6830945313415872, 0.6776220912718907, 0.6456416023530093, 0.6340362477836592, 0.5595843665394066, 0.5675557670686644, 0.34351700231383653, 0.7237308297251812, 0.3691778381831775]

      Automatic Differentiation ​

      Julia has quite a few (maybe too many) AD tools. For the purpose of this tutorial, we will use:

      1. ForwardDiff.jl – For Jacobian-Vector Product (JVP)

      2. Zygote.jl – For Vector-Jacobian Product (VJP)

      Slight Detour: We have had several questions regarding if we will be considering any other AD system for the reverse-diff backend. For now we will stick to Zygote.jl, however once we have tested Lux extensively with Enzyme.jl, we will make the switch.

      Even though, theoretically, a VJP (Vector-Jacobian product - reverse autodiff) and a JVP (Jacobian-Vector product - forward-mode autodiff) are similar—they compute a product of a Jacobian and a vector—they differ by the computational complexity of the operation. In short, when you have a large number of parameters (hence a wide matrix), a JVP is less efficient computationally than a VJP, and, conversely, a JVP is more efficient when the Jacobian matrix is a tall matrix.

      julia
      using ComponentArrays, ForwardDiff, Zygote

      Gradients ​

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      julia
      f(x) = x' * x / 2
+∇f(x) = x  # \`∇\` can be typed as \`\\nabla<TAB>\`
+v = randn(rng, Float32, 4)
      4-element Vector{Float32}:
+ -0.4051151
+ -0.4593922
+  0.92155594
+  1.1871622

      Let's use ForwardDiff and Zygote to compute the gradients.

      julia
      println("Actual Gradient: ", ∇f(v))
+println("Computed Gradient via Reverse Mode AD (Zygote): ", only(Zygote.gradient(f, v)))
+println("Computed Gradient via Forward Mode AD (ForwardDiff): ", ForwardDiff.gradient(f, v))
      Actual Gradient: Float32[-0.4051151, -0.4593922, 0.92155594, 1.1871622]
+Computed Gradient via Reverse Mode AD (Zygote): Float32[-0.4051151, -0.4593922, 0.92155594, 1.1871622]
+Computed Gradient via Forward Mode AD (ForwardDiff): Float32[-0.4051151, -0.4593922, 0.92155594, 1.1871622]

      Note that AD.gradient will only work for scalar valued outputs.

      Jacobian-Vector Product ​

      I will defer the discussion on forward-mode AD to https://book.sciml.ai/notes/08-Forward-Mode_Automatic_Differentiation_(AD)_via_High_Dimensional_Algebras/. Here let us just look at a mini example on how to use it.

      julia
      f(x) = x .* x ./ 2
+x = randn(rng, Float32, 5)
+v = ones(Float32, 5)
      5-element Vector{Float32}:
+ 1.0
+ 1.0
+ 1.0
+ 1.0
+ 1.0

      Construct the pushforward function. We will write out the function here but in practice we recommend using SparseDiffTools.auto_jacvec!

      First we need to create a Tag for ForwardDiff. It is enough to know that this is something that you must do. For more details, see the ForwardDiff Documentation!

      julia
      struct TestTag end

      Going in the details of what is function is doing is beyond the scope of this tutorial. But in short, it is constructing a new Dual Vector with the partials set to the input to the pushforward function. When this is propagated through the original function we get the value and the jvp

      julia
      function pushforward_forwarddiff(f, x)
+    T = eltype(x)
+    function pushforward(v)
+        v_ = reshape(v, axes(x))
+        y = ForwardDiff.Dual{
+            ForwardDiff.Tag{TestTag, T}, T, 1}.(x, ForwardDiff.Partials.(tuple.(v_)))
+        res = vec(f(y))
+        return ForwardDiff.value.(res), vec(ForwardDiff.partials.(res, 1))
+    end
+    return pushforward
+end
+
+pf_f = pushforward_forwarddiff(f, x)
      (::Main.var"##225".var"#pushforward#1"{typeof(Main.var"##225".f), Vector{Float32}, DataType}) (generic function with 1 method)

      Compute the jvp.

      julia
      val, jvp = pf_f(v)
+println("Computed Value: f(", x, ") = ", val)
+println("JVP: ", jvp[1])
      Computed Value: f(Float32[-0.877497, 1.1953009, -0.057005208, 0.25055695, 0.09351656]) = Float32[0.3850005, 0.71437216, 0.0016247969, 0.031389393, 0.0043726736]
+JVP: -0.877497

      Vector-Jacobian Product ​

      Using the same function and inputs, let us compute the VJP.

      julia
      val, pb_f = Zygote.pullback(f, x)
      (Float32[0.3850005, 0.71437216, 0.0016247969, 0.031389393, 0.0043726736], Zygote.var"#75#76"{Zygote.Pullback{Tuple{typeof(Main.var"##225".f), Vector{Float32}}, Tuple{Zygote.var"#3796#back#1207"{Zygote.var"#1203#1206"{Vector{Float32}, Vector{Float32}}}, Zygote.var"#3860#back#1233"{Zygote.ZBack{ChainRules.var"#slash_pullback_scalar#1558"{Vector{Float32}, Int64}}}, Zygote.Pullback{Tuple{typeof(Base.Broadcast.materialize), Vector{Float32}}, Tuple{}}}}}(∂(f)))

      Compute the vjp.

      julia
      vjp = only(pb_f(v))
+println("Computed Value: f(", x, ") = ", val)
+println("VJP: ", vjp[1])
      Computed Value: f(Float32[-0.877497, 1.1953009, -0.057005208, 0.25055695, 0.09351656]) = Float32[0.3850005, 0.71437216, 0.0016247969, 0.031389393, 0.0043726736]
+VJP: -0.877497

      Linear Regression ​

      `,27),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},y={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"40.51ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 17905.2 1000","aria-hidden":"true"},F=t('',1),C=[F],b=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 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      We can write f from scratch, but to demonstrate Lux, let us use the Dense layer.

      julia
      model = Dense(10 => 5)
+
+rng = Random.default_rng()
+Random.seed!(rng, 0)
      Random.TaskLocalRNG()

      Let us initialize the parameters and states (in this case it is empty) for the model.

      julia
      ps, st = Lux.setup(rng, model)
+ps = ps |> ComponentArray
      ComponentVector{Float32}(weight = Float32[-0.5583162 0.3457679 0.50863314 0.60294497 0.23095794 0.16602759 5.5791984f-6 0.61324424 -0.35419345 0.039559156; -0.05661944 -0.4899126 0.31236076 0.47100115 -0.5062956 -0.20445547 -0.03762182 0.5370978 0.22614014 0.27704597; 0.5198015 0.55730057 -0.34535396 -0.21587563 -0.12729146 -0.51019937 0.46597028 0.2918885 0.20849374 -0.4068233; 0.06026341 -0.11202827 0.31218112 0.14536527 -0.3413506 0.40088427 -0.48716235 -0.15096173 0.42526972 -0.3576447; 0.23414856 -0.5949539 -0.26137677 0.21756552 0.34443143 0.25046515 -0.049256783 -0.48404032 0.08254115 -0.5224755], bias = Float32[0.0; 0.0; 0.0; 0.0; 0.0;;])

      Set problem dimensions.

      julia
      n_samples = 20
+x_dim = 10
+y_dim = 5
      5

      Generate random ground truth W and b.

      julia
      W = randn(rng, Float32, y_dim, x_dim)
+b = randn(rng, Float32, y_dim)
      5-element Vector{Float32}:
+  0.68468636
+ -0.57578707
+  0.0594993
+ -0.9436797
+  1.5164032

      Generate samples with additional noise.

      julia
      x_samples = randn(rng, Float32, x_dim, n_samples)
+y_samples = W * x_samples .+ b .+ 0.01f0 .* randn(rng, Float32, y_dim, n_samples)
+println("x shape: ", size(x_samples), "; y shape: ", size(y_samples))
      x shape: (10, 20); y shape: (5, 20)

      For updating our parameters let's use Optimisers.jl. We will use Stochastic Gradient Descent (SGD) with a learning rate of 0.01.

      julia
      using Optimisers
+
+opt = Optimisers.Descent(0.01f0)
      Descent(0.01f0)

      Initialize the initial state of the optimiser

      julia
      opt_state = Optimisers.setup(opt, ps)
      Leaf(Descent(0.01), nothing)

      Define the loss function

      julia
      function mse(model, ps, st, X, y)
+    y_pred, st_new = model(X, ps, st)
+    return sum(abs2, y_pred .- y), st_new
+end
+mse(weight, bias, X, y) = sum(abs2, weight * X .+ bias .- y)
+loss_function(ps, X, y) = mse(model, ps, st, X, y)
+
+println("Loss Value with ground true parameters: ", mse(W, b, x_samples, y_samples))
+
+for i in 1:100
+    # In actual code, don't use globals. But here I will simply for the sake of
+    # demonstration
+    global ps, st, opt_state
+    # Compute the gradient using the pullback API to update the states
+    (loss, st), pb_f = Zygote.pullback(loss_function, ps, x_samples, y_samples)
+    # We pass nothing as the seed for \`st\`, since we don't want to propagate any gradient
+    # for st
+    gs = pb_f((one(loss), nothing))[1]
+    # Update model parameters
+    # \`Optimisers.update\` can be used if mutation is not desired
+    opt_state, ps = Optimisers.update!(opt_state, ps, gs)
+    (i % 10 == 1 || i == 100) && println(lazy"Loss Value after $i iterations: $loss")
+end
      Loss Value with ground true parameters: 0.009175307
+┌ Warning: Assignment to \`pb_f\` in soft scope is ambiguous because a global variable by the same name exists: \`pb_f\` will be treated as a new local. Disambiguate by using \`local pb_f\` to suppress this warning or \`global pb_f\` to assign to the existing global variable.
+└ @ /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/docs/src/tutorials/beginner/1_Basics.md:15
+Loss Value after 1 iterations: 812.3374
+Loss Value after 11 iterations: 5.479181
+Loss Value after 21 iterations: 0.806523
+Loss Value after 31 iterations: 0.1775011
+Loss Value after 41 iterations: 0.046897847
+Loss Value after 51 iterations: 0.015412594
+Loss Value after 61 iterations: 0.007253055
+Loss Value after 71 iterations: 0.0050410302
+Loss Value after 81 iterations: 0.0044205473
+Loss Value after 91 iterations: 0.004241652
+Loss Value after 100 iterations: 0.0041917767

      Appendix ​

      julia
      using InteractiveUtils
+InteractiveUtils.versioninfo()
+if @isdefined(LuxCUDA) && CUDA.functional(); println(); CUDA.versioninfo(); end
+if @isdefined(LuxAMDGPU) && LuxAMDGPU.functional(); println(); AMDGPU.versioninfo(); end
      Julia Version 1.10.2
+Commit bd47eca2c8a (2024-03-01 10:14 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 48 × AMD EPYC 7402 24-Core Processor
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
+Threads: 48 default, 0 interactive, 24 GC (on 2 virtual cores)
+Environment:
+  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
+  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6
+  JULIA_PROJECT = /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/docs
+  JULIA_AMDGPU_LOGGING_ENABLED = true
+  JULIA_DEBUG = Literate
+  JULIA_CPU_THREADS = 2
+  JULIA_NUM_THREADS = 48
+  JULIA_LOAD_PATH = @:@v#.#:@stdlib
+  JULIA_CUDA_HARD_MEMORY_LIMIT = 25%
+
+CUDA runtime 12.3, artifact installation
+CUDA driver 12.4
+NVIDIA driver 550.54.15
+
+CUDA libraries: 
+- CUBLAS: 12.3.4
+- CURAND: 10.3.4
+- CUFFT: 11.0.12
+- CUSOLVER: 11.5.4
+- CUSPARSE: 12.2.0
+- CUPTI: 21.0.0
+- NVML: 12.0.0+550.54.15
+
+Julia packages: 
+- CUDA: 5.2.0
+- CUDA_Driver_jll: 0.7.0+1
+- CUDA_Runtime_jll: 0.11.1+0
+
+Toolchain:
+- Julia: 1.10.2
+- LLVM: 15.0.7
+
+Environment:
+- JULIA_CUDA_HARD_MEMORY_LIMIT: 25%
+
+1 device:
+  0: NVIDIA A100-PCIE-40GB MIG 1g.5gb (sm_80, 4.518 GiB / 4.750 GiB available)
+┌ Warning: LuxAMDGPU is loaded but the AMDGPU is not functional.
+└ @ LuxAMDGPU ~/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6/packages/LuxAMDGPU/sGa0S/src/LuxAMDGPU.jl:19

      This page was generated using Literate.jl.

      `,29);function S(O,W,N,z,X,$){return i(),a("div",null,[p,s("p",null,[n("For our first example, consider a simple function computing "),s("mjx-container",h,[(i(),a("svg",d,k)),o]),n(", where "),s("mjx-container",c,[(i(),a("svg",Q,g)),u])]),E,s("p",null,[n("Finally, now let us consider a linear regression problem. From a set of data-points "),s("mjx-container",m,[(i(),a("svg",y,C)),b]),n(", we try to find a set of parameters "),s("mjx-container",v,[(i(),a("svg",f,x)),D]),n(" and "),s("mjx-container",A,[(i(),a("svg",_,H)),B]),n(", s.t. 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      Fitting a Polynomial using MLP ​

      In this tutorial we will fit a MultiLayer Perceptron (MLP) on data generated from a polynomial.

      Package Imports ​

      julia
      using Lux, ADTypes, LuxAMDGPU, LuxCUDA, Optimisers, Printf, Random, Statistics, Zygote
+using CairoMakie

      Dataset ​

      `,5),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.599ex",height:"2.351ex",role:"img",focusable:"false",viewBox:"0 -833.9 5126.6 1038.9","aria-hidden":"true"},h=s('',1),k=[h],r=A("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[A("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[A("mi",null,"y"),A("mo",null,"="),A("msup",null,[A("mi",null,"x"),A("mn",null,"2")]),A("mo",null,"−"),A("mn",null,"2"),A("mi",null,"x")])],-1),d=s(`
      julia
      function generate_data(rng::AbstractRNG)
+    x = reshape(collect(range(-2.0f0, 2.0f0, 128)), (1, 128))
+    y = evalpoly.(x, ((0, -2, 1),)) .+ randn(rng, (1, 128)) .* 0.1f0
+    return (x, y)
+end
      generate_data (generic function with 1 method)

      Initialize the random number generator and fetch the dataset.

      julia
      rng = MersenneTwister()
+Random.seed!(rng, 12345)
+
+(x, y) = generate_data(rng)
      (Float32[-2.0 -1.968504 -1.9370079 -1.9055119 -1.8740157 -1.8425196 -1.8110236 -1.7795275 -1.7480315 -1.7165354 -1.6850394 -1.6535434 -1.6220472 -1.5905511 -1.5590551 -1.527559 -1.496063 -1.464567 -1.4330709 -1.4015749 -1.3700787 -1.3385826 -1.3070866 -1.2755905 -1.2440945 -1.2125984 -1.1811024 -1.1496063 -1.1181102 -1.0866141 -1.0551181 -1.023622 -0.992126 -0.96062994 -0.92913383 -0.8976378 -0.86614174 -0.8346457 -0.8031496 -0.77165353 -0.7401575 -0.70866144 -0.6771653 -0.6456693 -0.61417323 -0.5826772 -0.5511811 -0.51968503 -0.48818898 -0.4566929 -0.42519686 -0.39370078 -0.36220473 -0.33070865 -0.2992126 -0.26771653 -0.23622048 -0.20472442 -0.17322835 -0.14173229 -0.11023622 -0.07874016 -0.047244094 -0.015748031 0.015748031 0.047244094 0.07874016 0.11023622 0.14173229 0.17322835 0.20472442 0.23622048 0.26771653 0.2992126 0.33070865 0.36220473 0.39370078 0.42519686 0.4566929 0.48818898 0.51968503 0.5511811 0.5826772 0.61417323 0.6456693 0.6771653 0.70866144 0.7401575 0.77165353 0.8031496 0.8346457 0.86614174 0.8976378 0.92913383 0.96062994 0.992126 1.023622 1.0551181 1.0866141 1.1181102 1.1496063 1.1811024 1.2125984 1.2440945 1.2755905 1.3070866 1.3385826 1.3700787 1.4015749 1.4330709 1.464567 1.496063 1.527559 1.5590551 1.5905511 1.6220472 1.6535434 1.6850394 1.7165354 1.7480315 1.7795275 1.8110236 1.8425196 1.8740157 1.9055119 1.9370079 1.968504 2.0], [8.11723579535073 7.8972862806322315 7.667572185253954 7.493641443881164 7.328542256257643 7.1081451188446065 6.754145700236098 6.73844851250885 6.698323804024227 6.3637494708272655 6.270117709011731 6.2419372753805 5.816280759896085 5.718319527208828 5.741347639508506 5.258118446989299 5.268165780092538 5.195746082529355 5.032704772846244 4.733409783966572 4.520239616672976 4.369386593776045 4.107888442446331 4.182845399340577 4.002249800810884 3.8969011895086174 3.910820824989613 3.646440085736948 3.3343752660206305 3.3980378243437745 3.1887817476268587 2.9930802717826603 3.018980452144523 2.690492107796345 2.8576513349182378 2.4778283273281008 2.452401424624867 2.401875695877283 2.2896425232872755 2.2812518842985035 1.9742292519472466 1.7663454774622869 1.7829663021691418 1.6248666914928798 1.635090436697959 1.4887378757184528 1.4396068206428336 1.5047223947023354 1.2439428212858357 1.1770575798169982 1.0519113712665473 0.8008025630753797 0.8011788202541421 0.7702484835053167 0.9010273188596704 0.48114290312426095 0.4605012716399809 0.42308333113261615 0.2890108900859864 0.3324716507588617 0.2126899641074972 0.2560113968739265 0.08350192481301627 0.046225582753114294 -0.16118930624459 -0.013928769802494537 -0.030805824695545894 -0.10629780224701328 -0.17643440564041185 -0.2494508100897751 -0.3322350480467481 -0.45414851684613733 -0.6965624404632386 -0.38861245182183696 -0.4708530312086873 -0.6274991143463677 -0.5617763080815885 -0.6438360803492721 -0.7565600800322707 -0.5662591600023589 -0.6591533520776037 -0.9166793344639054 -0.8520467822193756 -0.9507226194240974 -1.0248823046771698 -0.97772916365376 -0.8199294436184201 -0.9080088282844027 -0.9682665790685976 -1.031816361263047 -0.9296919748814573 -1.1145618706755287 -1.2139119971536336 -1.0157839085777947 -0.9417175810509869 -0.9783498813733602 -0.9123675448444001 -1.138088633455826 -1.1212038088290894 -0.911429094488635 -1.023486657428913 -0.9287179111905346 -1.0396518660677925 -1.0370046468920306 -0.9846375721966646 -0.833026219703481 -0.8200258902651266 -0.789500663251252 -0.9068267920931062 -0.7284236770750803 -0.7093213401368348 -0.7048862544448803 -0.6215870033126495 -0.5892481295457608 -0.8462913756395639 -0.5544688796856879 -0.5805399434794658 -0.5761396334948753 -0.5851955365208916 -0.5561461874821676 -0.1969227628706652 -0.34073487813889014 -0.2738635064414512 -0.1425063756241582 -0.18330825579933746 -0.054321035831595324 -0.21213293699653427 0.049985105882301])

      Let's visualize the dataset

      julia
      begin
+    fig = Figure()
+    ax = CairoMakie.Axis(fig[1, 1]; xlabel="x", ylabel="y")
+
+    l = lines!(ax, x[1, :], x -> evalpoly(x, (0, -2, 1)); linewidth=3, color=:blue)
+    s = scatter!(ax, x[1, :], y[1, :]; markersize=12, alpha=0.5,
+        color=:orange, strokecolor=:black, strokewidth=2)
+
+    axislegend(ax, [l, s], ["True Quadratic Function", "Data Points"])
+
+    fig
+end

      Neural Network ​

      For this problem, you should not be using a neural network. But let's still do that!

      julia
      model = Chain(Dense(1 => 16, relu), Dense(16 => 1))
      Chain(
+    layer_1 = Dense(1 => 16, relu),     # 32 parameters
+    layer_2 = Dense(16 => 1),           # 17 parameters
+)         # Total: 49 parameters,
+          #        plus 0 states.

      Optimizer ​

      We will use Adam from Optimisers.jl

      julia
      opt = Adam(0.03f0)
      Adam(0.03, (0.9, 0.999), 1.0e-8)

      Loss Function ​

      We will use the Lux.Training API so we need to ensure that our loss function takes 4 inputs – model, parameters, states and data. The function must return 3 values – loss, updated_state, and any computed statistics.

      julia
      function loss_function(model, ps, st, data)
+    y_pred, st = Lux.apply(model, data[1], ps, st)
+    mse_loss = mean(abs2, y_pred .- data[2])
+    return mse_loss, st, ()
+end
      loss_function (generic function with 1 method)

      Training ​

      First we will create a Lux.Experimental.TrainState which is essentially a convenience wrapper over parameters, states and optimizer states.

      julia
      tstate = Lux.Experimental.TrainState(rng, model, opt)
      Lux.Experimental.TrainState{Lux.Chain{@NamedTuple{layer_1::Lux.Dense{true, typeof(NNlib.relu), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_2::Lux.Dense{true, typeof(identity), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing}, @NamedTuple{layer_1::@NamedTuple{weight::CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, bias::CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}}, layer_2::@NamedTuple{weight::CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, bias::CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}}}, @NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}}, @NamedTuple{layer_1::@NamedTuple{weight::Optimisers.Leaf{Optimisers.Adam, Tuple{CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, Tuple{Float32, Float32}}}, bias::Optimisers.Leaf{Optimisers.Adam, Tuple{CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, Tuple{Float32, Float32}}}}, layer_2::@NamedTuple{weight::Optimisers.Leaf{Optimisers.Adam, Tuple{CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, Tuple{Float32, Float32}}}, bias::Optimisers.Leaf{Optimisers.Adam, Tuple{CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, Tuple{Float32, Float32}}}}}}(Chain(), (layer_1 = (weight = Float32[0.36222202; 0.23371002; -0.49825558; -0.18142056; -0.13757975; -0.50849473; 0.13773328; -0.035294008; 0.21778254; 0.04964345; -0.56594235; -0.45329624; -0.08787567; 0.5648949; 0.5260752; -0.07562564;;], bias = Float32[0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0;;]), layer_2 = (weight = Float32[-0.14330137 -0.39328107 -0.18253882 -0.55998546 -0.5919335 -0.3069779 -0.39085856 -0.4838621 0.3979575 0.5851314 0.24242708 0.35374007 0.10175798 0.29761198 -0.34761065 -0.05758927], bias = Float32[0.0;;])), (layer_1 = NamedTuple(), layer_2 = NamedTuple()), (layer_1 = (weight = Leaf(Adam(0.03, (0.9, 0.999), 1.0e-8), (Float32[0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0;;], Float32[0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0;;], (0.9, 0.999))), bias = Leaf(Adam(0.03, (0.9, 0.999), 1.0e-8), (Float32[0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0;;], Float32[0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0;;], (0.9, 0.999)))), layer_2 = (weight = Leaf(Adam(0.03, (0.9, 0.999), 1.0e-8), (Float32[0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0], Float32[0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0], (0.9, 0.999))), bias = Leaf(Adam(0.03, (0.9, 0.999), 1.0e-8), (Float32[0.0;;], Float32[0.0;;], (0.9, 0.999))))), 0)

      Now we will use Zygote for our AD requirements.

      julia
      vjp_rule = AutoZygote()
      ADTypes.AutoZygote()

      Finally the training loop.

      julia
      function main(tstate::Lux.Experimental.TrainState, vjp, data, epochs)
+    data = data .|> gpu_device()
+    for epoch in 1:epochs
+        grads, loss, stats, tstate = Lux.Training.compute_gradients(
+            vjp, loss_function, data, tstate)
+        if epoch % 50 == 1 || epoch == epochs
+            @printf "Epoch: %3d \\t Loss: %.5g\\n" epoch loss
+        end
+        tstate = Lux.Training.apply_gradients(tstate, grads)
+    end
+    return tstate
+end
+
+dev_cpu = cpu_device()
+dev_gpu = gpu_device()
+
+tstate = main(tstate, vjp_rule, (x, y), 250)
+y_pred = dev_cpu(Lux.apply(tstate.model, dev_gpu(x), tstate.parameters, tstate.states)[1])
      Epoch:   1 	 Loss: 9.4373
+Epoch:  51 	 Loss: 0.086228
+Epoch: 101 	 Loss: 0.033642
+Epoch: 151 	 Loss: 0.021989
+Epoch: 201 	 Loss: 0.017344
+Epoch: 250 	 Loss: 0.013794

      Let's plot the results

      julia
      begin
+    fig = Figure()
+    ax = CairoMakie.Axis(fig[1, 1]; xlabel="x", ylabel="y")
+
+    l = lines!(ax, x[1, :], x -> evalpoly(x, (0, -2, 1)); linewidth=3)
+    s1 = scatter!(ax, x[1, :], y[1, :]; markersize=12, alpha=0.5,
+        color=:orange, strokecolor=:black, strokewidth=2)
+    s2 = scatter!(ax, x[1, :], y_pred[1, :]; markersize=12, alpha=0.5,
+        color=:green, strokecolor=:black, strokewidth=2)
+
+    axislegend(ax, [l, s1, s2], ["True Quadratic Function", "Actual Data", "Predictions"])
+
+    fig
+end

      Appendix ​

      julia
      using InteractiveUtils
+InteractiveUtils.versioninfo()
+if @isdefined(LuxCUDA) && CUDA.functional(); println(); CUDA.versioninfo(); end
+if @isdefined(LuxAMDGPU) && LuxAMDGPU.functional(); println(); AMDGPU.versioninfo(); end
      Julia Version 1.10.2
+Commit bd47eca2c8a (2024-03-01 10:14 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 48 × AMD EPYC 7402 24-Core Processor
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
+Threads: 48 default, 0 interactive, 24 GC (on 2 virtual cores)
+Environment:
+  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
+  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6
+  JULIA_PROJECT = /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/docs
+  JULIA_AMDGPU_LOGGING_ENABLED = true
+  JULIA_DEBUG = Literate
+  JULIA_CPU_THREADS = 2
+  JULIA_NUM_THREADS = 48
+  JULIA_LOAD_PATH = @:@v#.#:@stdlib
+  JULIA_CUDA_HARD_MEMORY_LIMIT = 25%
+
+CUDA runtime 12.3, artifact installation
+CUDA driver 12.4
+NVIDIA driver 550.54.15
+
+CUDA libraries: 
+- CUBLAS: 12.3.4
+- CURAND: 10.3.4
+- CUFFT: 11.0.12
+- CUSOLVER: 11.5.4
+- CUSPARSE: 12.2.0
+- CUPTI: 21.0.0
+- NVML: 12.0.0+550.54.15
+
+Julia packages: 
+- CUDA: 5.2.0
+- CUDA_Driver_jll: 0.7.0+1
+- CUDA_Runtime_jll: 0.11.1+0
+
+Toolchain:
+- Julia: 1.10.2
+- LLVM: 15.0.7
+
+Environment:
+- JULIA_CUDA_HARD_MEMORY_LIMIT: 25%
+
+1 device:
+  0: NVIDIA A100-PCIE-40GB MIG 1g.5gb (sm_80, 4.600 GiB / 4.750 GiB available)
+┌ Warning: LuxAMDGPU is loaded but the AMDGPU is not functional.
+└ @ LuxAMDGPU ~/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6/packages/LuxAMDGPU/sGa0S/src/LuxAMDGPU.jl:19

      This page was generated using Literate.jl.

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      Training a Simple LSTM ​

      In this tutorial we will go over using a recurrent neural network to classify clockwise and anticlockwise spirals. By the end of this tutorial you will be able to:

      1. Create custom Lux models.

      2. Become familiar with the Lux recurrent neural network API.

      3. Training using Optimisers.jl and Zygote.jl.

      Package Imports ​

      julia
      using ADTypes, Lux, LuxAMDGPU, LuxCUDA, JLD2, MLUtils, Optimisers, Zygote, Printf, Random,
+      Statistics

      Dataset ​

      We will use MLUtils to generate 500 (noisy) clockwise and 500 (noisy) anticlockwise spirals. Using this data we will create a MLUtils.DataLoader. Our dataloader will give us sequences of size 2 × seq_len × batch_size and we need to predict a binary value whether the sequence is clockwise or anticlockwise.

      julia
      function get_dataloaders(; dataset_size=1000, sequence_length=50)
+    # Create the spirals
+    data = [MLUtils.Datasets.make_spiral(sequence_length) for _ in 1:dataset_size]
+    # Get the labels
+    labels = vcat(repeat([0.0f0], dataset_size ÷ 2), repeat([1.0f0], dataset_size ÷ 2))
+    clockwise_spirals = [reshape(d[1][:, 1:sequence_length], :, sequence_length, 1)
+                         for d in data[1:(dataset_size ÷ 2)]]
+    anticlockwise_spirals = [reshape(
+                                 d[1][:, (sequence_length + 1):end], :, sequence_length, 1)
+                             for d in data[((dataset_size ÷ 2) + 1):end]]
+    x_data = Float32.(cat(clockwise_spirals..., anticlockwise_spirals...; dims=3))
+    # Split the dataset
+    (x_train, y_train), (x_val, y_val) = splitobs((x_data, labels); at=0.8, shuffle=true)
+    # Create DataLoaders
+    return (
+        # Use DataLoader to automatically minibatch and shuffle the data
+        DataLoader(collect.((x_train, y_train)); batchsize=128, shuffle=true),
+        # Don't shuffle the validation data
+        DataLoader(collect.((x_val, y_val)); batchsize=128, shuffle=false))
+end
      get_dataloaders (generic function with 1 method)

      Creating a Classifier ​

      We will be extending the Lux.AbstractExplicitContainerLayer type for our custom model since it will contain a lstm block and a classifier head.

      We pass the fieldnames lstm_cell and classifier to the type to ensure that the parameters and states are automatically populated and we don't have to define Lux.initialparameters and Lux.initialstates.

      To understand more about container layers, please look at Container Layer.

      julia
      struct SpiralClassifier{L, C} <:
+       Lux.AbstractExplicitContainerLayer{(:lstm_cell, :classifier)}
+    lstm_cell::L
+    classifier::C
+end

      We won't define the model from scratch but rather use the Lux.LSTMCell and Lux.Dense.

      julia
      function SpiralClassifier(in_dims, hidden_dims, out_dims)
+    return SpiralClassifier(
+        LSTMCell(in_dims => hidden_dims), Dense(hidden_dims => out_dims, sigmoid))
+end
      Main.var"##225".SpiralClassifier

      We can use default Lux blocks – Recurrence(LSTMCell(in_dims => hidden_dims) – instead of defining the following. But let's still do it for the sake of it.

      Now we need to define the behavior of the Classifier when it is invoked.

      julia
      function (s::SpiralClassifier)(
+        x::AbstractArray{T, 3}, ps::NamedTuple, st::NamedTuple) where {T}
+    # First we will have to run the sequence through the LSTM Cell
+    # The first call to LSTM Cell will create the initial hidden state
+    # See that the parameters and states are automatically populated into a field called
+    # \`lstm_cell\` We use \`eachslice\` to get the elements in the sequence without copying,
+    # and \`Iterators.peel\` to split out the first element for LSTM initialization.
+    x_init, x_rest = Iterators.peel(Lux._eachslice(x, Val(2)))
+    (y, carry), st_lstm = s.lstm_cell(x_init, ps.lstm_cell, st.lstm_cell)
+    # Now that we have the hidden state and memory in \`carry\` we will pass the input and
+    # \`carry\` jointly
+    for x in x_rest
+        (y, carry), st_lstm = s.lstm_cell((x, carry), ps.lstm_cell, st_lstm)
+    end
+    # After running through the sequence we will pass the output through the classifier
+    y, st_classifier = s.classifier(y, ps.classifier, st.classifier)
+    # Finally remember to create the updated state
+    st = merge(st, (classifier=st_classifier, lstm_cell=st_lstm))
+    return vec(y), st
+end

      Defining Accuracy, Loss and Optimiser ​

      Now let's define the binarycrossentropy loss. Typically it is recommended to use logitbinarycrossentropy since it is more numerically stable, but for the sake of simplicity we will use binarycrossentropy.

      julia
      function xlogy(x, y)
+    result = x * log(y)
+    return ifelse(iszero(x), zero(result), result)
+end
+
+function binarycrossentropy(y_pred, y_true)
+    y_pred = y_pred .+ eps(eltype(y_pred))
+    return mean(@. -xlogy(y_true, y_pred) - xlogy(1 - y_true, 1 - y_pred))
+end
+
+function compute_loss(model, ps, st, (x, y))
+    y_pred, st = model(x, ps, st)
+    return binarycrossentropy(y_pred, y), st, (; y_pred=y_pred)
+end
+
+matches(y_pred, y_true) = sum((y_pred .> 0.5f0) .== y_true)
+accuracy(y_pred, y_true) = matches(y_pred, y_true) / length(y_pred)
      accuracy (generic function with 1 method)

      Training the Model ​

      julia
      function main()
+    # Get the dataloaders
+    (train_loader, val_loader) = get_dataloaders()
+
+    # Create the model
+    model = SpiralClassifier(2, 8, 1)
+    rng = Xoshiro(0)
+
+    dev = gpu_device()
+    train_state = Lux.Experimental.TrainState(
+        rng, model, Adam(0.01f0); transform_variables=dev)
+
+    for epoch in 1:25
+        # Train the model
+        for (x, y) in train_loader
+            x = x |> dev
+            y = y |> dev
+
+            gs, loss, _, train_state = Lux.Experimental.compute_gradients(
+                AutoZygote(), compute_loss, (x, y), train_state)
+            train_state = Lux.Experimental.apply_gradients(train_state, gs)
+
+            @printf "Epoch [%3d]: Loss %4.5f\\n" epoch loss
+        end
+
+        # Validate the model
+        st_ = Lux.testmode(train_state.states)
+        for (x, y) in val_loader
+            x = x |> dev
+            y = y |> dev
+            loss, st_, ret = compute_loss(model, train_state.parameters, st_, (x, y))
+            acc = accuracy(ret.y_pred, y)
+            @printf "Validation: Loss %4.5f Accuracy %4.5f\\n" loss acc
+        end
+    end
+
+    return (train_state.parameters, train_state.states) |> cpu_device()
+end
+
+ps_trained, st_trained = main()
      Epoch [  1]: Loss 0.56263
+Epoch [  1]: Loss 0.50622
+Epoch [  1]: Loss 0.46754
+Epoch [  1]: Loss 0.45518
+Epoch [  1]: Loss 0.43237
+Epoch [  1]: Loss 0.40357
+Epoch [  1]: Loss 0.37433
+Validation: Loss 0.36939 Accuracy 1.00000
+Validation: Loss 0.38321 Accuracy 1.00000
+Epoch [  2]: Loss 0.37481
+Epoch [  2]: Loss 0.35556
+Epoch [  2]: Loss 0.32647
+Epoch [  2]: Loss 0.32097
+Epoch [  2]: Loss 0.29943
+Epoch [  2]: Loss 0.28412
+Epoch [  2]: Loss 0.26005
+Validation: Loss 0.25919 Accuracy 1.00000
+Validation: Loss 0.26821 Accuracy 1.00000
+Epoch [  3]: Loss 0.26588
+Epoch [  3]: Loss 0.24159
+Epoch [  3]: Loss 0.23038
+Epoch [  3]: Loss 0.22152
+Epoch [  3]: Loss 0.20744
+Epoch [  3]: Loss 0.20136
+Epoch [  3]: Loss 0.18646
+Validation: Loss 0.18102 Accuracy 1.00000
+Validation: Loss 0.18637 Accuracy 1.00000
+Epoch [  4]: Loss 0.17623
+Epoch [  4]: Loss 0.16670
+Epoch [  4]: Loss 0.16627
+Epoch [  4]: Loss 0.15707
+Epoch [  4]: Loss 0.15225
+Epoch [  4]: Loss 0.14029
+Epoch [  4]: Loss 0.13672
+Validation: Loss 0.12918 Accuracy 1.00000
+Validation: Loss 0.13293 Accuracy 1.00000
+Epoch [  5]: Loss 0.12726
+Epoch [  5]: Loss 0.12789
+Epoch [  5]: Loss 0.11814
+Epoch [  5]: Loss 0.10943
+Epoch [  5]: Loss 0.10736
+Epoch [  5]: Loss 0.10008
+Epoch [  5]: Loss 0.09878
+Validation: Loss 0.09405 Accuracy 1.00000
+Validation: Loss 0.09701 Accuracy 1.00000
+Epoch [  6]: Loss 0.09387
+Epoch [  6]: Loss 0.08977
+Epoch [  6]: Loss 0.08546
+Epoch [  6]: Loss 0.08282
+Epoch [  6]: Loss 0.07942
+Epoch [  6]: Loss 0.07283
+Epoch [  6]: Loss 0.07509
+Validation: Loss 0.06955 Accuracy 1.00000
+Validation: Loss 0.07227 Accuracy 1.00000
+Epoch [  7]: Loss 0.06925
+Epoch [  7]: Loss 0.06594
+Epoch [  7]: Loss 0.06383
+Epoch [  7]: Loss 0.05994
+Epoch [  7]: Loss 0.05758
+Epoch [  7]: Loss 0.05775
+Epoch [  7]: Loss 0.05475
+Validation: Loss 0.05197 Accuracy 1.00000
+Validation: Loss 0.05449 Accuracy 1.00000
+Epoch [  8]: Loss 0.05228
+Epoch [  8]: Loss 0.05002
+Epoch [  8]: Loss 0.04655
+Epoch [  8]: Loss 0.04395
+Epoch [  8]: Loss 0.04409
+Epoch [  8]: Loss 0.04332
+Epoch [  8]: Loss 0.04139
+Validation: Loss 0.03915 Accuracy 1.00000
+Validation: Loss 0.04145 Accuracy 1.00000
+Epoch [  9]: Loss 0.03956
+Epoch [  9]: Loss 0.03666
+Epoch [  9]: Loss 0.03553
+Epoch [  9]: Loss 0.03384
+Epoch [  9]: Loss 0.03446
+Epoch [  9]: Loss 0.03219
+Epoch [  9]: Loss 0.02961
+Validation: Loss 0.02991 Accuracy 1.00000
+Validation: Loss 0.03203 Accuracy 1.00000
+Epoch [ 10]: Loss 0.03070
+Epoch [ 10]: Loss 0.02812
+Epoch [ 10]: Loss 0.02747
+Epoch [ 10]: Loss 0.02620
+Epoch [ 10]: Loss 0.02516
+Epoch [ 10]: Loss 0.02568
+Epoch [ 10]: Loss 0.02363
+Validation: Loss 0.02351 Accuracy 1.00000
+Validation: Loss 0.02541 Accuracy 1.00000
+Epoch [ 11]: Loss 0.02379
+Epoch [ 11]: Loss 0.02360
+Epoch [ 11]: Loss 0.02179
+Epoch [ 11]: Loss 0.02033
+Epoch [ 11]: Loss 0.02039
+Epoch [ 11]: Loss 0.01950
+Epoch [ 11]: Loss 0.02115
+Validation: Loss 0.01913 Accuracy 1.00000
+Validation: Loss 0.02080 Accuracy 1.00000
+Epoch [ 12]: Loss 0.01892
+Epoch [ 12]: Loss 0.01786
+Epoch [ 12]: Loss 0.01832
+Epoch [ 12]: Loss 0.01683
+Epoch [ 12]: Loss 0.01617
+Epoch [ 12]: Loss 0.01823
+Epoch [ 12]: Loss 0.01779
+Validation: Loss 0.01608 Accuracy 1.00000
+Validation: Loss 0.01752 Accuracy 1.00000
+Epoch [ 13]: Loss 0.01481
+Epoch [ 13]: Loss 0.01561
+Epoch [ 13]: Loss 0.01593
+Epoch [ 13]: Loss 0.01432
+Epoch [ 13]: Loss 0.01573
+Epoch [ 13]: Loss 0.01389
+Epoch [ 13]: Loss 0.01494
+Validation: Loss 0.01388 Accuracy 1.00000
+Validation: Loss 0.01514 Accuracy 1.00000
+Epoch [ 14]: Loss 0.01335
+Epoch [ 14]: Loss 0.01329
+Epoch [ 14]: Loss 0.01391
+Epoch [ 14]: Loss 0.01310
+Epoch [ 14]: Loss 0.01329
+Epoch [ 14]: Loss 0.01209
+Epoch [ 14]: Loss 0.01129
+Validation: Loss 0.01222 Accuracy 1.00000
+Validation: Loss 0.01335 Accuracy 1.00000
+Epoch [ 15]: Loss 0.01293
+Epoch [ 15]: Loss 0.01176
+Epoch [ 15]: Loss 0.01128
+Epoch [ 15]: Loss 0.01138
+Epoch [ 15]: Loss 0.01119
+Epoch [ 15]: Loss 0.01150
+Epoch [ 15]: Loss 0.01013
+Validation: Loss 0.01094 Accuracy 1.00000
+Validation: Loss 0.01196 Accuracy 1.00000
+Epoch [ 16]: Loss 0.01111
+Epoch [ 16]: Loss 0.01155
+Epoch [ 16]: Loss 0.01045
+Epoch [ 16]: Loss 0.01038
+Epoch [ 16]: Loss 0.00986
+Epoch [ 16]: Loss 0.00926
+Epoch [ 16]: Loss 0.01058
+Validation: Loss 0.00990 Accuracy 1.00000
+Validation: Loss 0.01085 Accuracy 1.00000
+Epoch [ 17]: Loss 0.00961
+Epoch [ 17]: Loss 0.00939
+Epoch [ 17]: Loss 0.01024
+Epoch [ 17]: Loss 0.00949
+Epoch [ 17]: Loss 0.00934
+Epoch [ 17]: Loss 0.00900
+Epoch [ 17]: Loss 0.00861
+Validation: Loss 0.00904 Accuracy 1.00000
+Validation: Loss 0.00990 Accuracy 1.00000
+Epoch [ 18]: Loss 0.00919
+Epoch [ 18]: Loss 0.00851
+Epoch [ 18]: Loss 0.00921
+Epoch [ 18]: Loss 0.00895
+Epoch [ 18]: Loss 0.00814
+Epoch [ 18]: Loss 0.00790
+Epoch [ 18]: Loss 0.00914
+Validation: Loss 0.00831 Accuracy 1.00000
+Validation: Loss 0.00911 Accuracy 1.00000
+Epoch [ 19]: Loss 0.00879
+Epoch [ 19]: Loss 0.00821
+Epoch [ 19]: Loss 0.00771
+Epoch [ 19]: Loss 0.00754
+Epoch [ 19]: Loss 0.00763
+Epoch [ 19]: Loss 0.00819
+Epoch [ 19]: Loss 0.00725
+Validation: Loss 0.00767 Accuracy 1.00000
+Validation: Loss 0.00842 Accuracy 1.00000
+Epoch [ 20]: Loss 0.00766
+Epoch [ 20]: Loss 0.00682
+Epoch [ 20]: Loss 0.00756
+Epoch [ 20]: Loss 0.00719
+Epoch [ 20]: Loss 0.00725
+Epoch [ 20]: Loss 0.00777
+Epoch [ 20]: Loss 0.00760
+Validation: Loss 0.00713 Accuracy 1.00000
+Validation: Loss 0.00783 Accuracy 1.00000
+Epoch [ 21]: Loss 0.00663
+Epoch [ 21]: Loss 0.00737
+Epoch [ 21]: Loss 0.00708
+Epoch [ 21]: Loss 0.00655
+Epoch [ 21]: Loss 0.00692
+Epoch [ 21]: Loss 0.00675
+Epoch [ 21]: Loss 0.00652
+Validation: Loss 0.00664 Accuracy 1.00000
+Validation: Loss 0.00730 Accuracy 1.00000
+Epoch [ 22]: Loss 0.00615
+Epoch [ 22]: Loss 0.00571
+Epoch [ 22]: Loss 0.00629
+Epoch [ 22]: Loss 0.00674
+Epoch [ 22]: Loss 0.00678
+Epoch [ 22]: Loss 0.00690
+Epoch [ 22]: Loss 0.00588
+Validation: Loss 0.00621 Accuracy 1.00000
+Validation: Loss 0.00684 Accuracy 1.00000
+Epoch [ 23]: Loss 0.00587
+Epoch [ 23]: Loss 0.00625
+Epoch [ 23]: Loss 0.00642
+Epoch [ 23]: Loss 0.00557
+Epoch [ 23]: Loss 0.00585
+Epoch [ 23]: Loss 0.00597
+Epoch [ 23]: Loss 0.00643
+Validation: Loss 0.00583 Accuracy 1.00000
+Validation: Loss 0.00642 Accuracy 1.00000
+Epoch [ 24]: Loss 0.00560
+Epoch [ 24]: Loss 0.00568
+Epoch [ 24]: Loss 0.00568
+Epoch [ 24]: Loss 0.00549
+Epoch [ 24]: Loss 0.00585
+Epoch [ 24]: Loss 0.00556
+Epoch [ 24]: Loss 0.00554
+Validation: Loss 0.00549 Accuracy 1.00000
+Validation: Loss 0.00604 Accuracy 1.00000
+Epoch [ 25]: Loss 0.00557
+Epoch [ 25]: Loss 0.00522
+Epoch [ 25]: Loss 0.00536
+Epoch [ 25]: Loss 0.00513
+Epoch [ 25]: Loss 0.00540
+Epoch [ 25]: Loss 0.00509
+Epoch [ 25]: Loss 0.00569
+Validation: Loss 0.00517 Accuracy 1.00000
+Validation: Loss 0.00570 Accuracy 1.00000

      Saving the Model ​

      We can save the model using JLD2 (and any other serialization library of your choice) Note that we transfer the model to CPU before saving. Additionally, we recommend that you don't save the model

      julia
      @save "trained_model.jld2" {compress = true} ps_trained st_trained

      Let's try loading the model

      julia
      @load "trained_model.jld2" ps_trained st_trained
      2-element Vector{Symbol}:
+ :ps_trained
+ :st_trained

      Appendix ​

      julia
      using InteractiveUtils
+InteractiveUtils.versioninfo()
+if @isdefined(LuxCUDA) && CUDA.functional(); println(); CUDA.versioninfo(); end
+if @isdefined(LuxAMDGPU) && LuxAMDGPU.functional(); println(); AMDGPU.versioninfo(); end
      Julia Version 1.10.2
+Commit bd47eca2c8a (2024-03-01 10:14 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 48 × AMD EPYC 7402 24-Core Processor
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
+Threads: 48 default, 0 interactive, 24 GC (on 2 virtual cores)
+Environment:
+  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
+  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6
+  JULIA_PROJECT = /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/docs
+  JULIA_AMDGPU_LOGGING_ENABLED = true
+  JULIA_DEBUG = Literate
+  JULIA_CPU_THREADS = 2
+  JULIA_NUM_THREADS = 48
+  JULIA_LOAD_PATH = @:@v#.#:@stdlib
+  JULIA_CUDA_HARD_MEMORY_LIMIT = 25%
+
+CUDA runtime 12.3, artifact installation
+CUDA driver 12.4
+NVIDIA driver 550.54.15
+
+CUDA libraries: 
+- CUBLAS: 12.3.4
+- CURAND: 10.3.4
+- CUFFT: 11.0.12
+- CUSOLVER: 11.5.4
+- CUSPARSE: 12.2.0
+- CUPTI: 21.0.0
+- NVML: 12.0.0+550.54.15
+
+Julia packages: 
+- CUDA: 5.2.0
+- CUDA_Driver_jll: 0.7.0+1
+- CUDA_Runtime_jll: 0.11.1+0
+
+Toolchain:
+- Julia: 1.10.2
+- LLVM: 15.0.7
+
+Environment:
+- JULIA_CUDA_HARD_MEMORY_LIMIT: 25%
+
+1 device:
+  0: NVIDIA A100-PCIE-40GB MIG 1g.5gb (sm_80, 4.141 GiB / 4.750 GiB available)
+┌ Warning: LuxAMDGPU is loaded but the AMDGPU is not functional.
+└ @ LuxAMDGPU ~/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6/packages/LuxAMDGPU/sGa0S/src/LuxAMDGPU.jl:19

      This page was generated using Literate.jl.

      `,38),h=[l];function e(t,k,c,E,r,d){return i(),a("div",null,h)}const y=s(p,[["render",e]]);export{g as __pageData,y as default}; diff --git a/v0.5.30/assets/tutorials_beginner_3_SimpleRNN.md.SS1AvA0i.lean.js b/v0.5.30/assets/tutorials_beginner_3_SimpleRNN.md.SS1AvA0i.lean.js new file mode 100644 index 000000000..706d05303 --- /dev/null +++ b/v0.5.30/assets/tutorials_beginner_3_SimpleRNN.md.SS1AvA0i.lean.js @@ -0,0 +1 @@ +import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.BfjuC5t1.js";const g=JSON.parse('{"title":"Training a Simple LSTM","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/beginner/3_SimpleRNN.md","filePath":"tutorials/beginner/3_SimpleRNN.md","lastUpdated":null}'),p={name:"tutorials/beginner/3_SimpleRNN.md"},l=n("",38),h=[l];function e(t,k,c,E,r,d){return i(),a("div",null,h)}const y=s(p,[["render",e]]);export{g as __pageData,y as default}; diff --git a/v0.5.30/assets/tutorials_beginner_4_SimpleChains.md.CoBtejGc.js b/v0.5.30/assets/tutorials_beginner_4_SimpleChains.md.CoBtejGc.js new file mode 100644 index 000000000..3f7d2566d --- /dev/null +++ b/v0.5.30/assets/tutorials_beginner_4_SimpleChains.md.CoBtejGc.js @@ -0,0 +1,115 @@ +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.BfjuC5t1.js";const y=JSON.parse('{"title":"MNIST Classification with SimpleChains","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/beginner/4_SimpleChains.md","filePath":"tutorials/beginner/4_SimpleChains.md","lastUpdated":null}'),t={name:"tutorials/beginner/4_SimpleChains.md"},l=n(`

      MNIST Classification with SimpleChains ​

      SimpleChains.jl is an excellent framework for training small neural networks. In this tutorial we will demonstrate how to use the same API as Lux.jl to train a model using SimpleChains.jl. We will use the tutorial from SimpleChains.jl as a reference.

      Package Imports ​

      julia
      using Lux, ADTypes, MLUtils, Optimisers, Zygote, OneHotArrays, Random, Statistics, Printf
+import MLDatasets: MNIST
+import SimpleChains: static

      Loading MNIST ​

      julia
      function loadmnist(batchsize, train_split)
+    # Load MNIST
+    N = 2000
+    dataset = MNIST(; split=:train)
+    imgs = dataset.features[:, :, 1:N]
+    labels_raw = dataset.targets[1:N]
+
+    # Process images into (H,W,C,BS) batches
+    x_data = Float32.(reshape(imgs, size(imgs, 1), size(imgs, 2), 1, size(imgs, 3)))
+    y_data = onehotbatch(labels_raw, 0:9)
+    (x_train, y_train), (x_test, y_test) = splitobs((x_data, y_data); at=train_split)
+
+    return (
+        # Use DataLoader to automatically minibatch and shuffle the data
+        DataLoader(collect.((x_train, y_train)); batchsize, shuffle=true),
+        # Don't shuffle the test data
+        DataLoader(collect.((x_test, y_test)); batchsize, shuffle=false))
+end
      loadmnist (generic function with 1 method)

      Define the Model ​

      julia
      lux_model = Chain(Conv((5, 5), 1 => 6, relu), MaxPool((2, 2)),
+    Conv((5, 5), 6 => 16, relu), MaxPool((2, 2)), FlattenLayer(3),
+    Chain(Dense(256 => 128, relu), Dense(128 => 84, relu), Dense(84 => 10)))
      Chain(
+    layer_1 = Conv((5, 5), 1 => 6, relu),  # 156 parameters
+    layer_2 = MaxPool((2, 2)),
+    layer_3 = Conv((5, 5), 6 => 16, relu),  # 2_416 parameters
+    layer_4 = MaxPool((2, 2)),
+    layer_5 = FlattenLayer(),
+    layer_6 = Dense(256 => 128, relu),  # 32_896 parameters
+    layer_7 = Dense(128 => 84, relu),   # 10_836 parameters
+    layer_8 = Dense(84 => 10),          # 850 parameters
+)         # Total: 47_154 parameters,
+          #        plus 0 states.

      We now need to convert the lux_model to SimpleChains.jl. We need to do this by defining the ToSimpleChainsAdaptor and providing the input dimensions.

      julia
      adaptor = ToSimpleChainsAdaptor((static(28), static(28), static(1)))
+simple_chains_model = adaptor(lux_model)
      SimpleChainsLayer()  # 47_154 parameters

      Helper Functions ​

      julia
      logitcrossentropy(y_pred, y) = mean(-sum(y .* logsoftmax(y_pred); dims=1))
+
+function loss(model, ps, st, (x, y))
+    y_pred, st = model(x, ps, st)
+    return logitcrossentropy(y_pred, y), st, (;)
+end
+
+function accuracy(model, ps, st, dataloader)
+    total_correct, total = 0, 0
+    st = Lux.testmode(st)
+    for (x, y) in dataloader
+        target_class = onecold(y)
+        predicted_class = onecold(Array(first(model(x, ps, st))))
+        total_correct += sum(target_class .== predicted_class)
+        total += length(target_class)
+    end
+    return total_correct / total
+end
      accuracy (generic function with 1 method)

      Define the Training Loop ​

      julia
      function train(model; rng=Xoshiro(0), kwargs...)
+    train_dataloader, test_dataloader = loadmnist(128, 0.9)
+
+    train_state = Lux.Experimental.TrainState(
+        rng, model, Adam(3.0f-4); transform_variables=identity)
+
+    ### Lets train the model
+    nepochs = 10
+    for epoch in 1:nepochs
+        stime = time()
+        for (x, y) in train_dataloader
+            (gs, _, _, train_state) = Lux.Experimental.compute_gradients(
+                AutoZygote(), loss, (x, y), train_state)
+            train_state = Lux.Experimental.apply_gradients(train_state, gs)
+        end
+        ttime = time() - stime
+
+        tr_acc = accuracy(
+            model, train_state.parameters, train_state.states, train_dataloader) * 100
+        te_acc = accuracy(
+            model, train_state.parameters, train_state.states, test_dataloader) * 100
+
+        @printf "[%2d/%2d] \\t Time %.2fs \\t Training Accuracy: %.2f%% \\t Test Accuracy: %.2f%%\\n" epoch nepochs ttime tr_acc te_acc
+    end
+end
      train (generic function with 1 method)

      Finally Training the Model ​

      First we will train the Lux model

      julia
      train(lux_model)
      [ 1/10] 	 Time 84.57s 	 Training Accuracy: 24.11% 	 Test Accuracy: 24.00%
+[ 2/10] 	 Time 48.82s 	 Training Accuracy: 46.89% 	 Test Accuracy: 47.50%
+[ 3/10] 	 Time 48.37s 	 Training Accuracy: 68.06% 	 Test Accuracy: 67.50%
+[ 4/10] 	 Time 48.83s 	 Training Accuracy: 74.33% 	 Test Accuracy: 72.50%
+[ 5/10] 	 Time 48.44s 	 Training Accuracy: 80.61% 	 Test Accuracy: 79.00%
+[ 6/10] 	 Time 44.90s 	 Training Accuracy: 82.83% 	 Test Accuracy: 82.50%
+[ 7/10] 	 Time 47.44s 	 Training Accuracy: 84.72% 	 Test Accuracy: 83.00%
+[ 8/10] 	 Time 49.94s 	 Training Accuracy: 85.61% 	 Test Accuracy: 84.00%
+[ 9/10] 	 Time 49.01s 	 Training Accuracy: 85.83% 	 Test Accuracy: 84.50%
+[10/10] 	 Time 48.72s 	 Training Accuracy: 87.61% 	 Test Accuracy: 85.50%

      Now we will train the SimpleChains model

      julia
      train(simple_chains_model)
      [ 1/10] 	 Time 885.21s 	 Training Accuracy: 29.78% 	 Test Accuracy: 27.00%
+[ 2/10] 	 Time 15.95s 	 Training Accuracy: 40.83% 	 Test Accuracy: 38.00%
+[ 3/10] 	 Time 15.94s 	 Training Accuracy: 60.06% 	 Test Accuracy: 55.50%
+[ 4/10] 	 Time 15.94s 	 Training Accuracy: 66.33% 	 Test Accuracy: 62.00%
+[ 5/10] 	 Time 15.94s 	 Training Accuracy: 74.28% 	 Test Accuracy: 71.00%
+[ 6/10] 	 Time 15.95s 	 Training Accuracy: 80.33% 	 Test Accuracy: 76.00%
+[ 7/10] 	 Time 15.94s 	 Training Accuracy: 82.94% 	 Test Accuracy: 81.00%
+[ 8/10] 	 Time 15.96s 	 Training Accuracy: 83.61% 	 Test Accuracy: 80.50%
+[ 9/10] 	 Time 15.95s 	 Training Accuracy: 85.61% 	 Test Accuracy: 82.00%
+[10/10] 	 Time 15.94s 	 Training Accuracy: 87.06% 	 Test Accuracy: 84.00%

      On my local machine we see a 3-4x speedup when using SimpleChains.jl. The conditions of the server this documentation is being built on is not ideal for CPU benchmarking hence, the speedup may not be as significant and even there might be regressions.

      Appendix ​

      julia
      using InteractiveUtils
+InteractiveUtils.versioninfo()
+if @isdefined(LuxCUDA) && CUDA.functional(); println(); CUDA.versioninfo(); end
+if @isdefined(LuxAMDGPU) && LuxAMDGPU.functional(); println(); AMDGPU.versioninfo(); end
      Julia Version 1.10.2
+Commit bd47eca2c8a (2024-03-01 10:14 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 48 × AMD EPYC 7402 24-Core Processor
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
+Threads: 48 default, 0 interactive, 24 GC (on 2 virtual cores)
+Environment:
+  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
+  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6
+  JULIA_PROJECT = /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/docs
+  JULIA_AMDGPU_LOGGING_ENABLED = true
+  JULIA_DEBUG = Literate
+  JULIA_CPU_THREADS = 2
+  JULIA_NUM_THREADS = 48
+  JULIA_LOAD_PATH = @:@v#.#:@stdlib
+  JULIA_CUDA_HARD_MEMORY_LIMIT = 25%

      This page was generated using Literate.jl.

      `,32),p=[l];function h(e,k,r,d,E,g){return a(),i("div",null,p)}const o=s(t,[["render",h]]);export{y as __pageData,o as default}; diff --git a/v0.5.30/assets/tutorials_beginner_4_SimpleChains.md.CoBtejGc.lean.js b/v0.5.30/assets/tutorials_beginner_4_SimpleChains.md.CoBtejGc.lean.js new file mode 100644 index 000000000..a1c7fab41 --- /dev/null +++ b/v0.5.30/assets/tutorials_beginner_4_SimpleChains.md.CoBtejGc.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.BfjuC5t1.js";const y=JSON.parse('{"title":"MNIST Classification with SimpleChains","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/beginner/4_SimpleChains.md","filePath":"tutorials/beginner/4_SimpleChains.md","lastUpdated":null}'),t={name:"tutorials/beginner/4_SimpleChains.md"},l=n("",32),p=[l];function h(e,k,r,d,E,g){return a(),i("div",null,p)}const o=s(t,[["render",h]]);export{y as __pageData,o as default}; diff --git a/v0.5.30/assets/tutorials_index.md.jZj6-Wv9.js b/v0.5.30/assets/tutorials_index.md.jZj6-Wv9.js new file mode 100644 index 000000000..5b9447015 --- /dev/null +++ b/v0.5.30/assets/tutorials_index.md.jZj6-Wv9.js @@ -0,0 +1 @@ +import{V as c,a as s,b as r,c as u}from"./chunks/theme.BUqgOrlt.js";import{c as g,J as a,w as t,p as i,o as d,a as n}from"./chunks/framework.BfjuC5t1.js";const L=JSON.parse('{"title":"","description":"","frontmatter":{"layout":"page"},"headers":[],"relativePath":"tutorials/index.md","filePath":"tutorials/index.md","lastUpdated":null}'),p={name:"tutorials/index.md"},f=Object.assign(p,{setup(h){const e='',l=[{avatar:"https://github.com/LuxDL.png",name:"Julia & Lux for the Uninitiated",desc:"A tutorial on how to get started with Julia and Lux for those who have never used Julia before.",links:[{icon:{svg:e},link:"beginner/1_Basics"}]},{avatar:"https://github.com/LuxDL.png",name:"Fitting a Polynomial using MLP",desc:"Learn the Basics of Lux by fitting a Multi-Layer Perceptron to a Polynomial.",links:[{icon:{svg:e},link:"beginner/2_PolynomialFitting"}]},{avatar:"https://github.com/LuxDL.png",name:"Training a Simple LSTM",desc:"Learn the API for defining Recurrent Models in Lux.",links:[{icon:{svg:e},link:"beginner/3_SimpleRNN"}]},{avatar:"https://github.com/PumasAI.png",name:"Use SimpleChains.jl as a Backend",desc:"Learn how to train small neural networks really fast",links:[{icon:{svg:e},link:"beginner/4_SimpleChains"}]}],o=[{avatar:"https://github.com/SciML.png",name:"MNIST Classification using Neural ODE",desc:"Train a Neural ODE to classify MNIST Images.",links:[{icon:{svg:e},link:"intermediate/1_NeuralODE"}]},{avatar:"https://github.com/TuringLang.png",name:"Bayesian Neural Networks",desc:"Figure out how to use Probabilistic Programming Frameworks like Turing with Lux.",links:[{icon:{svg:e},link:"intermediate/2_BayesianNN"}]},{avatar:"https://github.com/LuxDL.png",name:"Training a HyperNetwork",desc:"In this tutorial we will train a hypernetwork to work on multiple datasets by predicting neural network parameters.",orgLink:"intermediate/3_HyperNet",links:[{icon:{svg:e},link:"intermediate/3_HyperNet"}]}],m=[{avatar:"https://github.com/SciML.png",name:"Neural ODE to Model Gravitational Waveforms",desc:"Training a Neural ODE to fit simulated data of gravitational waveforms.",links:[{icon:{svg:e},link:"advanced/1_GravitationalWaveForm"}]}];return(v,b)=>(d(),g("div",null,[a(i(u),null,{default:t(()=>[a(i(c),null,{title:t(()=>[n("Tutorials")]),_:1}),a(i(s),null,{title:t(()=>[n("Beginners Tutorials")]),members:t(()=>[a(i(r),{size:"small",members:l})]),_:1}),a(i(s),null,{title:t(()=>[n("Intermediate Tutorials")]),members:t(()=>[a(i(r),{size:"small",members:o})]),_:1}),a(i(s),null,{title:t(()=>[n("Advanced Tutorials")]),members:t(()=>[a(i(r),{size:"small",members:m})]),_:1})]),_:1})]))}});export{L as __pageData,f as default}; 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diff --git a/v0.5.30/assets/tutorials_intermediate_1_NeuralODE.md.BYoRK3MI.js b/v0.5.30/assets/tutorials_intermediate_1_NeuralODE.md.BYoRK3MI.js new file mode 100644 index 000000000..470d7c3f4 --- /dev/null +++ b/v0.5.30/assets/tutorials_intermediate_1_NeuralODE.md.BYoRK3MI.js @@ -0,0 +1,253 @@ +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.BfjuC5t1.js";const c=JSON.parse('{"title":"MNIST Classification using Neural ODEs","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/intermediate/1_NeuralODE.md","filePath":"tutorials/intermediate/1_NeuralODE.md","lastUpdated":null}'),t={name:"tutorials/intermediate/1_NeuralODE.md"},e=n(`

      MNIST Classification using Neural ODEs ​

      To understand Neural ODEs, users should look up these lecture notes. We recommend users to directly use DiffEqFlux.jl, instead of implementing Neural ODEs from scratch.

      Package Imports ​

      julia
      using Lux, ComponentArrays, SciMLSensitivity, LuxAMDGPU, LuxCUDA, Optimisers,
+      OrdinaryDiffEq, Random, Statistics, Zygote, OneHotArrays, InteractiveUtils, Printf
+import MLDatasets: MNIST
+import MLUtils: DataLoader, splitobs
+
+CUDA.allowscalar(false)

      Loading MNIST ​

      julia
      function loadmnist(batchsize, train_split)
+    # Load MNIST: Only 1500 for demonstration purposes
+    N = 1500
+    dataset = MNIST(; split=:train)
+    imgs = dataset.features[:, :, 1:N]
+    labels_raw = dataset.targets[1:N]
+
+    # Process images into (H,W,C,BS) batches
+    x_data = Float32.(reshape(imgs, size(imgs, 1), size(imgs, 2), 1, size(imgs, 3)))
+    y_data = onehotbatch(labels_raw, 0:9)
+    (x_train, y_train), (x_test, y_test) = splitobs((x_data, y_data); at=train_split)
+
+    return (
+        # Use DataLoader to automatically minibatch and shuffle the data
+        DataLoader(collect.((x_train, y_train)); batchsize, shuffle=true),
+        # Don't shuffle the test data
+        DataLoader(collect.((x_test, y_test)); batchsize, shuffle=false))
+end
      loadmnist (generic function with 1 method)

      Define the Neural ODE Layer ​

      The NeuralODE is a ContainerLayer, which stores a model. The parameters and states of the NeuralODE are same as those of the underlying model.

      julia
      struct NeuralODE{M <: Lux.AbstractExplicitLayer, So, T, K} <:
+       Lux.AbstractExplicitContainerLayer{(:model,)}
+    model::M
+    solver::So
+    tspan::T
+    kwargs::K
+end
+
+function NeuralODE(
+        model::Lux.AbstractExplicitLayer; solver=Tsit5(), tspan=(0.0f0, 1.0f0), kwargs...)
+    return NeuralODE(model, solver, tspan, kwargs)
+end
      Main.var"##225".NeuralODE

      OrdinaryDiffEq.jl can deal with non-Vector Inputs! However, certain discrete sensitivities like ReverseDiffAdjoint can't handle non-Vector inputs. Hence, we need to convert the input and output of the ODE solver to a Vector.

      julia
      function (n::NeuralODE)(x, ps, st)
+    function dudt(u, p, t)
+        u_, st = n.model(reshape(u, size(x)), p, st)
+        return vec(u_)
+    end
+    prob = ODEProblem{false}(ODEFunction{false}(dudt), vec(x), n.tspan, ps)
+    return solve(prob, n.solver; n.kwargs...), st
+end
+
+@views diffeqsol_to_array(l::Int, x::ODESolution) = reshape(last(x.u), (l, :))
+@views diffeqsol_to_array(l::Int, x::AbstractMatrix) = reshape(x[:, end], (l, :))
      diffeqsol_to_array (generic function with 2 methods)

      Create and Initialize the Neural ODE Layer ​

      julia
      function create_model(model_fn=NeuralODE; dev=gpu_device(), use_named_tuple::Bool=false,
+        sensealg=InterpolatingAdjoint(; autojacvec=ZygoteVJP()))
+    # Construct the Neural ODE Model
+    model = Chain(FlattenLayer(),
+        Dense(784 => 20, tanh),
+        model_fn(Chain(Dense(20 => 10, tanh), Dense(10 => 10, tanh), Dense(10 => 20, tanh));
+            save_everystep=false, reltol=1.0f-3,
+            abstol=1.0f-3, save_start=false, sensealg),
+        Base.Fix1(diffeqsol_to_array, 20),
+        Dense(20 => 10))
+
+    rng = Random.default_rng()
+    Random.seed!(rng, 0)
+
+    ps, st = Lux.setup(rng, model)
+    ps = (use_named_tuple ? ps : ComponentArray(ps)) |> dev
+    st = st |> dev
+
+    return model, ps, st
+end
      create_model (generic function with 2 methods)

      Define Utility Functions ​

      julia
      logitcrossentropy(y_pred, y) = mean(-sum(y .* logsoftmax(y_pred); dims=1))
+
+function loss(x, y, model, ps, st)
+    y_pred, st = model(x, ps, st)
+    return logitcrossentropy(y_pred, y), st
+end
+
+function accuracy(model, ps, st, dataloader; dev=gpu_device())
+    total_correct, total = 0, 0
+    st = Lux.testmode(st)
+    cpu_dev = cpu_device()
+    for (x, y) in dataloader
+        target_class = onecold(y)
+        predicted_class = onecold(cpu_dev(first(model(dev(x), ps, st))))
+        total_correct += sum(target_class .== predicted_class)
+        total += length(target_class)
+    end
+    return total_correct / total
+end
      accuracy (generic function with 1 method)

      Training ​

      julia
      function train(model_function; cpu::Bool=false, kwargs...)
+    dev = cpu ? cpu_device() : gpu_device()
+    model, ps, st = create_model(model_function; dev, kwargs...)
+
+    # Training
+    train_dataloader, test_dataloader = loadmnist(128, 0.9)
+
+    opt = Adam(0.001f0)
+    st_opt = Optimisers.setup(opt, ps)
+
+    ### Warmup the Model
+    img = dev(train_dataloader.data[1][:, :, :, 1:1])
+    lab = dev(train_dataloader.data[2][:, 1:1])
+    loss(img, lab, model, ps, st)
+    (l, _), back = pullback(p -> loss(img, lab, model, p, st), ps)
+    back((one(l), nothing))
+
+    ### Lets train the model
+    nepochs = 9
+    for epoch in 1:nepochs
+        stime = time()
+        for (x, y) in train_dataloader
+            x = dev(x)
+            y = dev(y)
+            (l, st), back = pullback(p -> loss(x, y, model, p, st), ps)
+            ### We need to add \`nothing\`s equal to the number of returned values - 1
+            gs = back((one(l), nothing))[1]
+            st_opt, ps = Optimisers.update(st_opt, ps, gs)
+        end
+        ttime = time() - stime
+
+        tr_acc = accuracy(model, ps, st, train_dataloader; dev)
+        te_acc = accuracy(model, ps, st, test_dataloader; dev)
+        @printf "[%d/%d] \\t Time %.2fs \\t Training Accuracy: %.5f%% \\t Test Accuracy: %.5f%%\\n" epoch nepochs ttime tr_acc te_acc
+    end
+end
+
+train(NeuralODE)
      [1/9] 	 Time 3.31s 	 Training Accuracy: 0.50741% 	 Test Accuracy: 0.45333%
+[2/9] 	 Time 0.30s 	 Training Accuracy: 0.70741% 	 Test Accuracy: 0.66667%
+[3/9] 	 Time 0.44s 	 Training Accuracy: 0.77852% 	 Test Accuracy: 0.71333%
+[4/9] 	 Time 0.27s 	 Training Accuracy: 0.81037% 	 Test Accuracy: 0.75333%
+[5/9] 	 Time 0.30s 	 Training Accuracy: 0.82667% 	 Test Accuracy: 0.78000%
+[6/9] 	 Time 0.33s 	 Training Accuracy: 0.84148% 	 Test Accuracy: 0.78667%
+[7/9] 	 Time 0.34s 	 Training Accuracy: 0.85481% 	 Test Accuracy: 0.80667%
+[8/9] 	 Time 0.35s 	 Training Accuracy: 0.86815% 	 Test Accuracy: 0.82000%
+[9/9] 	 Time 0.34s 	 Training Accuracy: 0.87407% 	 Test Accuracy: 0.84000%

      We can also change the sensealg and train the model! GaussAdjoint allows you to use any arbitrary parameter structure and not just a flat vector (ComponentArray).

      julia
      train(NeuralODE; sensealg=GaussAdjoint(; autojacvec=ZygoteVJP()), use_named_tuple=true)
      [1/9] 	 Time 2.41s 	 Training Accuracy: 0.49630% 	 Test Accuracy: 0.38000%
+[2/9] 	 Time 0.32s 	 Training Accuracy: 0.70593% 	 Test Accuracy: 0.65333%
+[3/9] 	 Time 0.25s 	 Training Accuracy: 0.78296% 	 Test Accuracy: 0.72000%
+[4/9] 	 Time 0.33s 	 Training Accuracy: 0.80889% 	 Test Accuracy: 0.74000%
+[5/9] 	 Time 0.36s 	 Training Accuracy: 0.82370% 	 Test Accuracy: 0.76667%
+[6/9] 	 Time 0.37s 	 Training Accuracy: 0.84074% 	 Test Accuracy: 0.78667%
+[7/9] 	 Time 0.37s 	 Training Accuracy: 0.85630% 	 Test Accuracy: 0.81333%
+[8/9] 	 Time 0.34s 	 Training Accuracy: 0.86370% 	 Test Accuracy: 0.82000%
+[9/9] 	 Time 0.28s 	 Training Accuracy: 0.87704% 	 Test Accuracy: 0.82667%

      But remember some AD backends like ReverseDiff is not GPU compatible. For a model this size, you will notice that training time is significantly lower for training on CPU than on GPU.

      julia
      train(NeuralODE; sensealg=InterpolatingAdjoint(; autojacvec=ReverseDiffVJP()), cpu=true)
      [1/9] 	 Time 1.04s 	 Training Accuracy: 0.50963% 	 Test Accuracy: 0.43333%
+[2/9] 	 Time 0.26s 	 Training Accuracy: 0.69630% 	 Test Accuracy: 0.66000%
+[3/9] 	 Time 0.24s 	 Training Accuracy: 0.77926% 	 Test Accuracy: 0.71333%
+[4/9] 	 Time 0.24s 	 Training Accuracy: 0.80741% 	 Test Accuracy: 0.76667%
+[5/9] 	 Time 0.25s 	 Training Accuracy: 0.82519% 	 Test Accuracy: 0.78000%
+[6/9] 	 Time 0.25s 	 Training Accuracy: 0.84074% 	 Test Accuracy: 0.78667%
+[7/9] 	 Time 0.25s 	 Training Accuracy: 0.85333% 	 Test Accuracy: 0.80667%
+[8/9] 	 Time 0.25s 	 Training Accuracy: 0.86593% 	 Test Accuracy: 0.81333%
+[9/9] 	 Time 0.25s 	 Training Accuracy: 0.87704% 	 Test Accuracy: 0.82000%

      For completeness, let's also test out discrete sensitivities!

      julia
      train(NeuralODE; sensealg=ReverseDiffAdjoint(), cpu=true)
      [1/9] 	 Time 7.18s 	 Training Accuracy: 0.50963% 	 Test Accuracy: 0.43333%
+[2/9] 	 Time 6.91s 	 Training Accuracy: 0.69630% 	 Test Accuracy: 0.66000%
+[3/9] 	 Time 6.87s 	 Training Accuracy: 0.77926% 	 Test Accuracy: 0.71333%
+[4/9] 	 Time 7.30s 	 Training Accuracy: 0.80741% 	 Test Accuracy: 0.76667%
+[5/9] 	 Time 8.68s 	 Training Accuracy: 0.82519% 	 Test Accuracy: 0.78000%
+[6/9] 	 Time 9.59s 	 Training Accuracy: 0.84074% 	 Test Accuracy: 0.78667%
+[7/9] 	 Time 9.60s 	 Training Accuracy: 0.85333% 	 Test Accuracy: 0.80667%
+[8/9] 	 Time 9.82s 	 Training Accuracy: 0.86593% 	 Test Accuracy: 0.81333%
+[9/9] 	 Time 9.71s 	 Training Accuracy: 0.87704% 	 Test Accuracy: 0.82000%

      Alternate Implementation using Stateful Layer ​

      Starting v0.5.5, Lux provides a Lux.Experimental.StatefulLuxLayer which can be used to avoid the Boxing of st.

      julia
      struct StatefulNeuralODE{M <: Lux.AbstractExplicitLayer, So, T, K} <:
+       Lux.AbstractExplicitContainerLayer{(:model,)}
+    model::M
+    solver::So
+    tspan::T
+    kwargs::K
+end
+
+function StatefulNeuralODE(
+        model::Lux.AbstractExplicitLayer; solver=Tsit5(), tspan=(0.0f0, 1.0f0), kwargs...)
+    return StatefulNeuralODE(model, solver, tspan, kwargs)
+end
+
+function (n::StatefulNeuralODE)(x, ps, st)
+    st_model = Lux.StatefulLuxLayer(n.model, ps, st)
+    dudt(u, p, t) = st_model(u, p)
+    prob = ODEProblem{false}(ODEFunction{false}(dudt), x, n.tspan, ps)
+    return solve(prob, n.solver; n.kwargs...), st_model.st
+end

      Train the new Stateful Neural ODE ​

      julia
      train(StatefulNeuralODE)
      [1/9] 	 Time 1.33s 	 Training Accuracy: 0.49852% 	 Test Accuracy: 0.40667%
+[2/9] 	 Time 0.32s 	 Training Accuracy: 0.70296% 	 Test Accuracy: 0.66667%
+[3/9] 	 Time 0.35s 	 Training Accuracy: 0.78074% 	 Test Accuracy: 0.71333%
+[4/9] 	 Time 0.54s 	 Training Accuracy: 0.80741% 	 Test Accuracy: 0.76000%
+[5/9] 	 Time 0.31s 	 Training Accuracy: 0.82000% 	 Test Accuracy: 0.78000%
+[6/9] 	 Time 0.32s 	 Training Accuracy: 0.84444% 	 Test Accuracy: 0.79333%
+[7/9] 	 Time 0.37s 	 Training Accuracy: 0.85704% 	 Test Accuracy: 0.82000%
+[8/9] 	 Time 0.38s 	 Training Accuracy: 0.87037% 	 Test Accuracy: 0.80667%
+[9/9] 	 Time 0.39s 	 Training Accuracy: 0.88000% 	 Test Accuracy: 0.82667%

      We might not see a significant difference in the training time, but let us investigate the type stabilities of the layers.

      Type Stability ​

      julia
      model, ps, st = create_model(NeuralODE)
+
+model_stateful, ps_stateful, st_stateful = create_model(StatefulNeuralODE)
+
+x = gpu_device()(ones(Float32, 28, 28, 1, 3));

      NeuralODE is not type stable due to the boxing of st

      julia
      @code_warntype model(x, ps, st)
      MethodInstance for (::Lux.Chain{@NamedTuple{layer_1::Lux.FlattenLayer{Nothing}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Main.var"##225".NeuralODE{Lux.Chain{@NamedTuple{layer_1::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing}, OrdinaryDiffEq.Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, Tuple{Float32, Float32}, Base.Pairs{Symbol, Any, NTuple{5, Symbol}, @NamedTuple{save_everystep::Bool, reltol::Float32, abstol::Float32, save_start::Bool, sensealg::SciMLSensitivity.InterpolatingAdjoint{0, true, Val{:central}, SciMLSensitivity.ZygoteVJP}}}}, layer_4::Lux.WrappedFunction{Base.Fix1{typeof(Main.var"##225".diffeqsol_to_array), Int64}}, layer_5::Lux.Dense{true, typeof(identity), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing})(::CUDA.CuArray{Float32, 4, CUDA.Mem.DeviceBuffer}, ::ComponentArrays.ComponentVector{Float32, CUDA.CuArray{Float32, 1, CUDA.Mem.DeviceBuffer}, Tuple{ComponentArrays.Axis{(layer_1 = 1:0, layer_2 = ViewAxis(1:15700, Axis(weight = ViewAxis(1:15680, ShapedAxis((20, 784))), bias = ViewAxis(15681:15700, ShapedAxis((20, 1))))), layer_3 = ViewAxis(15701:16240, Axis(layer_1 = ViewAxis(1:210, Axis(weight = ViewAxis(1:200, ShapedAxis((10, 20))), bias = ViewAxis(201:210, ShapedAxis((10, 1))))), layer_2 = ViewAxis(211:320, Axis(weight = ViewAxis(1:100, ShapedAxis((10, 10))), bias = ViewAxis(101:110, ShapedAxis((10, 1))))), layer_3 = ViewAxis(321:540, Axis(weight = ViewAxis(1:200, ShapedAxis((20, 10))), bias = ViewAxis(201:220, ShapedAxis((20, 1))))))), layer_4 = 16241:16240, layer_5 = ViewAxis(16241:16450, Axis(weight = ViewAxis(1:200, ShapedAxis((10, 20))), bias = ViewAxis(201:210, ShapedAxis((10, 1))))))}}}, ::@NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}, layer_3::@NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}, layer_3::@NamedTuple{}}, layer_4::@NamedTuple{}, layer_5::@NamedTuple{}})
+  from (c::Lux.Chain)(x, ps, st::NamedTuple) @ Lux /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/src/layers/containers.jl:477
+Arguments
+  c::Lux.Chain{@NamedTuple{layer_1::Lux.FlattenLayer{Nothing}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Main.var"##225".NeuralODE{Lux.Chain{@NamedTuple{layer_1::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing}, OrdinaryDiffEq.Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, Tuple{Float32, Float32}, Base.Pairs{Symbol, Any, NTuple{5, Symbol}, @NamedTuple{save_everystep::Bool, reltol::Float32, abstol::Float32, save_start::Bool, sensealg::SciMLSensitivity.InterpolatingAdjoint{0, true, Val{:central}, SciMLSensitivity.ZygoteVJP}}}}, layer_4::Lux.WrappedFunction{Base.Fix1{typeof(Main.var"##225".diffeqsol_to_array), Int64}}, layer_5::Lux.Dense{true, typeof(identity), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing}
+  x::CUDA.CuArray{Float32, 4, CUDA.Mem.DeviceBuffer}
+  ps::ComponentArrays.ComponentVector{Float32, CUDA.CuArray{Float32, 1, CUDA.Mem.DeviceBuffer}, Tuple{ComponentArrays.Axis{(layer_1 = 1:0, layer_2 = ViewAxis(1:15700, Axis(weight = ViewAxis(1:15680, ShapedAxis((20, 784))), bias = ViewAxis(15681:15700, ShapedAxis((20, 1))))), layer_3 = ViewAxis(15701:16240, Axis(layer_1 = ViewAxis(1:210, Axis(weight = ViewAxis(1:200, ShapedAxis((10, 20))), bias = ViewAxis(201:210, ShapedAxis((10, 1))))), layer_2 = ViewAxis(211:320, Axis(weight = ViewAxis(1:100, ShapedAxis((10, 10))), bias = ViewAxis(101:110, ShapedAxis((10, 1))))), layer_3 = ViewAxis(321:540, Axis(weight = ViewAxis(1:200, ShapedAxis((20, 10))), bias = ViewAxis(201:220, ShapedAxis((20, 1))))))), layer_4 = 16241:16240, layer_5 = ViewAxis(16241:16450, Axis(weight = ViewAxis(1:200, ShapedAxis((10, 20))), bias = ViewAxis(201:210, ShapedAxis((10, 1))))))}}}
+  st::Core.Const((layer_1 = NamedTuple(), layer_2 = NamedTuple(), layer_3 = (layer_1 = NamedTuple(), layer_2 = NamedTuple(), layer_3 = NamedTuple()), layer_4 = NamedTuple(), layer_5 = NamedTuple()))
+Body::TUPLE{CUDA.CUARRAY{FLOAT32, 2, CUDA.MEM.DEVICEBUFFER}, NAMEDTUPLE{(:LAYER_1, :LAYER_2, :LAYER_3, :LAYER_4, :LAYER_5), <:TUPLE{@NAMEDTUPLE{}, @NAMEDTUPLE{}, ANY, @NAMEDTUPLE{}, @NAMEDTUPLE{}}}}
+1 ─ %1 = Base.getproperty(c, :layers)::@NamedTuple{layer_1::Lux.FlattenLayer{Nothing}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Main.var"##225".NeuralODE{Lux.Chain{@NamedTuple{layer_1::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing}, OrdinaryDiffEq.Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, Tuple{Float32, Float32}, Base.Pairs{Symbol, Any, NTuple{5, Symbol}, @NamedTuple{save_everystep::Bool, reltol::Float32, abstol::Float32, save_start::Bool, sensealg::SciMLSensitivity.InterpolatingAdjoint{0, true, Val{:central}, SciMLSensitivity.ZygoteVJP}}}}, layer_4::Lux.WrappedFunction{Base.Fix1{typeof(Main.var"##225".diffeqsol_to_array), Int64}}, layer_5::Lux.Dense{true, typeof(identity), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}
+│   %2 = Lux.applychain(%1, x, ps, st)::TUPLE{CUDA.CUARRAY{FLOAT32, 2, CUDA.MEM.DEVICEBUFFER}, NAMEDTUPLE{(:LAYER_1, :LAYER_2, :LAYER_3, :LAYER_4, :LAYER_5), <:TUPLE{@NAMEDTUPLE{}, @NAMEDTUPLE{}, ANY, @NAMEDTUPLE{}, @NAMEDTUPLE{}}}}
+└──      return %2

      We avoid the problem entirely by using StatefulNeuralODE

      julia
      @code_warntype model_stateful(x, ps_stateful, st_stateful)
      MethodInstance for (::Lux.Chain{@NamedTuple{layer_1::Lux.FlattenLayer{Nothing}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Main.var"##225".StatefulNeuralODE{Lux.Chain{@NamedTuple{layer_1::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing}, OrdinaryDiffEq.Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, Tuple{Float32, Float32}, Base.Pairs{Symbol, Any, NTuple{5, Symbol}, @NamedTuple{save_everystep::Bool, reltol::Float32, abstol::Float32, save_start::Bool, sensealg::SciMLSensitivity.InterpolatingAdjoint{0, true, Val{:central}, SciMLSensitivity.ZygoteVJP}}}}, layer_4::Lux.WrappedFunction{Base.Fix1{typeof(Main.var"##225".diffeqsol_to_array), Int64}}, layer_5::Lux.Dense{true, typeof(identity), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing})(::CUDA.CuArray{Float32, 4, CUDA.Mem.DeviceBuffer}, ::ComponentArrays.ComponentVector{Float32, CUDA.CuArray{Float32, 1, CUDA.Mem.DeviceBuffer}, Tuple{ComponentArrays.Axis{(layer_1 = 1:0, layer_2 = ViewAxis(1:15700, Axis(weight = ViewAxis(1:15680, ShapedAxis((20, 784))), bias = ViewAxis(15681:15700, ShapedAxis((20, 1))))), layer_3 = ViewAxis(15701:16240, Axis(layer_1 = ViewAxis(1:210, Axis(weight = ViewAxis(1:200, ShapedAxis((10, 20))), bias = ViewAxis(201:210, ShapedAxis((10, 1))))), layer_2 = ViewAxis(211:320, Axis(weight = ViewAxis(1:100, ShapedAxis((10, 10))), bias = ViewAxis(101:110, ShapedAxis((10, 1))))), layer_3 = ViewAxis(321:540, Axis(weight = ViewAxis(1:200, ShapedAxis((20, 10))), bias = ViewAxis(201:220, ShapedAxis((20, 1))))))), layer_4 = 16241:16240, layer_5 = ViewAxis(16241:16450, Axis(weight = ViewAxis(1:200, ShapedAxis((10, 20))), bias = ViewAxis(201:210, ShapedAxis((10, 1))))))}}}, ::@NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}, layer_3::@NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}, layer_3::@NamedTuple{}}, layer_4::@NamedTuple{}, layer_5::@NamedTuple{}})
+  from (c::Lux.Chain)(x, ps, st::NamedTuple) @ Lux /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/src/layers/containers.jl:477
+Arguments
+  c::Lux.Chain{@NamedTuple{layer_1::Lux.FlattenLayer{Nothing}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Main.var"##225".StatefulNeuralODE{Lux.Chain{@NamedTuple{layer_1::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing}, OrdinaryDiffEq.Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, Tuple{Float32, Float32}, Base.Pairs{Symbol, Any, NTuple{5, Symbol}, @NamedTuple{save_everystep::Bool, reltol::Float32, abstol::Float32, save_start::Bool, sensealg::SciMLSensitivity.InterpolatingAdjoint{0, true, Val{:central}, SciMLSensitivity.ZygoteVJP}}}}, layer_4::Lux.WrappedFunction{Base.Fix1{typeof(Main.var"##225".diffeqsol_to_array), Int64}}, layer_5::Lux.Dense{true, typeof(identity), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing}
+  x::CUDA.CuArray{Float32, 4, CUDA.Mem.DeviceBuffer}
+  ps::ComponentArrays.ComponentVector{Float32, CUDA.CuArray{Float32, 1, CUDA.Mem.DeviceBuffer}, Tuple{ComponentArrays.Axis{(layer_1 = 1:0, layer_2 = ViewAxis(1:15700, Axis(weight = ViewAxis(1:15680, ShapedAxis((20, 784))), bias = ViewAxis(15681:15700, ShapedAxis((20, 1))))), layer_3 = ViewAxis(15701:16240, Axis(layer_1 = ViewAxis(1:210, Axis(weight = ViewAxis(1:200, ShapedAxis((10, 20))), bias = ViewAxis(201:210, ShapedAxis((10, 1))))), layer_2 = ViewAxis(211:320, Axis(weight = ViewAxis(1:100, ShapedAxis((10, 10))), bias = ViewAxis(101:110, ShapedAxis((10, 1))))), layer_3 = ViewAxis(321:540, Axis(weight = ViewAxis(1:200, ShapedAxis((20, 10))), bias = ViewAxis(201:220, ShapedAxis((20, 1))))))), layer_4 = 16241:16240, layer_5 = ViewAxis(16241:16450, Axis(weight = ViewAxis(1:200, ShapedAxis((10, 20))), bias = ViewAxis(201:210, ShapedAxis((10, 1))))))}}}
+  st::Core.Const((layer_1 = NamedTuple(), layer_2 = NamedTuple(), layer_3 = (layer_1 = NamedTuple(), layer_2 = NamedTuple(), layer_3 = NamedTuple()), layer_4 = NamedTuple(), layer_5 = NamedTuple()))
+Body::Tuple{CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, @NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}, layer_3::@NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}, layer_3::@NamedTuple{}}, layer_4::@NamedTuple{}, layer_5::@NamedTuple{}}}
+1 ─ %1 = Base.getproperty(c, :layers)::@NamedTuple{layer_1::Lux.FlattenLayer{Nothing}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Main.var"##225".StatefulNeuralODE{Lux.Chain{@NamedTuple{layer_1::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing}, OrdinaryDiffEq.Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, Tuple{Float32, Float32}, Base.Pairs{Symbol, Any, NTuple{5, Symbol}, @NamedTuple{save_everystep::Bool, reltol::Float32, abstol::Float32, save_start::Bool, sensealg::SciMLSensitivity.InterpolatingAdjoint{0, true, Val{:central}, SciMLSensitivity.ZygoteVJP}}}}, layer_4::Lux.WrappedFunction{Base.Fix1{typeof(Main.var"##225".diffeqsol_to_array), Int64}}, layer_5::Lux.Dense{true, typeof(identity), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}
+│   %2 = Lux.applychain(%1, x, ps, st)::Tuple{CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, @NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}, layer_3::@NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}, layer_3::@NamedTuple{}}, layer_4::@NamedTuple{}, layer_5::@NamedTuple{}}}
+└──      return %2

      Note, that we still recommend using this layer internally and not exposing this as the default API to the users.

      Appendix ​

      julia
      using InteractiveUtils
+InteractiveUtils.versioninfo()
+if @isdefined(LuxCUDA) && CUDA.functional(); println(); CUDA.versioninfo(); end
+if @isdefined(LuxAMDGPU) && LuxAMDGPU.functional(); println(); AMDGPU.versioninfo(); end
      Julia Version 1.10.2
+Commit bd47eca2c8a (2024-03-01 10:14 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 48 × AMD EPYC 7402 24-Core Processor
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
+Threads: 48 default, 0 interactive, 24 GC (on 2 virtual cores)
+Environment:
+  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
+  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6
+  JULIA_PROJECT = /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/docs
+  JULIA_AMDGPU_LOGGING_ENABLED = true
+  JULIA_DEBUG = Literate
+  JULIA_CPU_THREADS = 2
+  JULIA_NUM_THREADS = 48
+  JULIA_LOAD_PATH = @:@v#.#:@stdlib
+  JULIA_CUDA_HARD_MEMORY_LIMIT = 25%
+
+CUDA runtime 12.3, artifact installation
+CUDA driver 12.4
+NVIDIA driver 550.54.15
+
+CUDA libraries: 
+- CUBLAS: 12.3.4
+- CURAND: 10.3.4
+- CUFFT: 11.0.12
+- CUSOLVER: 11.5.4
+- CUSPARSE: 12.2.0
+- CUPTI: 21.0.0
+- NVML: 12.0.0+550.54.15
+
+Julia packages: 
+- CUDA: 5.2.0
+- CUDA_Driver_jll: 0.7.0+1
+- CUDA_Runtime_jll: 0.11.1+0
+
+Toolchain:
+- Julia: 1.10.2
+- LLVM: 15.0.7
+
+Environment:
+- JULIA_CUDA_HARD_MEMORY_LIMIT: 25%
+
+1 device:
+  0: NVIDIA A100-PCIE-40GB MIG 1g.5gb (sm_80, 3.443 GiB / 4.750 GiB available)
+┌ Warning: LuxAMDGPU is loaded but the AMDGPU is not functional.
+└ @ LuxAMDGPU ~/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6/packages/LuxAMDGPU/sGa0S/src/LuxAMDGPU.jl:19

      This page was generated using Literate.jl.

      `,53),l=[e];function p(h,k,r,d,E,y){return a(),i("div",null,l)}const o=s(t,[["render",p]]);export{c as __pageData,o as default}; diff --git a/v0.5.30/assets/tutorials_intermediate_1_NeuralODE.md.BYoRK3MI.lean.js b/v0.5.30/assets/tutorials_intermediate_1_NeuralODE.md.BYoRK3MI.lean.js new file mode 100644 index 000000000..c54537abe --- /dev/null +++ b/v0.5.30/assets/tutorials_intermediate_1_NeuralODE.md.BYoRK3MI.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.BfjuC5t1.js";const c=JSON.parse('{"title":"MNIST Classification using Neural ODEs","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/intermediate/1_NeuralODE.md","filePath":"tutorials/intermediate/1_NeuralODE.md","lastUpdated":null}'),t={name:"tutorials/intermediate/1_NeuralODE.md"},e=n("",53),l=[e];function p(h,k,r,d,E,y){return a(),i("div",null,l)}const o=s(t,[["render",p]]);export{c as __pageData,o as default}; diff --git a/v0.5.30/assets/tutorials_intermediate_2_BayesianNN.md.Di-SHgr7.js b/v0.5.30/assets/tutorials_intermediate_2_BayesianNN.md.Di-SHgr7.js new file mode 100644 index 000000000..74ebfbde8 --- /dev/null +++ b/v0.5.30/assets/tutorials_intermediate_2_BayesianNN.md.Di-SHgr7.js @@ -0,0 +1,197 @@ +import{_ as n,c as i,m as A,a4 as s,o as a}from"./chunks/framework.BfjuC5t1.js";const t="/v0.5.30/assets/results.Dao8ZugC.gif",f=JSON.parse('{"title":"Bayesian Neural Network","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/intermediate/2_BayesianNN.md","filePath":"tutorials/intermediate/2_BayesianNN.md","lastUpdated":null}'),e={name:"tutorials/intermediate/2_BayesianNN.md"},E=s(`

      Bayesian Neural Network ​

      We borrow this tutorial from the official Turing Docs. We will show how the explicit parameterization of Lux enables first-class composability with packages which expect flattened out parameter vectors.

      We will use Turing.jl with Lux.jl to implement implementing a classification algorithm. Lets start by importing the relevant libraries.

      julia
      # Import libraries
+using Lux, Turing, CairoMakie, Random, Tracker, Functors, LinearAlgebra
+
+# Sampling progress
+Turing.setprogress!(true);
      [ Info: [Turing]: progress logging is enabled globally
+[ Info: [AdvancedVI]: global PROGRESS is set as true

      Generating data ​

      Our goal here is to use a Bayesian neural network to classify points in an artificial dataset. The code below generates data points arranged in a box-like pattern and displays a graph of the dataset we'll be working with.

      julia
      # Number of points to generate
+N = 80
+M = round(Int, N / 4)
+rng = Random.default_rng()
+Random.seed!(rng, 1234)
+
+# Generate artificial data
+x1s = rand(rng, Float32, M) * 4.5f0;
+x2s = rand(rng, Float32, M) * 4.5f0;
+xt1s = Array([[x1s[i] + 0.5f0; x2s[i] + 0.5f0] for i in 1:M])
+x1s = rand(rng, Float32, M) * 4.5f0;
+x2s = rand(rng, Float32, M) * 4.5f0;
+append!(xt1s, Array([[x1s[i] - 5.0f0; x2s[i] - 5.0f0] for i in 1:M]))
+
+x1s = rand(rng, Float32, M) * 4.5f0;
+x2s = rand(rng, Float32, M) * 4.5f0;
+xt0s = Array([[x1s[i] + 0.5f0; x2s[i] - 5.0f0] for i in 1:M])
+x1s = rand(rng, Float32, M) * 4.5f0;
+x2s = rand(rng, Float32, M) * 4.5f0;
+append!(xt0s, Array([[x1s[i] - 5.0f0; x2s[i] + 0.5f0] for i in 1:M]))
+
+# Store all the data for later
+xs = [xt1s; xt0s]
+ts = [ones(2 * M); zeros(2 * M)]
+
+# Plot data points
+
+function plot_data()
+    x1 = first.(xt1s)
+    y1 = last.(xt1s)
+    x2 = first.(xt0s)
+    y2 = last.(xt0s)
+
+    fig = Figure()
+    ax = CairoMakie.Axis(fig[1, 1]; xlabel="x", ylabel="y")
+
+    scatter!(ax, x1, y1; markersize=16, color=:red, strokecolor=:black, strokewidth=2)
+    scatter!(ax, x2, y2; markersize=16, color=:blue, strokecolor=:black, strokewidth=2)
+
+    return fig
+end
+
+plot_data()

      Building the Neural Network ​

      The next step is to define a feedforward neural network where we express our parameters as distributions, and not single points as with traditional neural networks. For this we will use Dense to define liner layers and compose them via Chain, both are neural network primitives from Lux. The network nn we will create will have two hidden layers with tanh activations and one output layer with sigmoid activation, as shown below.

      The nn is an instance that acts as a function and can take data, parameters and current state as inputs and output predictions. We will define distributions on the neural network parameters.

      julia
      # Construct a neural network using Lux
+nn = Chain(Dense(2 => 3, tanh), Dense(3 => 2, tanh), Dense(2 => 1, sigmoid))
+
+# Initialize the model weights and state
+ps, st = Lux.setup(rng, nn)
+
+Lux.parameterlength(nn) # number of paraemters in NN
      20

      The probabilistic model specification below creates a parameters variable, which has IID normal variables. The parameters represents all parameters of our neural net (weights and biases).

      julia
      # Create a regularization term and a Gaussian prior variance term.
+alpha = 0.09
+sig = sqrt(1.0 / alpha)
      3.3333333333333335

      Construct named tuple from a sampled parameter vector. We could also use ComponentArrays here and simply broadcast to avoid doing this. But let's do it this way to avoid dependencies.

      julia
      function vector_to_parameters(ps_new::AbstractVector, ps::NamedTuple)
+    @assert length(ps_new) == Lux.parameterlength(ps)
+    i = 1
+    function get_ps(x)
+        z = reshape(view(ps_new, i:(i + length(x) - 1)), size(x))
+        i += length(x)
+        return z
+    end
+    return fmap(get_ps, ps)
+end
      vector_to_parameters (generic function with 1 method)

      To interface with external libraries it is often desirable to use the StatefulLuxLayer to automatically handle the neural network states.

      julia
      const model = StatefulLuxLayer(nn, st)
+
+# Specify the probabilistic model.
+@model function bayes_nn(xs, ts)
+    # Sample the parameters
+    nparameters = Lux.parameterlength(nn)
+    parameters ~ MvNormal(zeros(nparameters), Diagonal(abs2.(sig .* ones(nparameters))))
+
+    # Forward NN to make predictions
+    preds = Lux.apply(model, xs, vector_to_parameters(parameters, ps))
+
+    # Observe each prediction.
+    for i in eachindex(ts)
+        ts[i] ~ Bernoulli(preds[i])
+    end
+end
      bayes_nn (generic function with 2 methods)

      Inference can now be performed by calling sample. We use the HMC sampler here.

      julia
      # Perform inference.
+N = 5000
+ch = sample(bayes_nn(reduce(hcat, xs), ts), HMC(0.05, 4; adtype=AutoTracker()), N)
      Chains MCMC chain (5000×30×1 Array{Float64, 3}):
+
+Iterations        = 1:1:5000
+Number of chains  = 1
+Samples per chain = 5000
+Wall duration     = 24.99 seconds
+Compute duration  = 24.99 seconds
+parameters        = parameters[1], parameters[2], parameters[3], parameters[4], parameters[5], parameters[6], parameters[7], parameters[8], parameters[9], parameters[10], parameters[11], parameters[12], parameters[13], parameters[14], parameters[15], parameters[16], parameters[17], parameters[18], parameters[19], parameters[20]
+internals         = lp, n_steps, is_accept, acceptance_rate, log_density, hamiltonian_energy, hamiltonian_energy_error, numerical_error, step_size, nom_step_size
+
+Summary Statistics
+      parameters      mean       std      mcse   ess_bulk   ess_tail      rhat   ess_per_sec
+          Symbol   Float64   Float64   Float64    Float64    Float64   Float64       Float64
+
+   parameters[1]   -0.5133    1.8835    0.5330    13.1888    25.0326    1.4853        0.5277
+   parameters[2]   -5.3361    2.4104    0.6377    15.5139    36.9602    1.0376        0.6208
+   parameters[3]    0.3151    0.6835    0.1441    27.6358    50.3442    1.1216        1.1058
+   parameters[4]    1.9624    3.7648    1.1478    11.5629    25.5317    2.0118        0.4627
+   parameters[5]   -0.0914    0.6013    0.0858    52.3129    54.6520    1.1223        2.0932
+   parameters[6]    4.9348    2.3882    0.6909    12.4651    22.5599    1.8704        0.4988
+   parameters[7]   -1.6494    2.7707    0.8306    11.9136    35.7353    1.9059        0.4767
+   parameters[8]   -0.3367    1.5561    0.3957    15.3027    35.5527    1.2732        0.6123
+   parameters[9]   -0.6247    1.7715    0.4439    16.1582    41.0067    1.0886        0.6465
+  parameters[10]   -0.0485    2.6496    0.7711    12.0002    18.2390    1.6173        0.4802
+  parameters[11]   -2.7777    2.4100    0.6937    13.2493    54.0054    1.2589        0.5301
+  parameters[12]    1.7397    2.7286    0.8144    12.5350    30.6674    1.3093        0.5016
+  parameters[13]   -1.3065    3.0122    0.9212    11.3718    29.5307    1.8415        0.4550
+  parameters[14]    2.1359    1.7145    0.4376    16.0168    29.9135    1.1185        0.6409
+  parameters[15]   -2.2917    1.1075    0.2143    27.1032    53.9717    1.0339        1.0845
+  parameters[16]   -1.8241    1.7783    0.4754    14.8255    44.7465    1.2380        0.5932
+  parameters[17]   -2.9541    1.0941    0.1964    32.4857    49.3634    1.0550        1.2998
+  parameters[18]   -2.9283    3.1083    0.9424    13.4337    49.1159    1.4880        0.5375
+  parameters[19]   -5.8506    1.2702    0.1981    41.3283    64.0949    1.0032        1.6537
+  parameters[20]   -3.6909    1.8615    0.5266    13.1481    52.3750    1.6064        0.5261
+
+Quantiles
+      parameters      2.5%     25.0%     50.0%     75.0%     97.5%
+          Symbol   Float64   Float64   Float64   Float64   Float64
+
+   parameters[1]   -2.9584   -2.1586   -0.3884    0.5613    4.2684
+   parameters[2]   -9.8741   -7.2592   -4.9623   -3.2715   -1.7035
+   parameters[3]   -0.6888   -0.1073    0.1721    0.5713    2.2193
+   parameters[4]   -5.7669   -1.4891    3.0249    5.1736    7.8110
+   parameters[5]   -1.2037   -0.4726   -0.1166    0.2270    1.2686
+   parameters[6]    1.5300    2.9517    4.4678    6.7396   10.5049
+   parameters[7]   -5.8618   -4.2435   -1.3364    0.6954    3.0399
+   parameters[8]   -3.2162   -1.3171   -0.3432    0.4455    3.4264
+   parameters[9]   -4.2319   -1.6828   -0.5051    0.6070    2.9411
+  parameters[10]   -6.1276   -1.8893    0.2035    1.6808    4.6669
+  parameters[11]   -6.8391   -4.9499   -2.5672   -0.5826    1.1874
+  parameters[12]   -3.4081   -0.4600    2.2126    3.9338    5.8529
+  parameters[13]   -6.1325   -3.7644   -2.1160    1.6571    3.6084
+  parameters[14]   -1.1205    1.0660    1.9677    3.1250    5.5755
+  parameters[15]   -4.6287   -3.0619   -2.1911   -1.5340   -0.1136
+  parameters[16]   -5.3259   -3.0340   -1.9008   -0.9440    1.7702
+  parameters[17]   -5.6472   -3.5470   -2.8160   -2.2108   -1.0283
+  parameters[18]   -6.7277   -5.2922   -4.2915    0.7602    2.7335
+  parameters[19]   -8.5012   -6.5957   -5.8670   -5.0328   -3.3450
+  parameters[20]   -6.7333   -5.1577   -3.8273   -2.2208   -0.3195

      Now we extract the parameter samples from the sampled chain as θ (this is of size 5000 x 20 where 5000 is the number of iterations and 20 is the number of parameters). We'll use these primarily to determine how good our model's classifier is.

      julia
      # Extract all weight and bias parameters.
+θ = MCMCChains.group(ch, :parameters).value;

      Prediction Visualization ​

      julia
      # A helper to run the nn through data \`x\` using parameters \`θ\`
+nn_forward(x, θ) = model(x, vector_to_parameters(θ, ps))
+
+# Plot the data we have.
+fig = plot_data()
+
+# Find the index that provided the highest log posterior in the chain.
+_, i = findmax(ch[:lp])
+
+# Extract the max row value from i.
+i = i.I[1]
+
+# Plot the posterior distribution with a contour plot
+x1_range = collect(range(-6; stop=6, length=25))
+x2_range = collect(range(-6; stop=6, length=25))
+Z = [nn_forward([x1, x2], θ[i, :])[1] for x1 in x1_range, x2 in x2_range]
+contour!(x1_range, x2_range, Z; linewidth=3, colormap=:seaborn_bright)
+fig

      The contour plot above shows that the MAP method is not too bad at classifying our data. Now we can visualize our predictions.

      `,32),l={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},h={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.222ex"},xmlns:"http://www.w3.org/2000/svg",width:"46.264ex",height:"6.301ex",role:"img",focusable:"false",viewBox:"0 -1361 20448.8 2785.1","aria-hidden":"true"},p=s('',1),g=[p],r=A("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[A("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[A("mi",null,"p"),A("mo",{stretchy:"false"},"("),A("mrow",{"data-mjx-texclass":"ORD"},[A("mover",null,[A("mi",null,"x"),A("mo",{stretchy:"false"},"~")])]),A("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),A("mi",null,"X"),A("mo",null,","),A("mi",null,"α"),A("mo",{stretchy:"false"},")"),A("mo",null,"="),A("msub",null,[A("mo",{"data-mjx-texclass":"OP"},"∫"),A("mrow",{"data-mjx-texclass":"ORD"},[A("mi",null,"θ")])]),A("mi",null,"p"),A("mo",{stretchy:"false"},"("),A("mrow",{"data-mjx-texclass":"ORD"},[A("mover",null,[A("mi",null,"x"),A("mo",{stretchy:"false"},"~")])]),A("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),A("mi",null,"θ"),A("mo",{stretchy:"false"},")"),A("mi",null,"p"),A("mo",{stretchy:"false"},"("),A("mi",null,"θ"),A("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),A("mi",null,"X"),A("mo",null,","),A("mi",null,"α"),A("mo",{stretchy:"false"},")"),A("mo",null,"≈"),A("munder",null,[A("mo",{"data-mjx-texclass":"OP"},"∑"),A("mrow",{"data-mjx-texclass":"ORD"},[A("mi",null,"θ"),A("mo",null,"∼"),A("mi",null,"p"),A("mo",{stretchy:"false"},"("),A("mi",null,"θ"),A("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),A("mi",null,"X"),A("mo",null,","),A("mi",null,"α"),A("mo",{stretchy:"false"},")")])]),A("msub",null,[A("mi",null,"f"),A("mrow",{"data-mjx-texclass":"ORD"},[A("mi",null,"θ")])]),A("mo",{stretchy:"false"},"("),A("mrow",{"data-mjx-texclass":"ORD"},[A("mover",null,[A("mi",null,"x"),A("mo",{stretchy:"false"},"~")])]),A("mo",{stretchy:"false"},")")])],-1),k=s(`

      The nn_predict function takes the average predicted value from a network parameterized by weights drawn from the MCMC chain.

      julia
      # Return the average predicted value across multiple weights.
+nn_predict(x, θ, num) = mean([first(nn_forward(x, view(θ, i, :))) for i in 1:10:num])
      nn_predict (generic function with 1 method)

      Next, we use the nn_predict function to predict the value at a sample of points where the x1 and x2 coordinates range between -6 and 6. As we can see below, we still have a satisfactory fit to our data, and more importantly, we can also see where the neural network is uncertain about its predictions much easier–-those regions between cluster boundaries.

      Plot the average prediction.

      julia
      fig = plot_data()
+
+n_end = 1500
+x1_range = collect(range(-6; stop=6, length=25))
+x2_range = collect(range(-6; stop=6, length=25))
+Z = [nn_predict([x1, x2], θ, n_end)[1] for x1 in x1_range, x2 in x2_range]
+contour!(x1_range, x2_range, Z; linewidth=3, colormap=:seaborn_bright)
+fig

      Suppose we are interested in how the predictive power of our Bayesian neural network evolved between samples. In that case, the following graph displays an animation of the contour plot generated from the network weights in samples 1 to 5,000.

      julia
      fig = plot_data()
+Z = [first(nn_forward([x1, x2], θ[1, :])) for x1 in x1_range, x2 in x2_range]
+c = contour!(x1_range, x2_range, Z; linewidth=3, colormap=:seaborn_bright)
+record(fig, "results.gif", 1:250:size(θ, 1)) do i
+    fig.current_axis[].title = "Iteration: $i"
+    Z = [first(nn_forward([x1, x2], θ[i, :])) for x1 in x1_range, x2 in x2_range]
+    c[3] = Z
+    return fig
+end
      "results.gif"

      Appendix ​

      julia
      using InteractiveUtils
+InteractiveUtils.versioninfo()
+if @isdefined(LuxCUDA) && CUDA.functional(); println(); CUDA.versioninfo(); end
+if @isdefined(LuxAMDGPU) && LuxAMDGPU.functional(); println(); AMDGPU.versioninfo(); end
      Julia Version 1.10.2
+Commit bd47eca2c8a (2024-03-01 10:14 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 48 × AMD EPYC 7402 24-Core Processor
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
+Threads: 48 default, 0 interactive, 24 GC (on 2 virtual cores)
+Environment:
+  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
+  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6
+  JULIA_PROJECT = /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/docs
+  JULIA_AMDGPU_LOGGING_ENABLED = true
+  JULIA_DEBUG = Literate
+  JULIA_CPU_THREADS = 2
+  JULIA_NUM_THREADS = 48
+  JULIA_LOAD_PATH = @:@v#.#:@stdlib
+  JULIA_CUDA_HARD_MEMORY_LIMIT = 25%

      This page was generated using Literate.jl.

      `,16);function d(C,Q,B,I,v,o){return a(),i("div",null,[E,A("mjx-container",l,[(a(),i("svg",h,g)),r]),k])}const y=n(e,[["render",d]]);export{f as __pageData,y as default}; diff --git a/v0.5.30/assets/tutorials_intermediate_2_BayesianNN.md.Di-SHgr7.lean.js b/v0.5.30/assets/tutorials_intermediate_2_BayesianNN.md.Di-SHgr7.lean.js new file mode 100644 index 000000000..0ea627784 --- /dev/null +++ b/v0.5.30/assets/tutorials_intermediate_2_BayesianNN.md.Di-SHgr7.lean.js @@ -0,0 +1 @@ +import{_ as n,c as i,m as A,a4 as s,o as a}from"./chunks/framework.BfjuC5t1.js";const t="/v0.5.30/assets/results.Dao8ZugC.gif",f=JSON.parse('{"title":"Bayesian Neural Network","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/intermediate/2_BayesianNN.md","filePath":"tutorials/intermediate/2_BayesianNN.md","lastUpdated":null}'),e={name:"tutorials/intermediate/2_BayesianNN.md"},E=s("",32),l={class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},h={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.222ex"},xmlns:"http://www.w3.org/2000/svg",width:"46.264ex",height:"6.301ex",role:"img",focusable:"false",viewBox:"0 -1361 20448.8 2785.1","aria-hidden":"true"},p=s("",1),g=[p],r=A("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[A("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[A("mi",null,"p"),A("mo",{stretchy:"false"},"("),A("mrow",{"data-mjx-texclass":"ORD"},[A("mover",null,[A("mi",null,"x"),A("mo",{stretchy:"false"},"~")])]),A("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),A("mi",null,"X"),A("mo",null,","),A("mi",null,"α"),A("mo",{stretchy:"false"},")"),A("mo",null,"="),A("msub",null,[A("mo",{"data-mjx-texclass":"OP"},"∫"),A("mrow",{"data-mjx-texclass":"ORD"},[A("mi",null,"θ")])]),A("mi",null,"p"),A("mo",{stretchy:"false"},"("),A("mrow",{"data-mjx-texclass":"ORD"},[A("mover",null,[A("mi",null,"x"),A("mo",{stretchy:"false"},"~")])]),A("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),A("mi",null,"θ"),A("mo",{stretchy:"false"},")"),A("mi",null,"p"),A("mo",{stretchy:"false"},"("),A("mi",null,"θ"),A("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),A("mi",null,"X"),A("mo",null,","),A("mi",null,"α"),A("mo",{stretchy:"false"},")"),A("mo",null,"≈"),A("munder",null,[A("mo",{"data-mjx-texclass":"OP"},"∑"),A("mrow",{"data-mjx-texclass":"ORD"},[A("mi",null,"θ"),A("mo",null,"∼"),A("mi",null,"p"),A("mo",{stretchy:"false"},"("),A("mi",null,"θ"),A("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),A("mi",null,"X"),A("mo",null,","),A("mi",null,"α"),A("mo",{stretchy:"false"},")")])]),A("msub",null,[A("mi",null,"f"),A("mrow",{"data-mjx-texclass":"ORD"},[A("mi",null,"θ")])]),A("mo",{stretchy:"false"},"("),A("mrow",{"data-mjx-texclass":"ORD"},[A("mover",null,[A("mi",null,"x"),A("mo",{stretchy:"false"},"~")])]),A("mo",{stretchy:"false"},")")])],-1),k=s("",16);function d(C,Q,B,I,v,o){return a(),i("div",null,[E,A("mjx-container",l,[(a(),i("svg",h,g)),r]),k])}const y=n(e,[["render",d]]);export{f as __pageData,y as default}; diff --git a/v0.5.30/assets/tutorials_intermediate_3_HyperNet.md.DFqj-uR3.js b/v0.5.30/assets/tutorials_intermediate_3_HyperNet.md.DFqj-uR3.js new file mode 100644 index 000000000..c1486426b --- /dev/null +++ b/v0.5.30/assets/tutorials_intermediate_3_HyperNet.md.DFqj-uR3.js @@ -0,0 +1,206 @@ +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.BfjuC5t1.js";const c=JSON.parse('{"title":"Training a HyperNetwork on MNIST and FashionMNIST","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/intermediate/3_HyperNet.md","filePath":"tutorials/intermediate/3_HyperNet.md","lastUpdated":null}'),h={name:"tutorials/intermediate/3_HyperNet.md"},t=n(`

      Training a HyperNetwork on MNIST and FashionMNIST ​

      Package Imports ​

      julia
      using Lux, ADTypes, ComponentArrays, LuxAMDGPU, LuxCUDA, MLDatasets, MLUtils, OneHotArrays,
+      Optimisers, Printf, Random, Setfield, Statistics, Zygote
+
+CUDA.allowscalar(false)

      Loading Datasets ​

      julia
      function load_dataset(::Type{dset}, n_train::Int, n_eval::Int, batchsize::Int) where {dset}
+    imgs, labels = dset(:train)[1:n_train]
+    x_train, y_train = reshape(imgs, 28, 28, 1, n_train), onehotbatch(labels, 0:9)
+
+    imgs, labels = dset(:test)[1:n_eval]
+    x_test, y_test = reshape(imgs, 28, 28, 1, n_eval), onehotbatch(labels, 0:9)
+
+    return (DataLoader((x_train, y_train); batchsize=min(batchsize, n_train), shuffle=true),
+        DataLoader((x_test, y_test); batchsize=min(batchsize, n_eval), shuffle=false))
+end
+
+function load_datasets(n_train=1024, n_eval=32, batchsize=256)
+    return load_dataset.((MNIST, FashionMNIST), n_train, n_eval, batchsize)
+end
      load_datasets (generic function with 4 methods)

      Implement a HyperNet Layer ​

      julia
      struct HyperNet{W <: Lux.AbstractExplicitLayer, C <: Lux.AbstractExplicitLayer, A} <:
+       Lux.AbstractExplicitContainerLayer{(:weight_generator, :core_network)}
+    weight_generator::W
+    core_network::C
+    ca_axes::A
+end
+
+function HyperNet(w::Lux.AbstractExplicitLayer, c::Lux.AbstractExplicitLayer)
+    ca_axes = Lux.initialparameters(Random.default_rng(), c) |> ComponentArray |> getaxes
+    return HyperNet(w, c, ca_axes)
+end
+
+function Lux.initialparameters(rng::AbstractRNG, h::HyperNet)
+    return (weight_generator=Lux.initialparameters(rng, h.weight_generator),)
+end
+
+function (hn::HyperNet)(x, ps, st::NamedTuple)
+    ps_new, st_ = hn.weight_generator(x, ps.weight_generator, st.weight_generator)
+    @set! st.weight_generator = st_
+    return ComponentArray(vec(ps_new), hn.ca_axes), st
+end
+
+function (hn::HyperNet)((x, y)::T, ps, st::NamedTuple) where {T <: Tuple}
+    ps_ca, st = hn(x, ps, st)
+    pred, st_ = hn.core_network(y, ps_ca, st.core_network)
+    @set! st.core_network = st_
+    return pred, st
+end

      Create and Initialize the HyperNet ​

      julia
      function create_model()
+    # Doesn't need to be a MLP can have any Lux Layer
+    core_network = Chain(FlattenLayer(), Dense(784, 256, relu), Dense(256, 10))
+    weight_generator = Chain(Embedding(2 => 32), Dense(32, 64, relu),
+        Dense(64, Lux.parameterlength(core_network)))
+
+    model = HyperNet(weight_generator, core_network)
+    return model
+end
      create_model (generic function with 1 method)

      Define Utility Functions ​

      julia
      logitcrossentropy(y_pred, y) = mean(-sum(y .* logsoftmax(y_pred); dims=1))
+
+function loss(model, ps, st, (data_idx, x, y))
+    y_pred, st = model((data_idx, x), ps, st)
+    return logitcrossentropy(y_pred, y), st, (;)
+end
+
+function accuracy(model, ps, st, dataloader, data_idx, gdev=gpu_device())
+    total_correct, total = 0, 0
+    st = Lux.testmode(st)
+    cpu_dev = cpu_device()
+    for (x, y) in dataloader
+        x = x |> gdev
+        y = y |> gdev
+        target_class = onecold(cpu_dev(y))
+        predicted_class = onecold(cpu_dev(model((data_idx, x), ps, st)[1]))
+        total_correct += sum(target_class .== predicted_class)
+        total += length(target_class)
+    end
+    return total_correct / total
+end
      accuracy (generic function with 2 methods)

      Training ​

      julia
      function train()
+    model = create_model()
+    dataloaders = load_datasets()
+
+    dev = gpu_device()
+
+    rng = Xoshiro(0)
+
+    train_state = Lux.Experimental.TrainState(
+        rng, model, Adam(3.0f-4); transform_variables=dev)
+
+    ### Lets train the model
+    nepochs = 10
+    for epoch in 1:nepochs, data_idx in 1:2
+        train_dataloader, test_dataloader = dataloaders[data_idx]
+
+        stime = time()
+        for (x, y) in train_dataloader
+            x = x |> dev
+            y = y |> dev
+            (gs, _, _, train_state) = Lux.Experimental.compute_gradients(
+                AutoZygote(), loss, (data_idx, x, y), train_state)
+            train_state = Lux.Experimental.apply_gradients(train_state, gs)
+        end
+        ttime = time() - stime
+
+        train_acc = round(
+            accuracy(model, train_state.parameters, train_state.states,
+                train_dataloader, data_idx, dev) * 100;
+            digits=2)
+        test_acc = round(
+            accuracy(model, train_state.parameters, train_state.states,
+                test_dataloader, data_idx, dev) * 100;
+            digits=2)
+
+        data_name = data_idx == 1 ? "MNIST" : "FashionMNIST"
+
+        @printf "[%3d/%3d] \\t %12s \\t Time %.5fs \\t Training Accuracy: %.2f%% \\t Test Accuracy: %.2f%%\\n" epoch nepochs data_name ttime train_acc test_acc
+    end
+
+    println()
+
+    for data_idx in 1:2
+        train_dataloader, test_dataloader = dataloaders[data_idx]
+        train_acc = round(
+            accuracy(model, train_state.parameters, train_state.states,
+                train_dataloader, data_idx, dev) * 100;
+            digits=2)
+        test_acc = round(
+            accuracy(model, train_state.parameters, train_state.states,
+                test_dataloader, data_idx, dev) * 100;
+            digits=2)
+
+        data_name = data_idx == 1 ? "MNIST" : "FashionMNIST"
+
+        @printf "[FINAL] \\t %12s \\t Training Accuracy: %.2f%% \\t Test Accuracy: %.2f%%\\n" data_name train_acc test_acc
+    end
+end
+
+train()
      [  1/ 10] 	        MNIST 	 Time 62.70427s 	 Training Accuracy: 76.27% 	 Test Accuracy: 78.12%
+[  1/ 10] 	 FashionMNIST 	 Time 0.17746s 	 Training Accuracy: 54.98% 	 Test Accuracy: 50.00%
+[  2/ 10] 	        MNIST 	 Time 0.03860s 	 Training Accuracy: 75.49% 	 Test Accuracy: 71.88%
+[  2/ 10] 	 FashionMNIST 	 Time 0.05287s 	 Training Accuracy: 56.45% 	 Test Accuracy: 65.62%
+[  3/ 10] 	        MNIST 	 Time 0.03839s 	 Training Accuracy: 81.84% 	 Test Accuracy: 78.12%
+[  3/ 10] 	 FashionMNIST 	 Time 0.03281s 	 Training Accuracy: 62.21% 	 Test Accuracy: 56.25%
+[  4/ 10] 	        MNIST 	 Time 0.03007s 	 Training Accuracy: 82.62% 	 Test Accuracy: 81.25%
+[  4/ 10] 	 FashionMNIST 	 Time 0.03060s 	 Training Accuracy: 66.41% 	 Test Accuracy: 56.25%
+[  5/ 10] 	        MNIST 	 Time 0.03625s 	 Training Accuracy: 81.54% 	 Test Accuracy: 81.25%
+[  5/ 10] 	 FashionMNIST 	 Time 0.02937s 	 Training Accuracy: 65.72% 	 Test Accuracy: 71.88%
+[  6/ 10] 	        MNIST 	 Time 0.03049s 	 Training Accuracy: 90.53% 	 Test Accuracy: 90.62%
+[  6/ 10] 	 FashionMNIST 	 Time 0.02975s 	 Training Accuracy: 69.14% 	 Test Accuracy: 62.50%
+[  7/ 10] 	        MNIST 	 Time 0.04204s 	 Training Accuracy: 92.68% 	 Test Accuracy: 90.62%
+[  7/ 10] 	 FashionMNIST 	 Time 0.02972s 	 Training Accuracy: 75.10% 	 Test Accuracy: 68.75%
+[  8/ 10] 	        MNIST 	 Time 0.03066s 	 Training Accuracy: 93.85% 	 Test Accuracy: 90.62%
+[  8/ 10] 	 FashionMNIST 	 Time 0.03352s 	 Training Accuracy: 74.02% 	 Test Accuracy: 71.88%
+[  9/ 10] 	        MNIST 	 Time 0.02887s 	 Training Accuracy: 94.53% 	 Test Accuracy: 93.75%
+[  9/ 10] 	 FashionMNIST 	 Time 0.03016s 	 Training Accuracy: 76.76% 	 Test Accuracy: 71.88%
+[ 10/ 10] 	        MNIST 	 Time 0.02880s 	 Training Accuracy: 94.73% 	 Test Accuracy: 87.50%
+[ 10/ 10] 	 FashionMNIST 	 Time 0.02935s 	 Training Accuracy: 80.08% 	 Test Accuracy: 65.62%
+
+[FINAL] 	        MNIST 	 Training Accuracy: 91.70% 	 Test Accuracy: 78.12%
+[FINAL] 	 FashionMNIST 	 Training Accuracy: 80.08% 	 Test Accuracy: 65.62%

      Appendix ​

      julia
      using InteractiveUtils
+InteractiveUtils.versioninfo()
+if @isdefined(LuxCUDA) && CUDA.functional(); println(); CUDA.versioninfo(); end
+if @isdefined(LuxAMDGPU) && LuxAMDGPU.functional(); println(); AMDGPU.versioninfo(); end
      Julia Version 1.10.2
+Commit bd47eca2c8a (2024-03-01 10:14 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 48 × AMD EPYC 7402 24-Core Processor
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
+Threads: 48 default, 0 interactive, 24 GC (on 2 virtual cores)
+Environment:
+  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
+  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6
+  JULIA_PROJECT = /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/docs
+  JULIA_AMDGPU_LOGGING_ENABLED = true
+  JULIA_DEBUG = Literate
+  JULIA_CPU_THREADS = 2
+  JULIA_NUM_THREADS = 48
+  JULIA_LOAD_PATH = @:@v#.#:@stdlib
+  JULIA_CUDA_HARD_MEMORY_LIMIT = 25%
+
+CUDA runtime 12.3, artifact installation
+CUDA driver 12.4
+NVIDIA driver 550.54.15
+
+CUDA libraries: 
+- CUBLAS: 12.3.4
+- CURAND: 10.3.4
+- CUFFT: 11.0.12
+- CUSOLVER: 11.5.4
+- CUSPARSE: 12.2.0
+- CUPTI: 21.0.0
+- NVML: 12.0.0+550.54.15
+
+Julia packages: 
+- CUDA: 5.2.0
+- CUDA_Driver_jll: 0.7.0+1
+- CUDA_Runtime_jll: 0.11.1+0
+
+Toolchain:
+- Julia: 1.10.2
+- LLVM: 15.0.7
+
+Environment:
+- JULIA_CUDA_HARD_MEMORY_LIMIT: 25%
+
+1 device:
+  0: NVIDIA A100-PCIE-40GB MIG 1g.5gb (sm_80, 3.443 GiB / 4.750 GiB available)
+┌ Warning: LuxAMDGPU is loaded but the AMDGPU is not functional.
+└ @ LuxAMDGPU ~/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6/packages/LuxAMDGPU/sGa0S/src/LuxAMDGPU.jl:19

      This page was generated using Literate.jl.

      `,22),p=[t];function l(k,e,r,E,d,g){return a(),i("div",null,p)}const F=s(h,[["render",l]]);export{c as __pageData,F as default}; diff --git a/v0.5.30/assets/tutorials_intermediate_3_HyperNet.md.DFqj-uR3.lean.js b/v0.5.30/assets/tutorials_intermediate_3_HyperNet.md.DFqj-uR3.lean.js new file mode 100644 index 000000000..15df1741a --- /dev/null +++ b/v0.5.30/assets/tutorials_intermediate_3_HyperNet.md.DFqj-uR3.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.BfjuC5t1.js";const c=JSON.parse('{"title":"Training a HyperNetwork on MNIST and FashionMNIST","description":"","frontmatter":{},"headers":[],"relativePath":"tutorials/intermediate/3_HyperNet.md","filePath":"tutorials/intermediate/3_HyperNet.md","lastUpdated":null}'),h={name:"tutorials/intermediate/3_HyperNet.md"},t=n("",22),p=[t];function l(k,e,r,E,d,g){return a(),i("div",null,p)}const F=s(h,[["render",l]]);export{c as __pageData,F as default}; diff --git a/v0.5.30/ecosystem.html b/v0.5.30/ecosystem.html new file mode 100644 index 000000000..bf8dc4870 --- /dev/null +++ b/v0.5.30/ecosystem.html @@ -0,0 +1,24 @@ + + + + + + Lux.jl Documentation + + + + + + + + + + + + + +
      Lux.jl Documentation

      Appearance

      Ecosystem

      Frameworks Extending Lux.jl

      DiffEqFlux.jl

      DiffEqFlux.jl

      Universal neural differential equations with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learning (SciML) and physics-informed machine learning methods

      SciMLSensitivity.jl

      SciMLSensitivity.jl

      A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, discretize-then-optimize, adjoint methods, and more for ODEs, SDEs, DDEs, DAEs, etc.

      NeuralPDE.jl

      NeuralPDE.jl

      Physics-Informed Neural Networks (PINN) and Deep BSDE Solvers of Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

      NeuralLyapunov.jl

      NeuralLyapunov.jl

      A library for searching for neural Lyapunov functions in Julia

      DeepEquilibriumNetworks.jl

      DeepEquilibriumNetworks.jl

      Implicit Layer Machine Learning via Deep Equilibrium Networks, O(1) backpropagation with accelerated convergence

      AbstractCosmologicalEmulators.jl

      AbstractCosmologicalEmulators.jl

      Repository containing the abstract interface to the emulators used in the CosmologicalEmulators organization

      ContinuousNormalizingFlows.jl

      ContinuousNormalizingFlows.jl

      Implementations of Infinitesimal Continuous Normalizing Flows Algorithms in Julia

      Sophon.jl

      Sophon.jl

      Efficient, Accurate, and Streamlined Training of Physics-Informed Neural Networks

      DataDrivenDiffEq.jl

      DataDrivenDiffEq.jl

      Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization

      NeuralGraphPDE.jl

      NeuralGraphPDE.jl

      Integrating Neural Ordinary Differential Equations, the Method of Lines, and Graph Neural Networks

      Solaris.jl

      Solaris.jl

      Lightweight module for fusing physical and neural models

      Boltz.jl

      Boltz.jl

      Accelerate your ML research using pre-built Deep Learning Models with Lux

      GeometricMachineLearning.jl

      GeometricMachineLearning.jl

      Structure Preserving Machine Learning Models in Julia

      Automatic Differentiation

      Zygote.jl

      Zygote.jl

      Lux.jl default choice for AD

      Tracker.jl

      Tracker.jl

      Well tested and robust AD library (might fail on edge cases)

      ForwardDiff.jl

      ForwardDiff.jl

      For forward mode AD support

      ReverseDiff.jl

      ReverseDiff.jl

      Tape based reverse mode AD (might fail on edge cases and doesn't work on GPU)

      Enzyme.jl

      Enzyme.jl

      Experimental Support but will become the Future Default

      Data Manipulation, Data Loading & Datasets

      Augmentor.jl

      Augmentor.jl

      Data augmentation for machine learning

      MLUtils.jl

      MLUtils.jl

      Utilities and abstractions for Machine Learning tasks

      MLDatasets.jl

      MLDatasets.jl

      Utility package for accessing common Machine Learning datasets in Julia

      Images.jl

      Images.jl

      An image library for Julia

      DataAugmentation.jl

      DataAugmentation.jl

      Flexible data augmentation library for machine and deep learning

      Neural Network Primitives

      NNlib.jl

      NNlib.jl

      Neural Network primitives with multiple backends

      LuxLib.jl

      LuxLib.jl

      Backend for Lux.jl

      Optimization

      Optimization.jl

      Optimization.jl

      Unified API for Optimization in Julia

      Optimisers.jl

      Optimisers.jl

      Optimisers.jl defines many standard optimisers and utilities for learning loops

      ParameterSchedulers.jl

      ParameterSchedulers.jl

      Common hyperparameter scheduling for ML

      Parameter Manipulation

      Functors.jl

      Functors.jl

      Parameterise all the things

      ComponentArrays.jl

      ComponentArrays.jl

      Arrays with arbitrarily nested named components

      Serialization

      Serialization.jl

      Serialization.jl

      Provides serialization of Julia objects

      JLD2.jl

      JLD2.jl

      HDF5-compatible file format in pure Julia

      Testing Utilities

      FiniteDiff.jl

      FiniteDiff.jl

      Fast non-allocating calculations of gradients, Jacobians, and Hessians with sparsity support

      FiniteDifferences.jl

      FiniteDifferences.jl

      High accuracy derivatives, estimated via numerical finite differences (formerly FDM.jl)

      JET.jl

      JET.jl

      JET employs Julia's type inference system to detect potential bugs and type instabilities

      LuxTestUtils.jl

      LuxTestUtils.jl

      Collection of Functions useful for testing various packages in the Lux Ecosystem

      Training Visualization & Logging

      MLFlowClient.jl

      MLFlowClient.jl

      Julia client for MLFlow

      TensorBoardLogger.jl

      TensorBoardLogger.jl

      Easy peasy logging to TensorBoard with Julia

      Wandb.jl

      Wandb.jl

      Unofficial Julia bindings for logging experiments to wandb.ai

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      Lux.jl Documentation

      Appearance


      Trusted by

      Scientific Computing

      SciML.ai

      Machine Learning

      Structure Preserving

      GeometricML.jl

      Machine Learning

      Physical Systems

      MeshGraphNets.jl

      Graph Neural Nets

      Citation ​

      If you found this library to be useful in academic work, then please cite:

      bibtex
      @software{pal2023lux,
+  author    = {Pal, Avik},
+  title     = {{Lux: Explicit Parameterization of Deep Neural Networks in Julia}},
+  month     = {April},
+  year      = 2023,
+  note      = {If you use this software, please cite it as below.},
+  publisher = {Zenodo},
+  version   = {v0.5.0},
+  doi       = {10.5281/zenodo.7808904},
+  url       = {https://doi.org/10.5281/zenodo.7808904}
+}
      bibtex
      @thesis{pal2023efficient,
+  title     = {{On Efficient Training \& Inference of Neural Differential Equations}},
+  author    = {Pal, Avik},
+  year      = {2023},
+  school    = {Massachusetts Institute of Technology}
+}
      + + + + \ No newline at end of file diff --git a/v0.5.30/introduction/index.html b/v0.5.30/introduction/index.html new file mode 100644 index 000000000..04e50139c --- /dev/null +++ b/v0.5.30/introduction/index.html @@ -0,0 +1,111 @@ + + + + + + Getting Started | Lux.jl Documentation + + + + + + + + + + + + + +
      Lux.jl Documentation

      Appearance


      Trusted by

      Scientific Computing

      SciML.ai

      Machine Learning

      Structure Preserving

      GeometricML.jl

      Machine Learning

      Physical Systems

      MeshGraphNets.jl

      Graph Neural Nets

      Getting Started ​

      Installation ​

      Install Julia v1.10 or above. Lux.jl is available through the Julia package manager. You can enter it by pressing ] in the REPL and then typing

      julia
      pkg> add Lux

      Alternatively, you can also do

      julia
      import Pkg; Pkg.add("Lux")

      Quickstart ​

      Pre-Requisites

      You need to install Optimisers and Zygote if not done already. Pkg.add(["Optimisers", "Zygote"])

      julia
      using Lux, Random, Optimisers, Zygote
+# using LuxCUDA, LuxAMDGPU, Metal # Optional packages for GPU support

      We take randomness very seriously

      julia
      # Seeding
+rng = Random.default_rng()
+Random.seed!(rng, 0)
      Random.TaskLocalRNG()

      Build the model

      julia
      # Construct the layer
+model = Chain(Dense(128, 256, tanh), Chain(Dense(256, 1, tanh), Dense(1, 10)))
      Chain(
+    layer_1 = Dense(128 => 256, tanh_fast),  # 33_024 parameters
+    layer_2 = Dense(256 => 1, tanh_fast),  # 257 parameters
+    layer_3 = Dense(1 => 10),           # 20 parameters
+)         # Total: 33_301 parameters,
+          #        plus 0 states.

      Models don't hold parameters and states so initialize them. From there on, we just use our standard AD and Optimisers API.

      julia
      # Get the device determined by Lux
+device = gpu_device()
+
+# Parameter and State Variables
+ps, st = Lux.setup(rng, model) .|> device
+
+# Dummy Input
+x = rand(rng, Float32, 128, 2) |> device
+
+# Run the model
+y, st = Lux.apply(model, x, ps, st)
+
+# Gradients
+## Pullback API to capture change in state
+(l, st_), pb = pullback(p -> Lux.apply(model, x, p, st), ps)
+gs = pb((one.(l), nothing))[1]
+
+# Optimization
+st_opt = Optimisers.setup(Adam(0.0001f0), ps)
+st_opt, ps = Optimisers.update(st_opt, ps, gs)
      ((layer_1 = (weight = Leaf(Adam(0.0001, (0.9, 0.999), 1.0e-8), (Float32[0.00313608 0.00806096 … 0.00476192 0.00732118; -0.00447309 -0.0119719 … -0.00822211 -0.0110335; … ; -0.00294453 -0.00749935 … -0.00426221 -0.00678769; 0.000750543 0.00195163 … 0.00120731 0.00178011], Float32[9.83485f-7 6.49782f-6 … 2.26756f-6 5.3599f-6; 2.00083f-6 1.43324f-5 … 6.76022f-6 1.21738f-5; … ; 8.67016f-7 5.62395f-6 … 1.81662f-6 4.60721f-6; 5.63307f-8 3.80882f-7 … 1.45758f-7 3.16876f-7], (0.81, 0.998001))), bias = Leaf(Adam(0.0001, (0.9, 0.999), 1.0e-8), (Float32[0.00954525; -0.0146331; … ; -0.00881351; 0.00233261;;], Float32[9.11106f-6; 2.14125f-5; … ; 7.76769f-6; 5.44098f-7;;], (0.81, 0.998001)))), layer_2 = (weight = Leaf(Adam(0.0001, (0.9, 0.999), 1.0e-8), (Float32[-0.0104967 0.0714637 … -0.0224641 0.108277], Float32[1.10179f-5 0.000510699 … 5.04628f-5 0.00117238], (0.81, 0.998001))), bias = Leaf(Adam(0.0001, (0.9, 0.999), 1.0e-8), (Float32[0.178909;;], Float32[0.0032008;;], (0.81, 0.998001)))), layer_3 = (weight = Leaf(Adam(0.0001, (0.9, 0.999), 1.0e-8), (Float32[-0.105128; -0.105128; … ; -0.105128; -0.105128;;], Float32[0.00110518; 0.00110518; … ; 0.00110518; 0.00110518;;], (0.81, 0.998001))), bias = Leaf(Adam(0.0001, (0.9, 0.999), 1.0e-8), (Float32[0.2; 0.2; … ; 0.2; 0.2;;], Float32[0.00399995; 0.00399995; … ; 0.00399995; 0.00399995;;], (0.81, 0.998001))))), (layer_1 = (weight = Float32[-0.11044693 0.10963185 … 0.097855344 -0.009167461; -0.0110904 0.07588978 … -0.03180492 0.088967875; … ; 0.01864451 -0.034903362 … -0.016194405 0.019176451; -0.09216565 -0.047490627 … -0.08869007 0.009417342], bias = Float32[-9.999999f-5; 9.999998f-5; … ; 9.999999f-5; -9.9999954f-5;;]), layer_2 = (weight = Float32[0.05391791 -0.103956826 … -0.050862882 0.020512676], bias = Float32[-0.0001;;]), layer_3 = (weight = Float32[-0.6546853; 0.6101978; … ; 0.41120994; 0.5494141;;], bias = Float32[-0.0001; -0.0001; … ; -0.0001; -0.0001;;])))

      Defining Custom Layers ​

      julia
      using Lux, Random, Optimisers, Zygote
+# using LuxCUDA, LuxAMDGPU, Metal # Optional packages for GPU support
+import Lux.Experimental: @compact

      We will define a custom MLP using the @compact macro. The macro takes in a list of parameters, layers and states, and a function defining the forward pass of the neural network.

      julia
      n_in = 1
+n_out = 1
+nlayers = 3
+
+model = @compact(w1=Dense(n_in, 128),
+    w2=[Dense(128, 128) for i in 1:nlayers],
+    w3=Dense(128, n_out),
+    act=relu) do x
+    embed = act(w1(x))
+    for w in w2
+        embed = act(w(embed))
+    end
+    out = w3(embed)
+    return out
+end
      @compact(
+    w1 = Dense(1 => 128),               # 256 parameters
+    w2 = NamedTuple(
+        1 = Dense(128 => 128),          # 16_512 parameters
+        2 = Dense(128 => 128),          # 16_512 parameters
+        3 = Dense(128 => 128),          # 16_512 parameters
+    ),
+    w3 = Dense(128 => 1),               # 129 parameters
+    act = relu,
+) do x 
+    embed = act(w1(x))
+    for w = w2
+        embed = act(w(embed))
+    end
+    out = w3(embed)
+    return out
+end       # Total: 49_921 parameters,
+          #        plus 1 states.

      We can initialize the model and train it with the same code as before!

      julia
      ps, st = Lux.setup(Xoshiro(0), model)
+
+model(randn(n_in, 32), ps, st)  # 1×32 Matrix as output.
+
+x_data = collect(-2.0f0:0.1f0:2.0f0)'
+y_data = 2 .* x_data .- x_data .^ 3
+st_opt = Optimisers.setup(Adam(), ps)
+
+for epoch in 1:1000
+    global st  # Put this in a function in real use-cases
+    (loss, st), pb = Zygote.pullback(ps) do p
+        y, st_ = model(x_data, p, st)
+        return sum(abs2, y .- y_data), st_
+    end
+    gs = only(pb((one(loss), nothing)))
+    epoch % 100 == 1 && println("Epoch: $(epoch) | Loss: $(loss)")
+    Optimisers.update!(st_opt, ps, gs)
+end
      Epoch: 1 | Loss: 84.32512
+Epoch: 101 | Loss: 0.08861052
+Epoch: 201 | Loss: 0.007037298
+Epoch: 301 | Loss: 0.005391656
+Epoch: 401 | Loss: 0.014058021
+Epoch: 501 | Loss: 0.0022117028
+Epoch: 601 | Loss: 0.0015865607
+Epoch: 701 | Loss: 0.21984956
+Epoch: 801 | Loss: 0.00019668281
+Epoch: 901 | Loss: 0.0018975141

      Additional Packages ​

      LuxDL hosts various packages that provide additional functionality for Lux.jl. All packages mentioned in this documentation are available via the Julia General Registry.

      You can install all those packages via import Pkg; Pkg.add(<package name>).

      GPU Support ​

      GPU Support for Lux.jl requires loading additional packages:

      + + + + \ No newline at end of file diff --git a/v0.5.30/introduction/overview.html b/v0.5.30/introduction/overview.html new file mode 100644 index 000000000..8c59ae614 --- /dev/null +++ b/v0.5.30/introduction/overview.html @@ -0,0 +1,24 @@ + + + + + + Why we wrote Lux? | Lux.jl Documentation + + + + + + + + + + + + + +
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      Why we wrote Lux? ​

      Julia already has quite a few well established Neural Network Frameworks – Flux & KNet. However, certain design elements – Coupled Model and Parameters & Internal Mutations – associated with these frameworks make them less compiler and user friendly. Making changes to address these problems in the respective frameworks would be too disruptive for users. Here comes in Lux: a neural network framework built completely using pure functions to make it both compiler and autodiff friendly.

      Design Principles ​

      • Layers must be immutable – cannot store any parameter/state but rather store the information to construct them

      • Layers are pure functions

      • Layers return a Tuple containing the result and the updated state

      • Given same inputs the outputs must be same – yes this must hold true even for stochastic functions. Randomness must be controlled using rngs passed in the state.

      • Easily extensible

      • Extensive Testing – All layers and features are tested across all supported AD backends across all supported hardware backends.

      Why use Lux over Flux? ​

      • Neural Networks for SciML: For SciML Applications (Neural ODEs, Deep Equilibrium Models) solvers typically expect a monolithic parameter vector. Flux enables this via its destructure mechanism, but destructure comes with various edge cases and limitations. Lux forces users to make an explicit distinction between state variables and parameter variables to avoid these issues. Also, it comes battery-included for distributed training.

      • Sensible display of Custom Layers – Ever wanted to see Pytorch like Network printouts or wondered how to extend the pretty printing of Flux's layers? Lux handles all of that by default.

      • Truly immutable models - No unexpected internal mutations since all layers are implemented as pure functions. All layers are also deterministic given the parameters and state: if a layer is supposed to be stochastic (say Dropout), the state must contain a seed which is then updated after the function call.

      • Easy Parameter Manipulation – By separating parameter data and layer structures, Lux makes implementing WeightNorm, SpectralNorm, etc. downright trivial. Without this separation, it is much harder to pass such parameters around without mutations which AD systems don't like.

      • Small Neural Networks on CPU – Lux is developed for training large neural networks. For smaller architectures, we recommend using SimpleChains.jl or even better use it in conjunction with Lux via ToSimpleChainsAdaptor.

      • Reliability – We have learned from the mistakes of the past with Flux and everything in our core framework is extensively tested, along with downstream CI to ensure that everything works as expected.

      Why not use Lux (and Julia for traditional Deep Learning in general) ? ​

      • Lack of Large Models Support – Classical deep learning is not Lux's primary focus. For these, python frameworks like PyTorch and Jax are better suited.

      • XLA Support – Lux doesn't compile to XLA which means no TPU support unfortunately.

      + + + + \ No newline at end of file diff --git a/v0.5.30/introduction/resources.html b/v0.5.30/introduction/resources.html new file mode 100644 index 000000000..51463d35b --- /dev/null +++ b/v0.5.30/introduction/resources.html @@ -0,0 +1,24 @@ + + + + + + Resources to Get Started | Lux.jl Documentation + + + + + + + + + + + + + +
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      Resources to Get Started ​

      • Go through the Quickstart Example.

      • Read the introductory tutorials on Julia and Lux.

      • Go through the examples sorted based on their complexity in the documentation.

      Have More Questions?

      For usage related questions, please use Github Discussions or JuliaLang Discourse (machine learning domain) which allows questions and answers to be indexed. To report bugs use github issues or even better send in a pull request.

      + + + + \ No newline at end of file diff --git a/v0.5.30/lux-logo-dark.svg b/v0.5.30/lux-logo-dark.svg new file mode 100644 index 000000000..ae8cbe3d9 --- /dev/null +++ b/v0.5.30/lux-logo-dark.svg @@ -0,0 +1,38 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.5.30/lux-logo.svg b/v0.5.30/lux-logo.svg new file mode 100644 index 000000000..0ba3c9000 --- /dev/null +++ b/v0.5.30/lux-logo.svg @@ -0,0 +1,38 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/v0.5.30/manual/debugging.html b/v0.5.30/manual/debugging.html new file mode 100644 index 000000000..8b6f816aa --- /dev/null +++ b/v0.5.30/manual/debugging.html @@ -0,0 +1,144 @@ + + + + + + Debugging Lux Models | Lux.jl Documentation + + + + + + + + + + + + + +
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      Debugging Lux Models ​

      Debugging DNNs can be very painful. Especially with the gigantic stacktraces for Lux, it is even harder to pin-point to which particular layer errored out. This page describes some useful tools that ship with Lux, that can help you debug your models.

      TL;DR

      Simply wrap your model with Lux.Experimental.@debug!!

      Don't Forget

      Remember to use the non Debug mode model after you finish debugging. Debug mode models are way slower.

      Let us construct a model which has an obviously incorrect dimension. In this example, you will see how easy it is to pin-point the problematic layer.

      Incorrect Model Specification: Dimension Mismatch Problems ​

      julia
      using Lux, Random
+
+model = Chain(Dense(1 => 16, relu), Chain(Dense(16 => 3), Dense(1 => 1)),
+    BatchNorm(1); disable_optimizations=true)
+
+model_debug = Lux.Experimental.@debug_mode model
      Chain(
+    layer_1 = DebugLayer(
+        layer = Dense(1 => 16, relu),   # 32 parameters
+    ),
+    layer_2 = Chain(
+        layer_1 = DebugLayer(
+            layer = Dense(16 => 3),     # 51 parameters
+        ),
+        layer_2 = DebugLayer(
+            layer = Dense(1 => 1),      # 2 parameters
+        ),
+    ),
+    layer_3 = DebugLayer(
+        layer = BatchNorm(1, affine=true, track_stats=true),  # 2 parameters, plus 3
+    ),
+)         # Total: 87 parameters,
+          #        plus 3 states.

      Note that we can use the parameters and states for model itself in model_debug, no need to make any changes. If you ran the original model this is the kind of error you would see:

      julia
      rng = Xoshiro(0)
+
+ps, st = Lux.setup(rng, model)
+x = randn(rng, Float32, 1, 1)
+
+try
+    model(x, ps, st)
+catch e
+    println(e)
+end
      DimensionMismatch("A has dimensions (1,1) but B has dimensions (3,1)")

      Ofcourse, this error will come with a detailed stacktrace, but it is still not very useful. Now let's try using the debug mode model:

      julia
      try
+    model_debug(x, ps, st)
+catch e
+    println(e)
+end
      [ Info: Input Type: Matrix{Float32} | Input Structure: (1, 1)
+[ Info: Running Layer: Dense(1 => 16, relu) at location model.layers.layer_1!
+[ Info: Output Type: Matrix{Float32} | Output Structure: (16, 1)
+[ Info: Input Type: Matrix{Float32} | Input Structure: (16, 1)
+[ Info: Running Layer: Dense(16 => 3) at location model.layers.layer_2.layers.layer_1!
+[ Info: Output Type: Matrix{Float32} | Output Structure: (3, 1)
+[ Info: Input Type: Matrix{Float32} | Input Structure: (3, 1)
+[ Info: Running Layer: Dense(1 => 1) at location model.layers.layer_2.layers.layer_2!
+┌ Error: Layer Dense(1 => 1) failed!! This layer is present at location model.layers.layer_2.layers.layer_2
+└ @ Lux.Experimental /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/src/contrib/debug.jl:110
+DimensionMismatch("A has dimensions (1,1) but B has dimensions (3,1)")

      See now we know that model.layers.layer_2.layers.layer_2 is the problematic layer. Let us fix that layer and see what happens:

      julia
      model = Chain(Dense(1 => 16, relu),
+    Chain(Dense(16 => 3),  // [!code --]
+    Chain(Dense(16 => 1),  // [!code ++]
+        Dense(1 => 1)),
+    BatchNorm(1); disable_optimizations=true)
      julia
      model_fixed = Chain(Dense(1 => 16, relu), Chain(Dense(16 => 1), Dense(1 => 1)),
+    BatchNorm(1); disable_optimizations=true)
+
+ps, st = Lux.setup(rng, model_fixed)
+
+model_fixed(x, ps, st)
      (Float32[0.0;;], (layer_1 = NamedTuple(), layer_2 = (layer_1 = NamedTuple(), layer_2 = NamedTuple()), layer_3 = (running_mean = Float32[-0.01397949], running_var = Float32[NaN], training = Val{true}())))

      Voila!! We have tracked down and fixed the problem.

      Tracking down NaNs ​

      Have you encountered those pesky little NaNs in your training? They are very hard to track down. We will create an artificially simulate NaNs in our model and see how we can track the offending layer.

      We can set nan_check to :forward, :backward or :both to check for NaNs in the debug model. (or even disable it by setting it to :none)

      julia
      model = Chain(Dense(1 => 16, relu), Chain(Dense(16 => 1), Dense(1 => 1)),
+    BatchNorm(1); disable_optimizations=true)
+
+ps, st = Lux.setup(rng, model)
+
+model_debug = Lux.Experimental.@debug_mode model nan_check=:both
      Chain(
+    layer_1 = DebugLayer(
+        layer = Dense(1 => 16, relu),   # 32 parameters
+    ),
+    layer_2 = Chain(
+        layer_1 = DebugLayer(
+            layer = Dense(16 => 1),     # 17 parameters
+        ),
+        layer_2 = DebugLayer(
+            layer = Dense(1 => 1),      # 2 parameters
+        ),
+    ),
+    layer_3 = DebugLayer(
+        layer = BatchNorm(1, affine=true, track_stats=true),  # 2 parameters, plus 3
+    ),
+)         # Total: 53 parameters,
+          #        plus 3 states.

      Let us set a value in the parameter to NaN:

      julia
      ps.layer_2.layer_2.weight[1, 1] = NaN
      NaN

      Now let us run the model

      julia
      model(x, ps, st)
      (Float32[NaN;;], (layer_1 = NamedTuple(), layer_2 = (layer_1 = NamedTuple(), layer_2 = NamedTuple()), layer_3 = (running_mean = Float32[NaN], running_var = Float32[NaN], training = Val{true}())))

      Ah as expected our output is NaN. But is is not very clear how to track where the first NaN occurred. Let's run the debug model and check:

      julia
      try
+    model_debug(x, ps, st)
+catch e
+    println(e)
+end
      [ Info: Input Type: Matrix{Float32} | Input Structure: (1, 1)
+[ Info: Running Layer: Dense(1 => 16, relu) at location model.layers.layer_1!
+[ Info: Output Type: Matrix{Float32} | Output Structure: (16, 1)
+[ Info: Input Type: Matrix{Float32} | Input Structure: (16, 1)
+[ Info: Running Layer: Dense(16 => 1) at location model.layers.layer_2.layers.layer_1!
+[ Info: Output Type: Matrix{Float32} | Output Structure: (1, 1)
+[ Info: Input Type: Matrix{Float32} | Input Structure: (1, 1)
+[ Info: Running Layer: Dense(1 => 1) at location model.layers.layer_2.layers.layer_2!
+DomainError((weight = Float32[NaN;;], bias = Float32[0.0;;]), "NaNs detected in parameters of layer Dense(1 => 1) at location model.layers.layer_2.layers.layer_2")

      And we have figured it out! The first NaN occurred in the parameters of model.layers.layer_2.layers.layer_2! But what if NaN occurs in the reverse pass! Let us define a custom layer and introduce a fake NaN in the backward pass.

      julia
      using ChainRulesCore, Zygote
+
+const CRC = ChainRulesCore
+
+offending_layer(x) = 2 .* x
      offending_layer (generic function with 1 method)
      julia
      model = Chain(Dense(1 => 16, relu), Chain(Dense(16 => 1), offending_layer),
+    BatchNorm(1); disable_optimizations=true)
+
+ps, st = Lux.setup(rng, model)
+
+model(x, ps, st)
      (Float32[0.0;;], (layer_1 = NamedTuple(), layer_2 = (layer_1 = NamedTuple(), layer_2 = NamedTuple()), layer_3 = (running_mean = Float32[-0.092828535], running_var = Float32[NaN], training = Val{true}())))

      Let us define a custom backward pass to introduce some NaNs:

      julia
      function CRC.rrule(::typeof(offending_layer), x)
+    y = offending_layer(x)
+    function ∇offending_layer(Δ)
+        Δ[1] = NaN
+        return NoTangent(), Δ
+    end
+    return y, ∇offending_layer
+end

      Let us compute the gradient of the layer now:

      julia
      Zygote.gradient(ps -> sum(first(model(x, ps, st))), ps)
      ((layer_1 = (weight = Float32[0.0; NaN; … ; NaN; 0.0;;], bias = Float32[0.0; NaN; … ; NaN; 0.0;;]), layer_2 = (layer_1 = (weight = Float32[NaN NaN … NaN NaN], bias = Float32[NaN;;]), layer_2 = nothing), layer_3 = (scale = Float32[0.0], bias = Fill(1.0f0, 1))),)

      Oh no!! A NaN is present in the gradient of ps. Let us run the debug model and see where the NaN occurred:

      julia
      model_debug = Lux.Experimental.@debug_mode model nan_check=:both
+
+try
+    Zygote.gradient(ps -> sum(first(model_debug(x, ps, st))), ps)
+catch e
+    println(e)
+end
      [ Info: Input Type: Matrix{Float32} | Input Structure: (1, 1)
+[ Info: Running Layer: Dense(1 => 16, relu) at location model.layers.layer_1!
+[ Info: Output Type: Matrix{Float32} | Output Structure: (16, 1)
+[ Info: Input Type: Matrix{Float32} | Input Structure: (16, 1)
+[ Info: Running Layer: Dense(16 => 1) at location model.layers.layer_2.layers.layer_1!
+[ Info: Output Type: Matrix{Float32} | Output Structure: (1, 1)
+[ Info: Input Type: Matrix{Float32} | Input Structure: (1, 1)
+[ Info: Running Layer: WrappedFunction(offending_layer) at location model.layers.layer_2.layers.layer_2!
+[ Info: Output Type: Matrix{Float32} | Output Structure: (1, 1)
+[ Info: Input Type: Matrix{Float32} | Input Structure: (1, 1)
+[ Info: Running Layer: BatchNorm(1, affine=true, track_stats=true) at location model.layers.layer_3!
+[ Info: Output Type: Matrix{Float32} | Output Structure: (1, 1)
+DomainError(Float32[NaN;;], "NaNs detected in pullback output for WrappedFunction(offending_layer) at location model.layers.layer_2.layers.layer_2!")

      And there you go our debug layer prints that the problem is in WrappedFunction(offending_layer) at location model.layers.layer_2.layers.layer_2! Once we fix the pullback of the layer, we will fix the NaNs.

      Conclusion ​

      In this manual section, we have discussed tracking down errors in Lux models. We have covered tracking incorrect model specifications and NaNs in forward and backward passes. However, remember that this is an Experimental feature, and there might be edge cases that don't work correctly. If you find any such cases, please open an issue on GitHub!

      + + + + \ No newline at end of file diff --git a/v0.5.30/manual/dispatch_custom_input.html b/v0.5.30/manual/dispatch_custom_input.html new file mode 100644 index 000000000..5e86a2b38 --- /dev/null +++ b/v0.5.30/manual/dispatch_custom_input.html @@ -0,0 +1,81 @@ + + + + + + Dispatching on Custom Input Types | Lux.jl Documentation + + + + + + + + + + + + + +
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      Dispatching on Custom Input Types ​

      Which function should participate in dispatch? ​

      • Defining a dispatch on (::Layer)(x::MyInputType, ps, st::NamedTuple) is inconvenient, since it requires the user to define a new method for every layer type.

      • (::AbstractExplicitLayer)(x::MyInputType, ps, st::NamedTuple) doesn't work.

      • Instead, we need to define the dispatch on Lux.apply(::AbstractExplicitLayer, x::MyInputType, ps, st::NamedTuple).

      Concrete Example ​

      Consider Neural ODEs. In these models, often time we want to every iteration of the neural network to take the current time as input. Here, we won't go through implementing an entire Neural ODE model. Instead we will define a time dependent version of Chain.

      Time-Dependent Chain Implementation ​

      julia
      using Lux, Random
+
+struct TDChain{L <: NamedTuple} <: Lux.AbstractExplicitContainerLayer{(:layers,)}
+    layers::L
+end
+
+function (l::TDChain)((x, t)::Tuple, ps, st::NamedTuple)
+    # Concatenate along the 2nd last dimension
+    sz = ntuple(i -> i == ndims(x) - 1 ? 1 : size(x, i), ndims(x))
+    t_ = ones(eltype(x), sz) .* t  # Needs to be modified for GPU
+    for name in keys(l.layers)
+        x, st_ = Lux.apply(getfield(l.layers, name), cat(x, t_; dims=ndims(x) - 1),
+                           getfield(ps, name), getfield(st, name))
+        st = merge(st, NamedTuple{(name,)}((st_,)))
+    end
+    return x, st
+end
+
+model = Chain(Dense(3, 4), TDChain((; d1=Dense(5, 4), d2=Dense(5, 4))), Dense(4, 1))
      Chain(
+    layer_1 = Dense(3 => 4),            # 16 parameters
+    layer_2 = TDChain(
+        layers = NamedTuple(
+            d1 = Dense(5 => 4),         # 24 parameters
+            d2 = Dense(5 => 4),         # 24 parameters
+        ),
+    ),
+    layer_3 = Dense(4 => 1),            # 5 parameters
+)         # Total: 69 parameters,
+          #        plus 0 states.

      Running the TDChain ​

      julia
      rng = MersenneTwister(0)
+ps, st = Lux.setup(rng, model)
+x = randn(rng, Float32, 3, 2)
+
+try
+    model(x, ps, st)
+catch e
+    Base.showerror(stdout, e)
+end
      MethodError: no method matching (::Main.TDChain{@NamedTuple{d1::Dense{true, typeof(identity), typeof(glorot_uniform), typeof(zeros32)}, d2::Dense{true, typeof(identity), typeof(glorot_uniform), typeof(zeros32)}}})(::Matrix{Float32}, ::@NamedTuple{d1::@NamedTuple{weight::Matrix{Float32}, bias::Matrix{Float32}}, d2::@NamedTuple{weight::Matrix{Float32}, bias::Matrix{Float32}}}, ::@NamedTuple{d1::@NamedTuple{}, d2::@NamedTuple{}})
+
+Closest candidates are:
+  (::Main.TDChain)(!Matched::Tuple, ::Any, ::NamedTuple)
+   @ Main dispatch_custom_input.md:29

      Writing the Correct Dispatch Rules ​

      • Create a Custom Layer storing the time.
      julia
      struct ArrayAndTime{A <: AbstractArray, T <: Real}
+    array::A
+    time::T
+end
      • Define the dispatch on Lux.apply(::AbstractExplicitLayer, x::ArrayAndTime, ps, st::NamedTuple).
      julia
      function Lux.apply(layer::Lux.AbstractExplicitLayer, x::ArrayAndTime, ps, st::NamedTuple)
+    y, st = layer(x.array, ps, st)
+    return ArrayAndTime(y, x.time), st
+end
+
+function Lux.apply(layer::TDChain, x::ArrayAndTime, ps, st::NamedTuple)
+    y, st = layer((x.array, x.time), ps, st)
+    return ArrayAndTime(y, x.time), st
+end
      • Run the model.
      julia
      xt = ArrayAndTime(x, 10.0f0)
+
+model(xt, ps, st)[1]
      Main.ArrayAndTime{Matrix{Float32}, Float32}(Float32[4.8016562 5.174927], 10.0f0)

      Using the Same Input for Non-TD Models ​

      Writing proper dispatch means we can simply replace the TDChain with a Chain (of course with dimension corrections) and the pipeline still works.

      julia
      model = Chain(Dense(3, 4), Chain((; d1=Dense(4, 4), d2=Dense(4, 4))), Dense(4, 1))
+
+ps, st = Lux.setup(rng, model)
+
+model(xt, ps, st)[1]
      Main.ArrayAndTime{Matrix{Float32}, Float32}(Float32[-0.08124366 -1.1121564], 10.0f0)
      + + + + \ No newline at end of file diff --git a/v0.5.30/manual/freezing_model_parameters.html b/v0.5.30/manual/freezing_model_parameters.html new file mode 100644 index 000000000..accddc7d3 --- /dev/null +++ b/v0.5.30/manual/freezing_model_parameters.html @@ -0,0 +1,82 @@ + + + + + + Freezing Model Parameters | Lux.jl Documentation + + + + + + + + + + + + + +
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      Freezing Model Parameters ​

      Warning

      API for freezing parameters should be considered experimental at this point.

      In this manual entry, we will go over how to freeze certain parameters in a model.

      Freezing Layers of a Particular Kind ​

      To freeze a particular kind of layer, let's say Dense in the following example. We can use Lux.Experimental.@layer_map and freeze layers if they are of type Dense.

      julia
      using Lux, Random
+
+rng = Random.default_rng()
+Random.seed!(rng, 0)
+
+model = Chain(Dense(3, 4), Chain(Dense(4, 4), Dropout(0.5f0), BatchNorm(4)),
+    Dense(4, 1); disable_optimizations=true)
+
+ps, st = Lux.setup(rng, model)
+
+x = randn(rng, Float32, 3, 2)
+
+model(x, ps, st)
+
+function freeze_dense(d::Lux.Dense, ps, st, ::String)
+    return Lux.freeze(d, ps, st, (:weight, :bias))
+end
+freeze_dense(l, ps, st, name) = (l, ps, st)
+
+model_frozen, ps_frozen, st_frozen = Lux.Experimental.@layer_map freeze_dense model ps st
+
+model_frozen(x, ps_frozen, st_frozen)
      (Float32[-0.53158027 0.53158027], (layer_1 = (frozen_params = (weight = Float32[-0.026350189 -0.5554656 -0.35653266; -0.17461072 0.6705545 0.29924855; -0.8935247 -0.42453378 -0.3020351; -0.7988979 -0.7666331 -0.7104237], bias = Float32[0.0; 0.0; 0.0; 0.0;;]), states = NamedTuple()), layer_2 = (layer_1 = (frozen_params = (weight = Float32[-0.47289538 -0.680748 0.1764085 0.34383082; 0.42747158 -0.13819042 -0.109261915 -0.6143286; -0.35790488 -0.20881107 0.70390546 0.48137343; 0.82561636 0.38187847 0.05779423 -0.35181466], bias = Float32[0.0; 0.0; 0.0; 0.0;;]), states = NamedTuple()), layer_2 = (rng = Random.Xoshiro(0x7c071df294e77583, 0xd36a58e0d4ae463e, 0x84df7ccd14e8a7b8, 0x727006748bb9e892, 0x22a21880af5dc689), training = Val{true}()), layer_3 = (running_mean = Float32[0.0, 0.021013658, -0.057823665, 0.0], running_var = Float32[0.9, 0.9088315, 0.9668715, 0.9], training = Val{true}())), layer_3 = (frozen_params = (weight = Float32[0.3981135 0.45468387 -0.07694905 0.8353388], bias = Float32[0.0;;]), states = NamedTuple())))

      Freezing by Layer Name ​

      When the function in layer_map is called, the 4th argument is the name of the layer. For example, if you want to freeze the 1st layer inside the inner Chain. The name for this would be <model>.layer_2.layer_1.

      julia
      
+function freeze_by_name(d, ps, st, name::String)
+    if name == "model.layer_2.layer_1"
+        return Lux.Experimental.freeze(d, ps, st, (:weight, :bias))
+    else
+        return d, ps, st
+    end
+end
      julia
      
+function freeze_dense(d::Dense, ps, st, ::String)
+    return Lux.Experimental.freeze(d, ps, st, (:weight, :bias))
+end
+freeze_dense(l, ps, st, _) = (l, ps, st)

      Freezing Part of the Parameters ​

      Instead of freezing all the parameters, we can simply specify (:weight,) to freeze only the weight parameter while training the bias parameter.

      julia
      
+function freeze_by_name(d, ps, st, name::String)
+    if name == "model.layer_2.layer_1"
+        return Lux.freeze(d, ps, st, (:weight,))
+    else
+        return d, ps, st
+    end
+end
      julia
      
+function freeze_by_name(d, ps, st, name::String)
+    if name == "model.layer_2.layer_1"
+        return Lux.freeze(d, ps, st, (:weight, :bias))
+    else
+        return d, ps, st
+    end
+end

      Freezing Part of a Chain ​

      Starting v0.4.22, we can directly index into a Chain. So freezing a part of a Chain, is extremely easy.

      julia
      using Lux, Random
+
+rng = Random.default_rng()
+Random.seed!(rng, 0)
+
+model = Chain(Dense(3, 4), Dense(4, 4), Dropout(0.5f0), BatchNorm(4), Dense(4, 1))
+
+model_frozen = Chain(model[1:2], Lux.freeze(model[3:4]), model[5])
+ps, st = Lux.setup(rng, model_frozen)
+
+x = randn(rng, Float32, 3, 2)
+
+model_frozen(x, ps, st)
      (Float32[-0.53158027 0.53158027], (layer_1 = NamedTuple(), layer_2 = NamedTuple(), layer_3 = (frozen_params = (layer_3 = NamedTuple(), layer_4 = (scale = Float32[1.0, 1.0, 1.0, 1.0], bias = Float32[0.0, 0.0, 0.0, 0.0])), states = (layer_3 = (rng = Random.Xoshiro(0x7c071df294e77583, 0xd36a58e0d4ae463e, 0x84df7ccd14e8a7b8, 0x727006748bb9e892, 0x22a21880af5dc689), training = Val{true}()), layer_4 = (running_mean = Float32[0.0, 0.021013658, -0.057823665, 0.0], running_var = Float32[0.9, 0.9088315, 0.9668715, 0.9], training = Val{true}()))), layer_4 = NamedTuple()))
      + + + + \ No newline at end of file diff --git a/v0.5.30/manual/gpu_management.html b/v0.5.30/manual/gpu_management.html new file mode 100644 index 000000000..5ebc3be11 --- /dev/null +++ b/v0.5.30/manual/gpu_management.html @@ -0,0 +1,49 @@ + + + + + + GPU Management | Lux.jl Documentation + + + + + + + + + + + + + +
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      GPU Management ​

      Info

      Starting from v0.5, Lux has transitioned to a new GPU management system. The old system using cpu and gpu functions is still in place but will be removed in v0.6. Using the old functions might lead to performance regressions if used inside performance critical code.

      Lux.jl can handle multiple GPU backends. Currently, the following backends are supported:

      julia
      using Lux, LuxCUDA, LuxAMDGPU  # Important to load trigger packages
+
+supported_gpu_backends()
      ("CUDA", "AMDGPU", "Metal")

      Metal Support

      Support for Metal GPUs should be considered extremely experimental at this point.

      Automatic Backend Management (Recommended Approach) ​

      Automatic Backend Management is done by two simple functions: cpu_device and gpu_device.

      • cpu_device: This is a simple function and just returns a LuxCPUDevice object.
      julia
      cdev = cpu_device()
      (::LuxCPUDevice) (generic function with 5 methods)
      julia
      x_cpu = randn(Float32, 3, 2)
      3×2 Matrix{Float32}:
+  0.433884   0.229779
+ -0.459193  -1.95972
+ -0.541064  -1.40102
      • gpu_device: This function performs automatic GPU device selection and returns an object.

        1. If no GPU is available, it returns a LuxCPUDevice object.

        2. If a LocalPreferences file is present, then the backend specified in the file is used. To set a backend, use Lux.gpu_backend!(<backend_name>). (a) If the trigger package corresponding to the device is not loaded, then a warning is displayed. (b) If no LocalPreferences file is present, then the first working GPU with loaded trigger package is used.

      julia
      gdev = gpu_device()
+
+x_gpu = x_cpu |> gdev
      3×2 CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}:
+  0.433884   0.229779
+ -0.459193  -1.95972
+ -0.541064  -1.40102
      julia
      (x_gpu |> cdev) ≈ x_cpu
      true

      Manual Backend Management ​

      Automatic Device Selection can be circumvented by directly using LuxCPUDevice and AbstractLuxGPUDevice objects.

      julia
      cdev = LuxCPUDevice()
+
+x_cpu = randn(Float32, 3, 2)
+
+if LuxCUDA.functional()
+    gdev = LuxCUDADevice()
+    x_gpu = x_cpu |> gdev
+elseif LuxAMDGPU.functional()
+    gdev = LuxAMDGPUDevice()
+    x_gpu = x_cpu |> gdev
+else
+    @info "No GPU is available. Using CPU."
+    x_gpu = x_cpu
+end
+
+(x_gpu |> cdev) ≈ x_cpu
      true
      + + + + \ No newline at end of file diff --git a/v0.5.30/manual/interface.html b/v0.5.30/manual/interface.html new file mode 100644 index 000000000..bfc43d85b --- /dev/null +++ b/v0.5.30/manual/interface.html @@ -0,0 +1,115 @@ + + + + + + Lux Interface | Lux.jl Documentation + + + + + + + + + + + + + +
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      Lux Interface ​

      Tip

      If you just want to define compatibility with Lux without actually using any of the other functionality provided by Lux (like layers), it is recommended to depend on LuxCore.jl instead of Lux.jl. LuxCore.jl is a significantly lighter dependency.

      First let's set the expectations straight.

      • Do you have to follow the interface? No.

      • Should you follow it? Probably yes.

      • Why? It provides the ability for frameworks built on top of Lux to be cross compatible. Additionally, any new functionality built into Lux, will just work for your framework.

      Warning

      The interface is optional for frameworks being developed independent of Lux. All functionality in the core library (and officially supported ones) must adhere to the interface

      Layer Interface ​

      Singular Layer ​

      If the layer doesn't contain any other Lux layer, then it is a Singular Layer. This means it should optionally subtype Lux.AbstractExplicitLayer but mandatorily define all the necessary functions mentioned in the docstrings. Consider a simplified version of Dense called Linear.

      First, setup the architectural details for this layer. Note, that the architecture doesn't contain any mutable structure like arrays. When in doubt, remember, once constructed a model architecture cannot change.

      Tip

      For people coming from Flux.jl background this might be weird. We recommend checking out the Flux to Lux migration guide first before proceeding.

      julia
      using Lux, Random
+
+struct Linear{F1, F2} <: Lux.AbstractExplicitLayer
+    in_dims::Int
+    out_dims::Int
+    init_weight::F1
+    init_bias::F2
+end
+
+function Linear(in_dims::Int, out_dims::Int; init_weight=Lux.glorot_uniform,
+    init_bias=Lux.zeros32)
+    return Linear{typeof(init_weight), typeof(init_bias)}(in_dims, out_dims, init_weight,
+        init_bias)
+end
+
+l = Linear(2, 4)
      Linear()

      Next, we need to implement functions which return the parameters and states for the layer. In case of Linear, the parameters are weight and bias while the states are empty. States become important when defining layers like BatchNorm, WeightNorm, etc. The recommended data structure for returning parameters is a NamedTuple, though anything satisfying the Parameter Interface is valid.

      julia
      function Lux.initialparameters(rng::AbstractRNG, l::Linear)
+    return (weight=l.init_weight(rng, l.out_dims, l.in_dims),
+            bias=l.init_bias(rng, l.out_dims, 1))
+end
+
+Lux.initialstates(::AbstractRNG, ::Linear) = NamedTuple()

      You could also implement Lux.parameterlength and Lux.statelength to prevent wasteful reconstruction of the parameters and states.

      julia
      # This works
+println("Parameter Length: ", Lux.parameterlength(l), "; State Length: ",
+    Lux.statelength(l))
+
+# But still recommened to define these
+Lux.parameterlength(l::Linear) = l.out_dims * l.in_dims + l.out_dims
+
+Lux.statelength(::Linear) = 0
      Parameter Length: 12; State Length: 0

      Tip

      You might notice that we don't pass in a PRNG for these functions. If your parameter length and/or state length depend on a random number generator, you should think really hard about what you are trying to do and why.

      Now, we need to define how the layer works. For this you make your layer a function with exactly 3 arguments – x the input, ps the parameters, and st the states. This function must return two things – y the output, and st_new the updated state.

      julia
      function (l::Linear)(x::AbstractMatrix, ps, st::NamedTuple)
+    y = ps.weight * x .+ ps.bias
+    return y, st
+end

      Finally, let's run this layer. If you have made this far into the documentation, we don't feel you need a refresher on that.

      julia
      rng = Random.default_rng()
+Random.seed!(rng, 0)
+
+ps, st = Lux.setup(rng, l)
+
+println("Parameter Length: ", Lux.parameterlength(l), "; State Length: ",
+    Lux.statelength(l))
+
+x = randn(rng, Float32, 2, 1)
+
+Lux.apply(l, x, ps, st) # or `l(x, ps, st)`
      (Float32[-0.15276335; 0.45325348; 1.0207279; 0.78226817;;], NamedTuple())

      Container Layer ​

      If your layer comprises of other Lux layers, then it is a Container Layer. Note that you could treat it as a Singular Layer, and it is still fine. FWIW, if you cannot subtype your layer with Lux.AbstractExplicitContainerLayer then you should go down the Singular Layer route. But subtyping allows us to bypass some of these common definitions. Let us now define a layer, which is basically a composition of two linear layers.

      julia
      struct ComposedLinear{L1, L2} <: Lux.AbstractExplicitContainerLayer{(:linear_1, :linear_2)}
+    linear_1::L1
+    linear_2::L2
+end
+
+function (cl::ComposedLinear)(x::AbstractMatrix, ps, st::NamedTuple)
+    # To access the parameters and states for `linear_1` we do `ps.linear_1` and
+    # `st.linear_1`. Similarly for `linear_2`
+    y, st_l1 = cl.linear_1(x, ps.linear_1, st.linear_1)
+    y, st_l2 = cl.linear_2(y, ps.linear_2, st.linear_2)
+    # Finally, we need to return the new state which has the exact structure as `st`
+    return y, (linear_1 = st_l1, linear_2 = st_l2)
+end

      Here, you will notice we have passed (:linear_1, :linear_2) to the supertype. It essentially informs the type that, <obj>.linear_1 and <obj>.linear_2 are Lux layers and we need to construct parameters and states for those. Let's construct these and see:

      julia
      model = ComposedLinear(Linear(2, 4), Linear(4, 2))
+display(model)
+
+ps, st = Lux.setup(rng, model)
+
+println("Parameters: ", ps)
+println("States: ", st)
+
+println("Parameter Length: ", Lux.parameterlength(model), "; State Length: ",
+    Lux.statelength(model))
+
+x = randn(rng, Float32, 2, 1)
+
+Lux.apply(model, x, ps, st) # or `model(x, ps, st)`
      (Float32[1.3410565; 0.78000563;;], (linear_1 = NamedTuple(), linear_2 = NamedTuple()))

      Parameter Interface ​

      We accept any parameter type as long as we can fetch the parameters using getproperty(obj, :parameter_name). This allows us to simultaneously support NamedTuples and ComponentArrays. Let us go through a concrete example of what it means. Consider Dense which expects two parameters named weight and bias.

      Info

      If you are defining your own parameter type, it is your responsibility to make sure that it works with the AutoDiff System you are using.

      julia
      using Lux, Random
+
+d = Dense(2, 3)
+rng = Random.default_rng()
+Random.seed!(rng, 0)
+
+ps_default, st = Lux.setup(rng, d)
+
+x = randn(rng, Float32, 2, 1)
+
+println("Result with `NamedTuple` parameters: ", first(d(x, ps_default, st)))
      Result with `NamedTuple` parameters: Float32[1.135916; 0.7668784; -1.0876652;;]

      Let, us define a custom parameter type with fields myweight and mybias but if we try to access weight we get back myweight, similar for bias.

      Warning

      This is for demonstrative purposes, don't try this at home!

      julia
      struct DenseLayerParameters{W, B}
+    myweight::W
+    mybias::B
+end
+
+function Base.getproperty(ps::DenseLayerParameters, x::Symbol)
+    if x == :weight
+        return getfield(ps, :myweight)
+    elseif x == :bias
+        return getfield(ps, :mybias)
+    end
+    return getfield(ps, x)
+end
+
+ps = DenseLayerParameters(ps_default.weight, ps_default.bias)
+
+println("Result with `DenseLayerParameters` parameters: ", first(d(x, ps, st)))
      Result with `DenseLayerParameters` parameters: Float32[1.135916; 0.7668784; -1.0876652;;]

      The takeaway from this shouldn't be – lets define weird parameter types. Simply because you can do weird things like this doesn't mean you should, since it only leads to bugs.

      Instead this shows the flexibility you have for how your parameters can be structured.

      State Interface ​

      States are always type constrained to be NamedTuple. The structure of the input state must match that of the output state, i.e. keys(st_in) == keys(st_out). This doesn't imply that types of the input and output state match. To generate efficient code, we often do dispatch on the state, for example, Dropout, BatchNorm, etc.

      + + + + \ No newline at end of file diff --git a/v0.5.30/manual/migrate_from_flux.html b/v0.5.30/manual/migrate_from_flux.html new file mode 100644 index 000000000..dd9d817b4 --- /dev/null +++ b/v0.5.30/manual/migrate_from_flux.html @@ -0,0 +1,98 @@ + + + + + + Migrating from Flux to Lux | Lux.jl Documentation + + + + + + + + + + + + + +
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      Migrating from Flux to Lux ​

      For the core library layers like Dense, Conv, etc. we have intentionally kept the API very similar to Flux. In most cases, replacing using Flux with using Lux should be enough to get you started. We cover the additional changes that you will have to make in the following example.

      julia
      using Lux, Random, NNlib, Zygote
+
+model = Chain(Dense(2 => 4), BatchNorm(4, relu), Dense(4 => 2))
+rng = Random.default_rng()
+x = randn(rng, Float32, 2, 4)
+
+ps, st = Lux.setup(rng, model)
+
+model(x, ps, st)
+
+gradient(ps -> sum(first(model(x, ps, st))), ps)
      julia
      using Flux, Random, NNlib, Zygote
+
+model = Chain(Dense(2 => 4), BatchNorm(4, relu), Dense(4 => 2))
+rng = Random.default_rng()
+x = randn(rng, Float32, 2, 4)
+
+
+
+model(x)
+
+gradient(model -> sum(model(x)), model)

      Implementing Custom Layers ​

      Flux and Lux operate under extremely different design philosophies regarding how layers should be implemented. A summary of the differences would be:

      • Flux stores everything in a single struct and relies on Functors.@functor and Flux.trainable to distinguish between trainable and non-trainable parameters.

      • Lux relies on the user to define Lux.initialparameters and Lux.initialstates to distinguish between trainable parameters (called "parameters") and non-trainable parameters (called "states"). Additionally, Lux layers define the model architecture, hence device transfer utilities like gpu_device, cpu_device, etc. cannot be applied on Lux layers, instead they need to be applied on the parameters and states.

      Let's work through a concrete example to demonstrate this. We will implement a very simple layer that computes A×B×x where A is not trainable and B is trainable.

      julia
      using Lux, Random, NNlib, Zygote
+
+struct LuxLinear <: Lux.AbstractExplicitLayer
+    init_A
+    init_B
+end
+
+function LuxLinear(A::AbstractArray, B::AbstractArray)
+    # Storing Arrays or any mutable structure inside a Lux Layer is not recommended
+    # instead we will convert this to a function to perform lazy initialization
+    return LuxLinear(() -> copy(A), () -> copy(B))
+end
+
+# `B` is a parameter
+Lux.initialparameters(::AbstractRNG, layer::LuxLinear) = (B=layer.init_B(),)
+
+# `A` is a state
+Lux.initialstates(::AbstractRNG, layer::LuxLinear) = (A=layer.init_A(),)
+
+(l::LuxLinear)(x, ps, st) = st.A * ps.B * x, st
      julia
      using Flux, Random, NNlib, Zygote, Optimisers
+
+struct FluxLinear
+    A
+    B
+end
+
+
+
+
+
+
+
+# `A` is not trainable
+Optimisers.trainable(f::FluxLinear) = (B=f.B,)
+
+# Needed so that both `A` and `B` can be transfered between devices
+Flux.@functor FluxLinear
+
+(l::FluxLinear)(x) = l.A * l.B * x

      Now let us run the model.

      julia
      rng = Random.default_rng()
+model = LuxLinear(randn(rng, 2, 4), randn(rng, 4, 2))
+x = randn(rng, 2, 1)
+
+ps, st = Lux.setup(rng, model)
+
+model(x, ps, st)
+
+gradient(ps -> sum(first(model(x, ps, st))), ps)
      julia
      rng = Random.default_rng()
+model = FluxLinear(randn(rng, 2, 4), randn(rng, 4, 2))
+x = randn(rng, 2, 1)
+
+
+
+model(x)
+
+gradient(model -> sum(model(x)), model)

      To reiterate some important points:

      • Don't store mutables like Arrays inside a Lux Layer.

      • Parameters and States should be constructured inside the respective initial* functions.

      Certain Important Implementation Details ​

      Training/Inference Mode ​

      Flux supports a mode called :auto which automatically decides if the user is training the model or running inference. This is the default mode for Flux.BatchNorm, Flux.GroupNorm, Flux.Dropout, etc. Lux doesn't support this mode (specifically to keep code simple and do exactly what the user wants), hence our default mode is training. This can be changed using Lux.testmode.

      Can we still use Flux Layers? ​

      If you have Flux loaded in your code, you can use the function FromFluxAdaptor to automatically convert your model to Lux. Note that in case a native Lux counterpart isn't available, we fallback to using Optimisers.destructure.

      + + + + \ No newline at end of file diff --git a/v0.5.30/manual/weight_initializers.html b/v0.5.30/manual/weight_initializers.html new file mode 100644 index 000000000..527b09488 --- /dev/null +++ b/v0.5.30/manual/weight_initializers.html @@ -0,0 +1,53 @@ + + + + + + Initializing Weights | Lux.jl Documentation + + + + + + + + + + + + + +
      Lux.jl Documentation

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      SciML.ai

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      MeshGraphNets.jl

      Graph Neural Nets

      Initializing Weights ​

      WeightInitializers.jl provides common weight initialization schemes for deep learning models.

      julia
      using WeightInitializers, Random
+
+# Fixing rng
+rng = Random.MersenneTwister(42)
      Random.MersenneTwister(42)
      julia
      # Explicit rng call
+weights = kaiming_normal(rng, 2, 5)
      2×5 Matrix{Float32}:
+ -0.351662   0.0171745   1.12442   -0.296372   -1.67094
+ -0.281053  -0.18941    -0.724099   0.0987538   0.634549
      julia
      # Default rng call
+weights = kaiming_normal(2, 5)
      2×5 Matrix{Float32}:
+ -0.227513  -0.265372   0.265788  1.29955  -0.192836
+  0.687611   0.454679  -0.433656  0.20548   0.292002
      julia
      # Passing kwargs (if needed) with explicit rng call
+weights_cl = kaiming_normal(rng; gain=1.0)
+weights = weights_cl(2, 5)
      2×5 Matrix{Float32}:
+ 0.484056   0.231723   0.164379   0.306147   0.18365
+ 0.0836414  0.666965  -0.396323  -0.711329  -0.382971
      julia
      # Passing kwargs (if needed) with default rng call
+weights_cl = kaiming_normal(; gain=1.0)
+weights = weights_cl(2, 5)
      2×5 Matrix{Float32}:
+ -0.160876  -0.187646   0.18794   0.918918  -0.136356
+  0.486214   0.321506  -0.306641  0.145296   0.206476

      To generate weights directly on GPU, pass in a CUDA.RNG. (Note that this is currently implemented only for NVIDIA GPUs)

      julia
      using LuxCUDA
+
+weights = kaiming_normal(CUDA.default_rng(), 2, 5)
      2×5 CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}:
+ -0.152879  0.151805  0.115322  0.0608437  -0.357408
+ -0.671014  0.283396  0.260171  0.425698   -0.701588

      You can also generate Complex Numbers:

      julia
      weights = kaiming_normal(CUDA.default_rng(), ComplexF32, 2, 5)
      2×5 CuArray{ComplexF32, 2, CUDA.Mem.DeviceBuffer}:
+ -0.239414-0.306575im  0.0877513-0.485896im  …  -0.328706-0.340686im
+ 0.0245199-0.04416im    0.252702-0.161867im       0.41303-0.533871im

      Quick examples ​

      The package is meant to be working with deep learning libraries such as (F)Lux. All the methods take as input the chosen rng type and the dimension for the array.

      julia
      weights = init(rng, dims...)

      The rng is optional, if not specified a default one will be used.

      julia
      weights = init(dims...)

      If there is the need to use keyword arguments the methods can be called with just the rng (optionally) and the keywords to get in return a function behaving like the two examples above.

      julia
      weights_init = init(rng; kwargs...)
+weights = weights_init(rng, dims...)
+
+# Or
+
+weights_init = init(; kwargs...)
+weights = weights_init(dims...)
      + + + + \ No newline at end of file diff --git a/v0.5.30/siteinfo.js b/v0.5.30/siteinfo.js new file mode 100644 index 000000000..5f84163a4 --- /dev/null +++ b/v0.5.30/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v0.5.30"; diff --git a/v0.5.30/tutorials/advanced/1_GravitationalWaveForm.html b/v0.5.30/tutorials/advanced/1_GravitationalWaveForm.html new file mode 100644 index 000000000..382708877 --- /dev/null +++ b/v0.5.30/tutorials/advanced/1_GravitationalWaveForm.html @@ -0,0 +1,326 @@ + + + + + + Training a Neural ODE to Model Gravitational Waveforms | Lux.jl Documentation + + + + + + + + + + + + + +
      Lux.jl Documentation

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      SciML.ai

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      Physical Systems

      MeshGraphNets.jl

      Graph Neural Nets

      Training a Neural ODE to Model Gravitational Waveforms ​

      This code is adapted from Astroinformatics/ScientificMachineLearning

      The code has been minimally adapted from Keith et. al. 2021 which originally used Flux.jl

      Package Imports ​

      julia
      using Lux, ComponentArrays, LineSearches, LuxAMDGPU, LuxCUDA, OrdinaryDiffEq, Optimization,
+      OptimizationOptimJL, Printf, Random, SciMLSensitivity
+using CairoMakie
+
+CUDA.allowscalar(false)

      Define some Utility Functions ​

      Tip

      This section can be skipped. It defines functions to simulate the model, however, from a scientific machine learning perspective, isn't super relevant.

      We need a very crude 2-body path. Assume the 1-body motion is a newtonian 2-body position vector r=r1−r2 and use Newtonian formulas to get r1, r2 (e.g. Theoretical Mechanics of Particles and Continua 4.3)

      julia
      function one2two(path, m₁, m₂)
+    M = m₁ + m₂
+    r₁ = m₂ / M .* path
+    r₂ = -m₁ / M .* path
+    return r₁, r₂
+end
      one2two (generic function with 1 method)

      Next we define a function to perform the change of variables: (χ(t),ϕ(t))↦(x(t),y(t))

      julia
      @views function soln2orbit(soln, model_params=nothing)
+    @assert size(soln, 1) ∈ [2, 4] "size(soln,1) must be either 2 or 4"
+
+    if size(soln, 1) == 2
+        χ = soln[1, :]
+        ϕ = soln[2, :]
+
+        @assert length(model_params)==3 "model_params must have length 3 when size(soln,2) = 2"
+        p, M, e = model_params
+    else
+        χ = soln[1, :]
+        ϕ = soln[2, :]
+        p = soln[3, :]
+        e = soln[4, :]
+    end
+
+    r = p ./ (1 .+ e .* cos.(χ))
+    x = r .* cos.(ϕ)
+    y = r .* sin.(ϕ)
+
+    orbit = vcat(x', y')
+    return orbit
+end
      soln2orbit (generic function with 2 methods)

      This function uses second-order one-sided difference stencils at the endpoints; see https://doi.org/10.1090/S0025-5718-1988-0935077-0

      julia
      function d_dt(v::AbstractVector, dt)
+    a = -3 / 2 * v[1] + 2 * v[2] - 1 / 2 * v[3]
+    b = (v[3:end] .- v[1:(end - 2)]) / 2
+    c = 3 / 2 * v[end] - 2 * v[end - 1] + 1 / 2 * v[end - 2]
+    return [a; b; c] / dt
+end
      d_dt (generic function with 1 method)

      This function uses second-order one-sided difference stencils at the endpoints; see https://doi.org/10.1090/S0025-5718-1988-0935077-0

      julia
      function d2_dt2(v::AbstractVector, dt)
+    a = 2 * v[1] - 5 * v[2] + 4 * v[3] - v[4]
+    b = v[1:(end - 2)] .- 2 * v[2:(end - 1)] .+ v[3:end]
+    c = 2 * v[end] - 5 * v[end - 1] + 4 * v[end - 2] - v[end - 3]
+    return [a; b; c] / (dt^2)
+end
      d2_dt2 (generic function with 1 method)

      Now we define a function to compute the trace-free moment tensor from the orbit

      julia
      function orbit2tensor(orbit, component, mass=1)
+    x = orbit[1, :]
+    y = orbit[2, :]
+
+    Ixx = x .^ 2
+    Iyy = y .^ 2
+    Ixy = x .* y
+    trace = Ixx .+ Iyy
+
+    if component[1] == 1 && component[2] == 1
+        tmp = Ixx .- trace ./ 3
+    elseif component[1] == 2 && component[2] == 2
+        tmp = Iyy .- trace ./ 3
+    else
+        tmp = Ixy
+    end
+
+    return mass .* tmp
+end
+
+function h_22_quadrupole_components(dt, orbit, component, mass=1)
+    mtensor = orbit2tensor(orbit, component, mass)
+    mtensor_ddot = d2_dt2(mtensor, dt)
+    return 2 * mtensor_ddot
+end
+
+function h_22_quadrupole(dt, orbit, mass=1)
+    h11 = h_22_quadrupole_components(dt, orbit, (1, 1), mass)
+    h22 = h_22_quadrupole_components(dt, orbit, (2, 2), mass)
+    h12 = h_22_quadrupole_components(dt, orbit, (1, 2), mass)
+    return h11, h12, h22
+end
+
+function h_22_strain_one_body(dt::T, orbit) where {T}
+    h11, h12, h22 = h_22_quadrupole(dt, orbit)
+
+    h₊ = h11 - h22
+    hₓ = T(2) * h12
+
+    scaling_const = √(T(π) / 5)
+    return scaling_const * h₊, -scaling_const * hₓ
+end
+
+function h_22_quadrupole_two_body(dt, orbit1, mass1, orbit2, mass2)
+    h11_1, h12_1, h22_1 = h_22_quadrupole(dt, orbit1, mass1)
+    h11_2, h12_2, h22_2 = h_22_quadrupole(dt, orbit2, mass2)
+    h11 = h11_1 + h11_2
+    h12 = h12_1 + h12_2
+    h22 = h22_1 + h22_2
+    return h11, h12, h22
+end
+
+function h_22_strain_two_body(dt::T, orbit1, mass1, orbit2, mass2) where {T}
+    # compute (2,2) mode strain from orbits of BH 1 of mass1 and BH2 of mass 2
+
+    @assert abs(mass1 + mass2 - 1.0)<1e-12 "Masses do not sum to unity"
+
+    h11, h12, h22 = h_22_quadrupole_two_body(dt, orbit1, mass1, orbit2, mass2)
+
+    h₊ = h11 - h22
+    hₓ = T(2) * h12
+
+    scaling_const = √(T(π) / 5)
+    return scaling_const * h₊, -scaling_const * hₓ
+end
+
+function compute_waveform(dt::T, soln, mass_ratio, model_params=nothing) where {T}
+    @assert mass_ratio≤1 "mass_ratio must be <= 1"
+    @assert mass_ratio≥0 "mass_ratio must be non-negative"
+
+    orbit = soln2orbit(soln, model_params)
+    if mass_ratio > 0
+        m₂ = inv(T(1) + mass_ratio)
+        m₁ = mass_ratio * m₂
+
+        orbit₁, orbit₂ = one2two(orbit, m₁, m₂)
+        waveform = h_22_strain_two_body(dt, orbit1, mass1, orbit2, mass2)
+    else
+        waveform = h_22_strain_one_body(dt, orbit)
+    end
+    return waveform
+end
      compute_waveform (generic function with 2 methods)

      Simulating the True Model ​

      RelativisticOrbitModel defines system of odes which describes motion of point like particle in schwarzschild background, uses

      u[1]=χu[2]=ϕ

      where, p, M, and e are constants

      julia
      function RelativisticOrbitModel(u, (p, M, e), t)
+    χ, ϕ = u
+
+    numer = (p - 2 - 2 * e * cos(χ)) * (1 + e * cos(χ))^2
+    denom = sqrt((p - 2)^2 - 4 * e^2)
+
+    χ̇ = numer * sqrt(p - 6 - 2 * e * cos(χ)) / (M * (p^2) * denom)
+    ϕ̇ = numer / (M * (p^(3 / 2)) * denom)
+
+    return [χ̇, ϕ̇]
+end
+
+mass_ratio = 0.0         # test particle
+u0 = Float64[π, 0.0]     # initial conditions
+datasize = 250
+tspan = (0.0f0, 6.0f4)   # timespace for GW waveform
+tsteps = range(tspan[1], tspan[2]; length=datasize)  # time at each timestep
+dt_data = tsteps[2] - tsteps[1]
+dt = 100.0
+const ode_model_params = [100.0, 1.0, 0.5]; # p, M, e

      Let's simulate the true model and plot the results using OrdinaryDiffEq.jl

      julia
      prob = ODEProblem(RelativisticOrbitModel, u0, tspan, ode_model_params)
+soln = Array(solve(prob, RK4(); saveat=tsteps, dt, adaptive=false))
+waveform = first(compute_waveform(dt_data, soln, mass_ratio, ode_model_params))
+
+begin
+    fig = Figure()
+    ax = CairoMakie.Axis(fig[1, 1]; xlabel="Time", ylabel="Waveform")
+
+    l = lines!(ax, tsteps, waveform; linewidth=2, alpha=0.75)
+    s = scatter!(ax, tsteps, waveform; markershape=:circle,
+        markersize=12, markeralpha=0.25, alpha=0.5)
+
+    axislegend(ax, [[l, s]], ["Waveform Data"])
+
+    fig
+end

      Defiing a Neural Network Model ​

      Next, we define the neural network model that takes 1 input (time) and has two outputs. We'll make a function ODE_model that takes the initial conditions, neural network parameters and a time as inputs and returns the derivatives.

      It is typically never recommended to use globals but incase you do use them, make sure to mark them as const.

      We will deviate from the standard Neural Network initialization and use WeightInitializers.jl,

      julia
      const nn = Chain(Base.Fix1(broadcast, cos),
+    Dense(1 => 32, cos; init_weight=truncated_normal(; std=1e-4)),
+    Dense(32 => 32, cos; init_weight=truncated_normal(; std=1e-4)),
+    Dense(32 => 2; init_weight=truncated_normal(; std=1e-4)))
+ps, st = Lux.setup(Xoshiro(), nn)
      ((layer_1 = NamedTuple(), layer_2 = (weight = Float32[-0.00011973267; -6.019302f-5; 9.096157f-5; 4.2661748f-5; 9.349409f-7; 0.00016044428; -9.652911f-6; -0.00013854839; 9.681807f-6; -2.8657123f-5; 0.00017334803; 2.4411342f-5; 9.011604f-5; 5.220362f-5; 0.00024906726; -2.4143723f-5; 0.00012566449; -4.8479058f-5; 4.074634f-5; 1.0247664f-5; -0.0001859722; 3.7356087f-5; -7.656956f-5; -1.2043876f-5; -8.47999f-5; -2.4505294f-5; -7.9587626f-5; -0.00022258626; -0.0001703838; 2.2777765f-5; 4.271127f-5; 6.0953906f-5;;], bias = Float32[0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0;;]), layer_3 = (weight = Float32[-1.0062973f-5 -0.0001435936 7.171802f-5 3.4863042f-6 0.00017328089 6.824237f-5 -0.00012931744 7.675739f-6 0.00022924854 -0.00011960628 0.00011614925 -0.00013504615 4.9548744f-5 1.507356f-5 -0.00010520048 9.820607f-5 0.00011530446 -5.298501f-5 3.924124f-5 -8.876832f-5 6.5198125f-5 4.548969f-5 5.3590033f-5 -0.000111658905 8.5903535f-5 -3.4463697f-5 0.00013809335 1.6326525f-5 6.29639f-5 6.3808046f-5 5.5576777f-5 -0.0001310525; -7.0357426f-5 9.636652f-5 -2.7267588f-5 -5.7131452f-5 0.00015933493 9.020348f-5 -1.280962f-5 -1.5835829f-5 1.2373991f-5 -0.0003102026 -1.5455973f-5 -5.0626495f-5 -7.3990675f-5 0.00022303218 -5.265653f-5 5.5802695f-5 0.000119704986 2.3875706f-5 2.6456584f-5 -1.1514318f-5 3.4455326f-5 8.091209f-5 -1.6922031f-5 -9.741731f-5 -0.00013727894 -9.3055656f-5 0.00014561473 -0.00012389639 5.852755f-5 -0.000109424866 -4.5462173f-5 0.00021897774; -5.4261145f-5 0.000121771845 0.00020005245 2.6634425f-5 -2.619291f-5 -0.00020373413 -1.2680036f-6 3.037937f-5 -5.047399f-5 -1.8179611f-6 9.946187f-5 5.8790112f-5 -0.00014307268 3.3849017f-5 -0.00016031059 2.021655f-6 -3.0627314f-5 4.2110256f-5 -2.9767696f-5 0.00021924138 2.025092f-5 0.00011184174 -0.00019683011 2.243284f-5 6.390769f-5 1.2823031f-6 0.00012127408 8.413545f-5 5.0939067f-5 -3.1260803f-5 7.489051f-5 -0.000117571406; 8.286847f-5 5.6977842f-5 -0.00011781059 -9.9578145f-5 -1.48217305f-5 7.6619406f-5 7.078823f-5 -1.2595202f-5 -1.8840798f-5 0.00013955703 7.530427f-5 -3.0709045f-5 0.0002204093 0.00010372281 0.00010360437 -4.6901005f-6 0.000103564205 9.927554f-5 0.00015315072 0.00016233182 -6.378829f-5 0.00027685237 -0.00022597678 0.00013754105 9.243972f-5 -0.00012381934 -0.00010605406 -0.0001433673 -2.6276277f-5 -0.00013443631 -0.00011772916 5.814016f-5; -0.00016425819 3.8754493f-5 -0.00016896137 6.288182f-5 -0.00023414425 -9.0244575f-5 -5.2501702f-5 1.4775569f-5 4.904329f-5 -1.5052479f-5 -2.7051257f-5 -3.614626f-5 0.00012460808 -0.00018959433 5.600226f-5 -5.7855483f-5 3.128997f-5 9.41794f-5 8.772447f-6 -0.00014428626 -3.1018924f-5 1.3908119f-6 -4.760862f-7 -0.00012216585 1.242881f-5 4.9815384f-7 -0.00010849579 -0.00010241591 0.00014788071 -8.60535f-5 -8.829287f-5 -5.122713f-5; 0.00011356168 2.7072892f-5 -9.253048f-5 -9.7144235f-5 -5.3558386f-5 -7.102739f-5 -0.00018623754 0.00013162836 -1.5184637f-5 -9.944188f-5 0.00014779605 -2.3400253f-5 -6.563826f-5 -7.489051f-5 -0.00012160472 -7.8382036f-5 9.002087f-5 -1.4130239f-5 3.6039422f-5 -0.00011180349 -6.0440257f-6 -0.0001540761 -5.739455f-6 5.1871833f-5 6.2550454f-5 -2.9444225f-5 4.1011826f-6 7.9901416f-5 5.603711f-5 -1.4256181f-5 3.4426583f-5 4.9856906f-5; -3.286154f-5 7.116674f-5 -4.1574076f-6 -0.00015561515 4.6678346f-5 0.0001754534 3.814063f-7 -0.00022762116 5.648911f-5 4.255361f-5 -8.870969f-5 1.8850651f-5 3.7530056f-6 -4.5058187f-5 -7.086632f-5 -0.0001447943 -9.620589f-5 0.000102021324 0.00017278506 -1.789651f-5 -0.00019770837 -0.00012196603 -0.00020703816 0.00014147113 0.000104440216 0.00011035788 1.3612266f-6 8.4339816f-5 0.00018007657 8.51515f-6 -2.6068446f-5 -8.29233f-5; -0.00017980425 0.00024446344 7.396711f-5 -0.00021361737 3.724509f-5 1.4738594f-5 0.000136625 2.9866022f-5 3.47192f-5 9.010391f-5 -0.00019570945 4.4907054f-5 9.772386f-6 -7.9038015f-5 -0.00033689776 -4.9428443f-5 4.496193f-5 -5.6542092f-5 -6.9646762f-6 -0.00019470662 5.1095558f-5 -0.00014013774 -9.7984426f-5 -0.00011226721 0.00031234138 -9.5950694f-5 -0.00014004567 4.6424328f-5 -4.7736758f-5 7.010866f-5 1.6203121f-5 4.6829777f-5; -8.708018f-5 -0.00016045521 -7.2275757f-6 6.393291f-5 0.00011965771 0.00011464074 -4.5697686f-7 8.0861464f-5 0.0001022533 5.646368f-5 0.000116467454 0.00017300091 2.5471847f-5 0.00020660755 -4.3006254f-5 0.00012930758 -1.0878323f-5 0.00011079276 0.00020138327 -0.00015660196 9.4770485f-6 3.581487f-5 -8.650456f-7 -0.00014728917 -4.715184f-5 -0.00010080215 2.8409338f-5 -6.403153f-5 0.00015295464 -0.00017042554 1.3564003f-6 -0.00011035926; -9.573557f-5 -6.596612f-5 4.345059f-5 0.00010860645 0.00019122523 5.4775028f-5 8.066031f-5 -6.302869f-5 2.8398154f-5 5.9679318f-5 4.9511655f-5 0.00012019725 7.560769f-5 3.4006407f-5 -7.405292f-6 -3.3514407f-5 -0.00013196601 8.2634935f-5 -1.6556698f-5 0.00011844044 -2.1374497f-5 -5.9172984f-5 0.0002714602 9.1502596f-5 -2.4370893f-5 -6.784604f-5 2.7011944f-5 -0.00012285201 -0.00018385517 9.90055f-5 1.537271f-5 -9.662465f-5; 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9.272404f-5 1.8320108f-5 7.896093f-5 0.00017118001 -0.0001250922 2.291453f-5 6.254659f-5 0.000116823874 -3.7232323f-5 -7.725545f-5 -1.972598f-5 -1.9868286f-5 2.5172509f-5 -5.481218f-5 0.00016046854 4.3901264f-6 -6.932835f-5 7.142715f-5 2.5496958f-5 -3.063386f-5 0.00016012261 -7.974759f-5 3.226735f-5 0.000104737555 -4.9273913f-5 -3.3438133f-5 0.00020110856 -0.00013596313 0.00015645802 -0.00012764387 0.00010554395 7.904172f-6; 7.832622f-5 0.00011860157 5.266906f-5 -7.044353f-5 3.933173f-5 1.6427433f-5 -0.00011026127 -4.351902f-5 0.00022462536 7.477401f-5 -9.0549554f-5 0.00016367993 -3.6606558f-5 5.467878f-5 -2.690087f-5 4.4372475f-5 -1.575863f-5 3.407016f-5 6.962714f-6 -0.00011319172 -1.3054113f-5 -4.122088f-5 3.6056736f-5 9.1263464f-5 7.2483024f-5 -0.00016864711 7.967744f-5 2.6180001f-5 -0.00015273914 -1.9276631f-5 6.645485f-5 -9.559493f-5; 4.3957913f-5 0.00014572433 -1.4306217f-5 -7.624112f-5 -2.9588346f-5 0.00014455158 4.0845338f-5 6.834219f-5 -9.741042f-5 -0.00014014456 -1.6901933f-5 1.7843891f-5 -0.00010838938 4.6790734f-5 0.00019295757 -6.0569873f-5 -0.00013637965 -3.0474872f-5 0.0001037594 0.00019073563 6.419302f-7 -0.00013129206 -0.000105330306 -1.7867922f-5 0.000115244446 -1.6840724f-5 -0.00016233283 0.000109826695 -5.968982f-7 -0.00013197932 -0.00013100801 8.5669435f-6; 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3.4252414f-5 1.7978846f-5 0.000169445 0.00018952793 -8.011082f-5 6.781402f-5 0.000120731675 1.5522899f-5 2.1491327f-5 -0.00013182944 -1.638258f-5 -9.910352f-5 1.763488f-5 -5.268952f-5 0.0001341999 0.00012931575 2.0700243f-5 -7.521594f-5 -8.710873f-5 -0.00025061367 -4.814495f-5 -5.369676f-5 8.906928f-5 -0.00012929876 3.5379262f-6 0.00019203326 -0.0001413457 0.00011003606 2.02384f-5 2.5250322f-6 -4.823328f-6 0.00017709933; 0.00010651335 3.9165167f-5 7.6804965f-5 0.00018133184 8.555229f-5 6.652526f-5 -0.00012029219 -7.9235f-5 -0.00020872283 -1.1949973f-5 -0.00013770128 -5.876042f-5 -4.9586248f-5 -9.1145936f-5 -0.00010791469 2.2212389f-5 2.3586554f-5 0.00013769098 0.000111135545 -9.670577f-5 -9.732586f-5 8.423925f-6 0.00017610678 9.734474f-5 1.8881644f-6 1.411364f-5 -5.9431986f-5 -1.2221734f-5 -8.04621f-5 -6.966804f-5 0.00023346557 -6.003869f-5; -3.876047f-5 0.00014561284 -4.148563f-5 8.296341f-5 -6.987597f-5 0.00013355879 -0.00011680688 4.320796f-6 3.716612f-5 -4.7806792f-5 -9.4781724f-5 5.3489697f-5 -1.4912613f-5 8.296775f-5 2.3379346f-6 -1.0566036f-5 -0.000108239285 -7.448106f-5 -3.0216563f-5 7.662209f-5 0.00014964533 -0.00011516985 -3.5049095f-5 -3.0671647f-5 -3.2881521f-6 -3.6293895f-5 7.330256f-7 -3.5557747f-5 4.4640456f-5 8.841141f-5 6.586005f-5 -0.00017228896; -1.24846265f-5 0.0001208953 0.00014398887 4.5776145f-5 -0.000115045936 -5.9687086f-6 6.0125035f-6 6.8744295f-5 8.819092f-6 6.5838617f-6 -8.074785f-6 8.18883f-6 8.1181395f-5 0.00016108702 2.6273632f-5 -3.1020445f-5 9.508686f-6 4.0793813f-5 -0.0001408116 3.1298189f-6 2.3511593f-5 -8.186044f-5 -0.00010960179 -0.00016496978 4.405605f-6 -6.639267f-5 -0.000101537495 7.49069f-6 0.00010797909 3.2122553f-5 0.00019854389 6.8400455f-5; -0.00017579607 4.488868f-5 -7.397126f-8 2.2734788f-5 4.2988877f-6 -0.00012200552 4.1339466f-5 2.328481f-5 4.1465668f-5 8.132256f-6 8.115436f-5 1.3009662f-5 -1.9977986f-5 -0.0001287793 -9.6333824f-5 2.874979f-5 -5.3080348f-5 -5.785651f-5 -6.20475f-5 5.9302507f-5 2.9213074f-5 9.509549f-5 -3.0428158f-5 0.00017109046 0.00020654775 5.3617234f-5 0.00010196593 0.0002069366 2.0894107f-5 1.6600687f-5 -7.48392f-5 0.00012764451; -1.6030723f-5 -1.9729712f-5 2.562178f-5 0.00022121618 0.00018367641 4.139218f-5 7.6101554f-5 0.00019930796 7.185698f-5 7.8943165f-5 -7.644431f-5 4.3318218f-5 -1.3253722f-5 -2.1225085f-5 -0.00016582398 -0.00018792605 -1.3799033f-5 0.0002778923 -0.000105594445 0.000120767974 3.4850607f-5 -4.4116554f-5 3.988118f-5 -4.367971f-5 0.00016983895 -4.00821f-5 -8.422913f-5 1.4080487f-5 9.899427f-6 4.9401973f-5 -3.4165874f-5 -7.69171f-5; 4.1773757f-5 0.00014913613 0.000126567 0.00017125023 -6.546571f-5 0.00033155672 0.00011466273 7.809752f-5 6.979409f-5 3.1921016f-5 6.510741f-5 -8.501913f-5 6.257237f-5 0.00011156401 -9.156247f-5 9.0500354f-5 9.2775146f-5 -6.766979f-6 -1.7866389f-5 -2.7544174f-5 -4.399843f-5 7.5294745f-5 0.00011452333 -8.9779605f-5 -0.0001744599 -0.00013224669 9.717873f-5 0.00013802775 2.7223847f-5 6.938874f-5 -0.00015714747 -3.729033f-5; -0.00010186369 1.8786994f-5 1.1669726f-5 3.7432466f-5 0.00014849601 -8.1198996f-5 1.2223435f-5 3.6235957f-5 -6.6038585f-5 -0.00020149031 -8.3387975f-5 -1.1616641f-5 3.861739f-5 5.2266863f-5 0.00017672828 -3.6429665f-5 0.0001213096 -0.0001294468 -9.729489f-5 0.00011058528 -4.197558f-6 0.00019134328 8.317239f-5 6.726744f-5 2.998288f-5 -0.0001831322 7.862825f-5 0.00014545645 -3.136986f-5 0.00011239314 0.0001090515 7.624094f-5; 0.00010192903 -6.524324f-5 7.143097f-5 -8.02076f-5 -1.0315073f-5 -7.236077f-5 -0.00015450438 -7.5828546f-5 -0.00017704595 5.233977f-5 -3.8811017f-5 -7.597749f-5 0.00018876392 -0.00013852713 -1.1569201f-5 -2.537716f-5 -0.00022445363 -4.2580206f-5 -0.00011457844 -0.00017382255 -1.9114601f-5 3.0382655f-5 9.44476f-5 -4.1854648f-5 0.00017476828 9.583724f-5 8.147809f-5 9.057342f-5 -0.00016546999 8.475024f-5 4.4872453f-5 8.55354f-5; 4.9008333f-5 -0.00015482772 -2.9896846f-5 -7.672894f-5 -7.277536f-5 -1.7218908f-5 -2.0766205f-5 0.00015757453 0.00016821099 0.00012837019 -0.00016522144 2.8738874f-5 -3.516303f-5 -0.000107145315 8.35585f-5 -1.5251731f-5 1.805957f-5 0.00013188834 -0.000100679004 0.00015572732 -8.925097f-5 0.00017002202 0.00010146622 -0.00024448716 0.00016385132 1.8185434f-5 -3.342352f-5 7.46513f-5 -0.00013326635 6.0554674f-5 7.850088f-5 -5.4996348f-5; -0.000119494725 -0.00025112068 0.00011172785 9.278077f-6 1.7621252f-5 -1.15393295f-5 3.6610567f-5 -2.8657137f-6 -4.93761f-5 3.655143f-5 -0.00012682205 -8.361162f-6 0.00018711382 -2.9714225f-5 3.2761087f-5 0.00015201842 -0.00010104727 -0.00012077274 -9.988359f-6 -0.00014403982 -7.473175f-5 -2.1082627f-5 -0.00021641343 2.9726623f-5 0.00014701443 -0.00015106272 2.60452f-5 -0.00020045234 7.8442135f-5 -6.923768f-5 5.397001f-5 4.615466f-6; -1.7326232f-5 -4.5282093f-5 -1.1445137f-5 6.4935935f-5 9.0735455f-5 -1.1834731f-5 -2.7228747f-5 -1.252255f-6 -8.46312f-5 -4.548237f-6 -2.6095266f-5 3.601256f-5 7.6172396f-6 -4.7420755f-5 -0.00021223628 1.2169157f-5 0.0001208721 -4.9286413f-5 -4.5233795f-5 -0.00019525501 2.342413f-5 -0.0001615138 -4.1510673f-5 4.5838387f-5 -0.00022700398 -6.700035f-5 -7.5483396f-5 -4.520957f-6 6.766729f-5 4.7984697f-5 0.00010202208 -7.772921f-5; 0.0001495528 0.00020418811 3.9540133f-5 -6.3646266f-6 6.240287f-5 0.00015583959 -9.5992895f-5 5.6563535f-5 7.875602f-5 -8.022817f-6 -6.209155f-5 3.4326014f-5 6.877887f-5 -8.3817555f-5 -9.155829f-5 -2.6342583f-5 -1.791582f-5 -7.3701696f-5 3.1804808f-5 -0.00022330634 -8.917969f-6 -0.00024460425 0.00014764017 7.990559f-5 1.008664f-5 0.00013233775 -0.00021250913 -6.5767315f-5 -0.00010873815 -2.6074382f-5 -8.926506f-5 -8.4303254f-5], bias = Float32[0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0;;]), layer_4 = (weight = Float32[0.00011602808 -0.000120417775 7.054768f-5 -0.0001364321 1.0047987f-5 -8.540841f-5 -2.2970164f-5 -3.7272024f-5 7.4761874f-6 1.3028075f-5 1.06746675f-5 -4.7827394f-5 3.6491794f-5 -8.778504f-5 -3.844625f-5 9.919472f-5 -9.7661235f-5 2.755268f-5 1.7365865f-5 -4.661768f-5 -0.00011277104 -2.358428f-5 0.00014879108 -0.00028839387 -8.063303f-5 -1.4004848f-5 5.652013f-5 4.9286264f-5 0.000105819985 4.3599415f-5 -0.00013917121 -0.000105863226; -9.1772155f-5 -0.00017995205 4.675251f-7 -5.2920554f-5 0.00014703989 0.00018397685 -6.5224354f-5 3.4467295f-5 5.9178594f-5 -0.00023862447 -6.239535f-5 -7.785182f-5 1.7593879f-5 -1.3778444f-5 6.928703f-5 -8.063013f-5 4.069519f-5 1.616499f-5 0.00013895672 8.854975f-5 0.00012469526 -4.8969636f-5 6.860495f-5 -1.4344437f-5 9.547716f-5 5.0288338f-5 -2.761656f-5 9.424831f-5 -0.0001829136 -8.509033f-5 -5.9762977f-5 2.7484823f-5], bias = Float32[0.0; 0.0;;])), (layer_1 = NamedTuple(), layer_2 = NamedTuple(), layer_3 = NamedTuple(), layer_4 = NamedTuple()))

      Similar to most DL frameworks, Lux defaults to using Float32, however, in this case we need Float64

      julia
      const params = ComponentArray{Float64}(ps)
+
+const nn_model = StatefulLuxLayer(nn, st)
      Lux.StatefulLuxLayer{true, Lux.Chain{@NamedTuple{layer_1::Lux.WrappedFunction{Base.Fix1{typeof(broadcast), typeof(cos)}}, layer_2::Lux.Dense{true, typeof(cos), PartialFunctions.PartialFunction{nothing, nothing, typeof(WeightInitializers.truncated_normal), Tuple{}, @NamedTuple{std::Float64}}, typeof(WeightInitializers.zeros32)}, layer_3::Lux.Dense{true, typeof(cos), PartialFunctions.PartialFunction{nothing, nothing, typeof(WeightInitializers.truncated_normal), Tuple{}, @NamedTuple{std::Float64}}, typeof(WeightInitializers.zeros32)}, layer_4::Lux.Dense{true, typeof(identity), PartialFunctions.PartialFunction{nothing, nothing, typeof(WeightInitializers.truncated_normal), Tuple{}, @NamedTuple{std::Float64}}, typeof(WeightInitializers.zeros32)}}, Nothing}, Nothing, @NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}, layer_3::@NamedTuple{}, layer_4::@NamedTuple{}}}(Chain(), nothing, (layer_1 = NamedTuple(), layer_2 = NamedTuple(), layer_3 = NamedTuple(), layer_4 = NamedTuple()), nothing)

      Now we define a system of odes which describes motion of point like particle with Newtonian physics, uses

      u[1]=χu[2]=ϕ

      where, p, M, and e are constants

      julia
      function ODE_model(u, nn_params, t)
+    χ, ϕ = u
+    p, M, e = ode_model_params
+
+    # In this example we know that `st` is am empty NamedTuple hence we can safely ignore
+    # it, however, in general, we should use `st` to store the state of the neural network.
+    y = 1 .+ nn_model([first(u)], nn_params)
+
+    numer = (1 + e * cos(χ))^2
+    denom = M * (p^(3 / 2))
+
+    χ̇ = (numer / denom) * y[1]
+    ϕ̇ = (numer / denom) * y[2]
+
+    return [χ̇, ϕ̇]
+end
      ODE_model (generic function with 1 method)

      Let us now simulate the neural network model and plot the results. We'll use the untrained neural network parameters to simulate the model.

      julia
      prob_nn = ODEProblem(ODE_model, u0, tspan, params)
+soln_nn = Array(solve(prob_nn, RK4(); u0, p=params, saveat=tsteps, dt, adaptive=false))
+waveform_nn = first(compute_waveform(dt_data, soln_nn, mass_ratio, ode_model_params))
+
+begin
+    fig = Figure()
+    ax = CairoMakie.Axis(fig[1, 1]; xlabel="Time", ylabel="Waveform")
+
+    l1 = lines!(ax, tsteps, waveform; linewidth=2, alpha=0.75)
+    s1 = scatter!(ax, tsteps, waveform; markershape=:circle, markersize=12,
+        markeralpha=0.25, alpha=0.5, strokewidth=2)
+
+    l2 = lines!(ax, tsteps, waveform_nn; linewidth=2, alpha=0.75)
+    s2 = scatter!(ax, tsteps, waveform_nn; markershape=:circle,
+        markersize=12, markeralpha=0.25, alpha=0.5, strokewidth=2)
+
+    axislegend(ax, [[l1, s1], [l2, s2]],
+        ["Waveform Data", "Waveform Neural Net (Untrained)"]; position=:lb)
+
+    fig
+end

      Setting Up for Training the Neural Network ​

      Next, we define the objective (loss) function to be minimized when training the neural differential equations.

      julia
      function loss(θ)
+    pred = Array(solve(prob_nn, RK4(); u0, p=θ, saveat=tsteps, dt, adaptive=false))
+    pred_waveform = first(compute_waveform(dt_data, pred, mass_ratio, ode_model_params))
+    loss = sum(abs2, waveform .- pred_waveform)
+    return loss, pred_waveform
+end
      loss (generic function with 1 method)

      Warmup the loss function

      julia
      loss(params)
      (0.17215171721421207, [-0.024249801535431388, -0.02346585418572156, -0.022681906836011435, -0.021357317180048352, -0.019464416988440935, -0.016963046554685536, -0.013800484708468138, -0.00990849440296376, -0.00520559267126083, 0.0004032969641172105, 0.007017656891419924, 0.014720493495480241, 0.02353090231748062, 0.033276169354516875, 0.043314705833896336, 0.05188106697558526, 0.054700333055434175, 0.0427238357065267, 0.002423105357175596, -0.06575883215773011, -0.11027317642844461, -0.07678253350835433, -0.0072353830951188206, 0.03869619541269424, 0.054302679477350145, 0.053010890392771556, 0.044889237694299845, 0.034846679863281424, 0.024936638661368058, 0.015923083057834027, 0.008021668513541608, 0.0012311811425605268, -0.004529475034590188, -0.009361716233634384, -0.013364035775378412, -0.016620815901878253, -0.019203788197126054, -0.021169013129862177, -0.022559076807699988, -0.023404004269245684, -0.023722253289358303, -0.023521083092865745, -0.022797843963709284, -0.021537669920586207, -0.019715602687456514, -0.017294276511174298, -0.014223184402618666, -0.010438139233305582, -0.005860520949963716, -0.00039881752053247047, 0.006043962037684947, 0.013554593203308008, 0.022161982187542492, 0.03173508798113943, 0.041733947747754976, 0.050644402047554236, 0.05475043416740677, 0.045981405841294294, 0.011152289366379492, -0.05420462270255706, -0.10786003980798775, -0.08685899277206673, -0.01774186110866609, 0.0338250226807328, 0.053499201452751846, 0.05400660035342886, 0.04644819440068384, 0.03644347334895938, 0.026379742162639767, 0.01716279566038105, 0.009056918301880643, 0.0020871637830344454, -0.003833000649596514, -0.008796465842887504, -0.012913937856553289, -0.01626587145143468, -0.018934307254695595, -0.02097197454005451, -0.0224295200316549, -0.023335406713336643, -0.023712900244009478, -0.02357041802509943, -0.022906394593631228, -0.021710058883234875, -0.019958459751178312, -0.01761360308066557, -0.014633651841338422, -0.010950330269378201, -0.006496278517170611, -0.00117520713687785, 0.00509967877361141, 0.012423985228668584, 0.02082949459404453, 0.03022588244507418, 0.04015436535793723, 0.049323788875630895, 0.05450738977182879, 0.04854762140980133, 0.018910188751749105, -0.042502139586782596, -0.10315104867281276, -0.09558611000472392, -0.028939522297792744, 0.02803995234799488, 0.052223130646726956, 0.054837231555989026, 0.04797944252126462, 0.03806268827600256, 0.027862360747976808, 0.018437229466984544, 0.010129000748480839, 0.002967092500939512, -0.0031100197038603306, -0.0082161156668996, -0.012446121061225964, -0.015901568755078654, -0.018652617240000398, -0.020768350144362, -0.02229141599601115, -0.023260958394085672, -0.023697093505961463, -0.02361282939105417, -0.023009218865298837, -0.021874751751256145, -0.020191745724326714, -0.017923246391015904, -0.015030312218619087, -0.011447676185503672, -0.0071116709655967255, -0.0019285321933857303, 0.00418515298414508, 0.011326237661996849, 0.01953487303756195, 0.02874787822057803, 0.03858428047507269, 0.047938884837366906, 0.05401544627420644, 0.05050337220632601, 0.0256911577239574, -0.030974995521538738, -0.09638900641676833, -0.102573566871294, -0.040619015798842875, 0.021284462092519427, 0.05040555779361737, 0.05546518394540094, 0.04946935076603893, 0.03970253564114501, 0.029377636383265602, 0.01975531095702029, 0.01123161885375543, 0.003879775858755852, -0.0023695397955581397, -0.00761096830444328, -0.011966053312152423, -0.015522255130645694, -0.018364387021327692, -0.020552878493211888, -0.022147379737285706, -0.02317926869799286, -0.02367518135491305, -0.023649303371970062, -0.02310461742752934, -0.02203298018800196, -0.020414371431591624, -0.018224930107454487, -0.015413676223328199, -0.011928852014086397, -0.007709193266232499, -0.0026602412566282306, 0.0032996827586000317, 0.010262587199066909, 0.018274577343534007, 0.027303342429091142, 0.03702853083260528, 0.0465057213069404, 0.05331917019944852, 0.051918238954459836, 0.03153306060791138, -0.019910122722075096, -0.08788362950254597, -0.10750094646131855, -0.05250722342833319, 0.013532854861997918, 0.0479619737149416, 0.055852146956217485, 0.050901076175073945, 0.04135375329743446, 0.03093541376814808, 0.02110756232480277, 0.01237125722871237, 0.004818557596569256, -0.0015962956792808102, -0.006991680144950654, -0.011469023119692376, -0.015132311698807245, -0.018060132121416765, -0.020332234338905318, -0.021995136036621243, -0.023091139245199024, -0.023646409526520064, -0.023679578179550936, -0.023193543086071973, -0.022182036958480172, -0.02063327847752358, -0.018513107066246644, -0.015785984296997794, -0.012396365770967076, -0.008287656846264849, -0.003368634740061504, 0.0024402092108903213, 0.00922922779343203, 0.017051490948011293, 0.02589298414209541, 0.03549058692942278, 0.04503937218323815, 0.05245167905094164, 0.05286401786344559, 0.0364818425938837, -0.009505948227704146, -0.07802438838691865, -0.11013670289983736, -0.06425595915170446, 0.004772010596095392, 0.04482024983889405, 0.055946769355377436, 0.05225496995452235, 0.04301460045508618, 0.03252435619257789, 0.022501895668115328, 0.013547176658980737, 0.0057907331212782714, -0.0008020753538423008, -0.006349674377069929, -0.01095520031828327, -0.014727439711552081, -0.017748123886680903, -0.02010087532816729, -0.021835155048116412, -0.0229959341098181, -0.023611652701661365, -0.02370339152416624, -0.023275956637742234, -0.022325259983575547, -0.020841440939984492, -0.018793020521969617, -0.016146637502150406, -0.012849766519993163, -0.008848805202157648, -0.004847843884322281])

      Now let us define a callback function to store the loss over time

      julia
      const losses = Float64[]
+
+function callback(θ, l, pred_waveform)
+    push!(losses, l)
+    @printf "Training %10s Iteration: %5d %10s Loss: %.10f\n" "" length(losses) "" l
+    return false
+end
      callback (generic function with 1 method)

      Training the Neural Network ​

      Training uses the BFGS optimizers. This seems to give good results because the Newtonian model seems to give a very good initial guess

      julia
      adtype = Optimization.AutoZygote()
+optf = Optimization.OptimizationFunction((x, p) -> loss(x), adtype)
+optprob = Optimization.OptimizationProblem(optf, params)
+res = Optimization.solve(
+    optprob, BFGS(; initial_stepnorm=0.01, linesearch=LineSearches.BackTracking());
+    callback, maxiters=1000)
      retcode: Success
+u: ComponentVector{Float64}(layer_1 = Float64[], layer_2 = (weight = [-0.00011973267100973714; -6.019301872584702e-5; 9.096157009471292e-5; 4.266174801152644e-5; 9.349408855980382e-7; 0.00016044428048176378; -9.652911103319343e-6; -0.0001385483919874571; 9.681806659489127e-6; -2.8657123039017627e-5; 0.00017334803123936343; 2.4411341655644033e-5; 9.011603833644094e-5; 5.220362072567235e-5; 0.0002490672632118383; -2.4143722839640925e-5; 0.00012566449004216483; -4.847905802303613e-5; 4.074634125572134e-5; 1.0247664249599429e-5; -0.0001859721960498307; 3.735608697743877e-5; -7.656955858682703e-5; -1.2043876267849151e-5; -8.479990356138734e-5; -2.4505294277351263e-5; -7.95876258051809e-5; -0.00022258625540396467; -0.00017038380610754774; 2.2777765479984303e-5; 4.27112718170935e-5; 6.095390563132088e-5;;], bias = [-1.164825726562541e-16; 7.32997919745033e-18; 9.983766760539752e-17; 7.770460759065174e-17; 1.7788999500159933e-18; 1.4588208534933488e-16; -1.2507218408227132e-17; -1.251678622168931e-16; 1.2733169472004439e-17; 7.135391304264406e-18; 2.484754549107743e-16; 6.723620038833896e-18; -2.2857880932878122e-17; 1.1538087757854018e-16; 2.463886399288879e-16; -1.3610381677146602e-17; 9.87350838026452e-17; -4.603549365892236e-17; 5.6417112338565525e-18; 2.1427353925903686e-17; -1.7516937468067382e-16; 9.686404129065536e-17; -1.1068338528151916e-16; -4.679508920209203e-18; 2.5985377908932743e-17; 2.0807714940635198e-17; -1.2025065573329291e-16; -2.2061612577673057e-16; -1.8567883300781978e-17; 2.482936980343263e-18; 3.4047360819198803e-18; 2.173035420130597e-18;;]), layer_3 = (weight = [-1.0061051374231235e-5 -0.0001435916774186004 7.171994459566595e-5 3.4882259809725193e-6 0.0001732828104890276 6.824429240293579e-5 -0.00012931552098380893 7.677660529568793e-6 0.00022925046598756195 -0.00011960435856381964 0.00011615116911923022 -0.00013504423165942132 4.9550665631964246e-5 1.5075481338853033e-5 -0.00010519855911629895 9.820798825457177e-5 0.00011530637950852913 -5.2983089493510066e-5 3.924316208794128e-5 -8.876639819719384e-5 6.520004628907118e-5 4.54916126058287e-5 5.359195440759037e-5 -0.00011165698285695655 8.590545715049844e-5 -3.446177558872437e-5 0.0001380952753846818 1.632844671472133e-5 6.296582526044495e-5 6.380996731094503e-5 5.557869828989134e-5 -0.0001310505749403198; -7.035733811956914e-5 9.636661037635938e-5 -2.7267500046794955e-5 -5.7131364302980244e-5 0.0001593350176682785 9.020356868692558e-5 -1.2809531983142202e-5 -1.5835740998076307e-5 1.2374078904182701e-5 -0.0003102025069545866 -1.5455885078912935e-5 -5.062640717536254e-5 -7.399058755421144e-5 0.00022303227218632536 -5.265644300546716e-5 5.5802782879406165e-5 0.00011970507388302038 2.3875793556877868e-5 2.6456672129067134e-5 -1.1514230538371901e-5 3.4455414277695585e-5 8.091217808957168e-5 -1.692194324444572e-5 -9.741722111524122e-5 -0.0001372788532188075 -9.305556828788522e-5 0.0001456148171547888 -0.000123896300794363 5.852763628187465e-5 -0.00010942477762167383 -4.5462085255925074e-5 0.00021897783211731302; -5.4259894708870824e-5 0.00012177309585758837 0.0002000537050168512 2.663567542704249e-5 -2.6191660394305017e-5 -0.00020373288239562497 -1.2667532285363746e-6 3.0380619906002633e-5 -5.047274058078849e-5 -1.8167106912177227e-6 9.94631180635115e-5 5.8791362649300245e-5 -0.00014307143388059756 3.3850267614707524e-5 -0.00016030934162183824 2.0229054786807387e-6 -3.062606370286228e-5 4.211150630517336e-5 -2.976644569052881e-5 0.00021924263168848616 2.025217040289681e-5 0.00011184299259703118 -0.00019682885718275532 2.2434090029220385e-5 6.390894017904274e-5 1.2835534750604354e-6 0.00012127533304528576 8.413669897497975e-5 5.094031698325898e-5 -3.125955222849255e-5 7.489175809105353e-5 -0.00011757015559333028; 8.287123114749126e-5 5.6980601816385334e-5 -0.00011780782892421003 -9.957538508861785e-5 -1.4818970835409752e-5 7.662216581117524e-5 7.079098782450589e-5 -1.2592442312985069e-5 -1.8838037926986118e-5 0.00013955978852645128 7.530702919645007e-5 -3.0706285310959205e-5 0.00022041206307656967 0.00010372556630935908 0.0001036071282712616 -4.687340829338635e-6 0.00010356696498527327 9.927829728875734e-5 0.00015315347468894462 0.00016233458359674242 -6.378553166108842e-5 0.00027685512964562096 -0.00022597401925414693 0.0001375438098464596 9.244247690256669e-5 -0.00012381657665646984 -0.0001060513002314226 -0.00014336454273257543 -2.6273517273907963e-5 -0.00013443355214367962 -0.00011772640368254384 5.8142917855357026e-5; -0.00016426227840953705 3.8750406823709946e-5 -0.00016896545741135337 6.287773693085625e-5 -0.00023414833150699074 -9.024866186905255e-5 -5.250578862277114e-5 1.4771482605049232e-5 4.903920388070612e-5 -1.5056565749805115e-5 -2.7055343813336912e-5 -3.6150345400787905e-5 0.00012460399273889032 -0.00018959841428684904 5.59981734875745e-5 -5.7859569202523714e-5 3.128588185403491e-5 9.417531226401265e-5 8.768360097489355e-6 -0.00014429034228331664 -3.1023010811836416e-5 1.3867254517356232e-6 -4.801726652450645e-7 -0.00012216993228893042 1.2424723430490129e-5 4.940673727242762e-7 -0.00010849987767530952 -0.00010241999290539078 0.00014787662338108665 -8.605758659203735e-5 -8.829695899865612e-5 -5.123121547174407e-5; 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0.00010192715870302892 -6.524511247321899e-5 7.142910197230408e-5 -8.020947263490455e-5 -1.0316943025699973e-5 -7.236264338629764e-5 -0.00015450624761784601 -7.583041571692478e-5 -0.00017704781914277154 5.233789868738397e-5 -3.881288632313899e-5 -7.597936184525612e-5 0.00018876205302162434 -0.00013852900139668946 -1.1571070735788319e-5 -2.5379029302584267e-5 -0.00022445549968310753 -4.258207611188304e-5 -0.00011458031060088479 -0.00017382442440053598 -1.91164707028623e-5 3.0380784828722702e-5 9.444572804581578e-5 -4.1856517618598036e-5 0.00017476641385669176 9.583537046650304e-5 8.147621718321227e-5 9.057154982672157e-5 -0.00016547185789007933 8.474836811741688e-5 4.487058338794814e-5 8.553353125548059e-5; 4.900922637414417e-5 -0.000154826828050608 -2.9895952805709688e-5 -7.672804507212121e-5 -7.277446432755613e-5 -1.7218015030562925e-5 -2.0765311758912264e-5 0.00015757541974987927 0.0001682118802515854 0.00012837107921466852 -0.00016522054805439193 2.8739767246117575e-5 -3.516213631275628e-5 -0.00010714442190266579 8.355939486742737e-5 -1.5250838017271136e-5 1.8060464086990835e-5 0.0001318892375517694 -0.00010067811102391554 0.0001557282141827111 -8.925007726550458e-5 0.00017002290975750095 0.00010146711271470889 -0.0002444862709429051 0.000163852213760656 1.818632723978417e-5 -3.342262583220846e-5 7.465219665997806e-5 -0.00013326545898355744 6.0555567203375304e-5 7.850177486641925e-5 -5.499545453250801e-5; -0.00011949762882137913 -0.00025112358742333346 0.00011172494816421646 9.275173960504754e-6 1.7618349028651443e-5 -1.1542232987953863e-5 3.660766344111685e-5 -2.8686171215320368e-6 -4.9379003376799704e-5 3.654852809560827e-5 -0.00012682495469630388 -8.364065598271848e-6 0.00018711091945008474 -2.9717128546307235e-5 3.275818346017579e-5 0.00015201551252104665 -0.00010105017316233472 -0.0001207756435003642 -9.991262578096234e-6 -0.00014404272258687495 -7.473465701036349e-5 -2.1085530880355043e-5 -0.00021641633828110176 2.972371987127045e-5 0.00014701153087955912 -0.00015106562239523654 2.60422963212703e-5 -0.00020045524468580904 7.843923196491998e-5 -6.924058141592579e-5 5.3967105140345805e-5 4.612562515123608e-6; -1.732914151749008e-5 -4.528500230468802e-5 -1.1448045914096435e-5 6.493302626234313e-5 9.073254605221222e-5 -1.1837639793015286e-5 -2.723165616577822e-5 -1.2551640546472034e-6 -8.463411231593561e-5 -4.551146137483005e-6 -2.6098174746802816e-5 3.6009650468376435e-5 7.6143304814989134e-6 -4.742366454399268e-5 -0.00021223918756532482 1.2166248236216557e-5 0.00012086919141633674 -4.928932193967629e-5 -4.523670449804695e-5 -0.00019525791740113269 2.342122152382682e-5 -0.00016151671170325227 -4.1513582434950056e-5 4.5835478342386437e-5 -0.0002270068931446655 -6.700325920780472e-5 -7.54863054661333e-5 -4.523866298604078e-6 6.766438437094556e-5 4.798178761314311e-5 0.00010201917157440278 -7.773211709524491e-5; 0.0001495518057810956 0.00020418711702514773 3.953914111772107e-5 -6.365618527335629e-6 6.240187704971275e-5 0.00015583859695763455 -9.599388666974163e-5 5.6562542714540895e-5 7.875502834504688e-5 -8.023809267608356e-6 -6.209254442072207e-5 3.4325022544369584e-5 6.87778787425581e-5 -8.38185465807251e-5 -9.155928509132557e-5 -2.6343574599006666e-5 -1.791681151079214e-5 -7.370268812227703e-5 3.1803815919564016e-5 -0.00022330733426205592 -8.918961237923293e-6 -0.00024460524090390393 0.0001476391748030524 7.990460054425742e-5 1.0085648146932791e-5 0.00013233675909869608 -0.00021251011875282548 -6.576830727569789e-5 -0.00010873914524270921 -2.6075373706400867e-5 -8.926604877050693e-5 -8.430424585530198e-5], bias = [1.921786307209035e-9; 8.789190050134396e-11; 1.2504148812771212e-9; 2.759638658565189e-9; -4.0864654563959214e-9; -1.5256145600285591e-9; -7.257926362306835e-10; -2.32442960482532e-9; 2.26637932249765e-9; 2.085537853776543e-9; -3.0927651263003428e-9; 1.1204678255460235e-9; 1.224877475321225e-9; 2.7271956201550424e-9; 1.020909304245852e-9; -6.646559494382461e-10; 3.899342734955543e-11; -8.234145849406738e-11; 1.581324318981226e-9; 1.3057169819360422e-9; 1.4432009549384312e-10; -3.935652982223644e-10; 1.2538523267575744e-9; 1.9956939078962535e-9; 2.55591752995915e-9; 4.101057123727002e-9; 2.329851411471181e-9; -1.8697572701351324e-9; 8.933663432767605e-10; -2.903453407028585e-9; -2.9091078170073337e-9; -9.91884728601028e-10;;]), layer_4 = (weight = [-0.0005572566820208557 -0.0007937026262524729 -0.0006027371350159636 -0.0008097167570915016 -0.0006632364353912129 -0.0007586931955229081 -0.0006962550015859167 -0.0007105567364154836 -0.0006658085334180905 -0.0006602566700924333 -0.0006626099449352349 -0.0007211122134551628 -0.0006367930196168518 -0.0007610696972092854 -0.0007117310752981213 -0.0005740901170262534 -0.0007709460867192456 -0.0006457321711362864 -0.0006559189228036226 -0.00071990248582105 -0.0007860558927556543 -0.00069686912726478 -0.0005244937356517977 -0.0009616786115207227 -0.0007539177071414011 -0.0006872892690566108 -0.0006167645875060232 -0.0006239984997886235 -0.0005674648472694767 -0.0006296852286443204 -0.0008124558416854573 -0.0007791480513692754; 0.00014216770893870395 5.398784074717275e-5 0.00023440740675234172 0.00018101927179873937 0.00038097963229907544 0.0004179167254411029 0.00016871553604570189 0.0002684071421866321 0.00029311844363497764 -4.684615903553573e-6 0.0001715444594282229 0.00015608806149225427 0.0002515337605158771 0.00022016138424090162 0.00030322691643611805 0.00015330975900653944 0.0002746350862441426 0.0002501048844999265 0.0003728965915869229 0.00032248962985238777 0.0003586351545196296 0.00018497025779880998 0.0003025448352555981 0.00021959541944993648 0.0003294169957206736 0.00028422808379670095 0.00020632328939831497 0.00032818817391118334 5.102628667107437e-5 0.00014884949250286642 0.00017417684072532018 0.00026142470856713477], bias = [-0.0006732848512731586; 0.00023393989498430928;;]))

      Visualizing the Results ​

      Let us now plot the loss over time

      julia
      begin
+    fig = Figure()
+    ax = CairoMakie.Axis(fig[1, 1]; xlabel="Iteration", ylabel="Loss")
+
+    lines!(ax, losses; linewidth=4, alpha=0.75)
+    scatter!(ax, 1:length(losses), losses; markershape=:circle,
+        markersize=12, markeralpha=0.25, strokewidth=2)
+
+    fig
+end

      Finally let us visualize the results

      julia
      prob_nn = ODEProblem(ODE_model, u0, tspan, res.u)
+soln_nn = Array(solve(prob_nn, RK4(); u0, p=res.u, saveat=tsteps, dt, adaptive=false))
+waveform_nn_trained = first(compute_waveform(
+    dt_data, soln_nn, mass_ratio, ode_model_params))
+
+begin
+    fig = Figure()
+    ax = CairoMakie.Axis(fig[1, 1]; xlabel="Time", ylabel="Waveform")
+
+    l1 = lines!(ax, tsteps, waveform; linewidth=2, alpha=0.75)
+    s1 = scatter!(ax, tsteps, waveform; markershape=:circle,
+        markeralpha=0.25, alpha=0.5, strokewidth=2, markersize=12)
+
+    l2 = lines!(ax, tsteps, waveform_nn; linewidth=2, alpha=0.75)
+    s2 = scatter!(ax, tsteps, waveform_nn; markershape=:circle,
+        markeralpha=0.25, alpha=0.5, strokewidth=2, markersize=12)
+
+    l3 = lines!(ax, tsteps, waveform_nn_trained; linewidth=2, alpha=0.75)
+    s3 = scatter!(ax, tsteps, waveform_nn_trained; markershape=:circle,
+        markeralpha=0.25, alpha=0.5, strokewidth=2, markersize=12)
+
+    axislegend(ax, [[l1, s1], [l2, s2], [l3, s3]],
+        ["Waveform Data", "Waveform Neural Net (Untrained)", "Waveform Neural Net"];
+        position=:lb)
+
+    fig
+end

      Appendix ​

      julia
      using InteractiveUtils
+InteractiveUtils.versioninfo()
+if @isdefined(LuxCUDA) && CUDA.functional(); println(); CUDA.versioninfo(); end
+if @isdefined(LuxAMDGPU) && LuxAMDGPU.functional(); println(); AMDGPU.versioninfo(); end
      Julia Version 1.10.2
+Commit bd47eca2c8a (2024-03-01 10:14 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 48 × AMD EPYC 7402 24-Core Processor
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
+Threads: 48 default, 0 interactive, 24 GC (on 2 virtual cores)
+Environment:
+  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
+  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6
+  JULIA_PROJECT = /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/docs
+  JULIA_AMDGPU_LOGGING_ENABLED = true
+  JULIA_DEBUG = Literate
+  JULIA_CPU_THREADS = 2
+  JULIA_NUM_THREADS = 48
+  JULIA_LOAD_PATH = @:@v#.#:@stdlib
+  JULIA_CUDA_HARD_MEMORY_LIMIT = 25%
+
+CUDA runtime 12.3, artifact installation
+CUDA driver 12.4
+NVIDIA driver 550.54.15
+
+CUDA libraries: 
+- CUBLAS: 12.3.4
+- CURAND: 10.3.4
+- CUFFT: 11.0.12
+- CUSOLVER: 11.5.4
+- CUSPARSE: 12.2.0
+- CUPTI: 21.0.0
+- NVML: 12.0.0+550.54.15
+
+Julia packages: 
+- CUDA: 5.2.0
+- CUDA_Driver_jll: 0.7.0+1
+- CUDA_Runtime_jll: 0.11.1+0
+
+Toolchain:
+- Julia: 1.10.2
+- LLVM: 15.0.7
+
+Environment:
+- JULIA_CUDA_HARD_MEMORY_LIMIT: 25%
+
+1 device:
+  0: NVIDIA A100-PCIE-40GB MIG 1g.5gb (sm_80, 4.600 GiB / 4.750 GiB available)
+┌ Warning: LuxAMDGPU is loaded but the AMDGPU is not functional.
+└ @ LuxAMDGPU ~/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6/packages/LuxAMDGPU/sGa0S/src/LuxAMDGPU.jl:19

      This page was generated using Literate.jl.

      + + + + \ No newline at end of file diff --git a/v0.5.30/tutorials/beginner/1_Basics.html b/v0.5.30/tutorials/beginner/1_Basics.html new file mode 100644 index 000000000..876cba510 --- /dev/null +++ b/v0.5.30/tutorials/beginner/1_Basics.html @@ -0,0 +1,262 @@ + + + + + + Julia & Lux for the Uninitiated | Lux.jl Documentation + + + + + + + + + + + + + +
      Lux.jl Documentation

      Appearance


      Trusted by

      Scientific Computing

      SciML.ai

      Machine Learning

      Structure Preserving

      GeometricML.jl

      Machine Learning

      Physical Systems

      MeshGraphNets.jl

      Graph Neural Nets

      Julia & Lux for the Uninitiated ​

      This is a quick intro to Lux loosely based on:

      1. PyTorch's tutorial.

      2. Flux's tutorial.

      3. Jax's tutorial.

      It introduces basic Julia programming, as well Zygote, a source-to-source automatic differentiation (AD) framework in Julia. We'll use these tools to build a very simple neural network. Let's start with importing Lux.jl

      julia
      using Lux, Random

      Now let us control the randomness in our code using proper Pseudo Random Number Generator (PRNG)

      julia
      rng = Random.default_rng()
+Random.seed!(rng, 0)
      Random.TaskLocalRNG()

      Arrays ​

      The starting point for all of our models is the Array (sometimes referred to as a Tensor in other frameworks). This is really just a list of numbers, which might be arranged into a shape like a square. Let's write down an array with three elements.

      julia
      x = [1, 2, 3]
      3-element Vector{Int64}:
+ 1
+ 2
+ 3

      Here's a matrix – a square array with four elements.

      julia
      x = [1 2; 3 4]
      2×2 Matrix{Int64}:
+ 1  2
+ 3  4

      We often work with arrays of thousands of elements, and don't usually write them down by hand. Here's how we can create an array of 5×3 = 15 elements, each a random number from zero to one.

      julia
      x = rand(rng, 5, 3)
      5×3 Matrix{Float64}:
+ 0.455238   0.746943   0.193291
+ 0.547642   0.746801   0.116989
+ 0.773354   0.97667    0.899766
+ 0.940585   0.0869468  0.422918
+ 0.0296477  0.351491   0.707534

      There's a few functions like this; try replacing rand with ones, zeros, or randn.

      By default, Julia works stores numbers is a high-precision format called Float64. In ML we often don't need all those digits, and can ask Julia to work with Float32 instead. We can even ask for more digits using BigFloat.

      julia
      x = rand(BigFloat, 5, 3)
      5×3 Matrix{BigFloat}:
+ 0.981339    0.793159  0.459019
+ 0.043883    0.624384  0.56055
+ 0.164786    0.524008  0.0355555
+ 0.414769    0.577181  0.621958
+ 0.00823197  0.30215   0.655881
      julia
      x = rand(Float32, 5, 3)
      5×3 Matrix{Float32}:
+ 0.567794   0.369178   0.342539
+ 0.0985227  0.201145   0.587206
+ 0.776598   0.148248   0.0851708
+ 0.723731   0.0770206  0.839303
+ 0.404728   0.230954   0.679087

      We can ask the array how many elements it has.

      julia
      length(x)
      15

      Or, more specifically, what size it has.

      julia
      size(x)
      (5, 3)

      We sometimes want to see some elements of the array on their own.

      julia
      x
      5×3 Matrix{Float32}:
+ 0.567794   0.369178   0.342539
+ 0.0985227  0.201145   0.587206
+ 0.776598   0.148248   0.0851708
+ 0.723731   0.0770206  0.839303
+ 0.404728   0.230954   0.679087
      julia
      x[2, 3]
      0.58720636f0

      This means get the second row and the third column. We can also get every row of the third column.

      julia
      x[:, 3]
      5-element Vector{Float32}:
+ 0.34253937
+ 0.58720636
+ 0.085170805
+ 0.8393034
+ 0.67908657

      We can add arrays, and subtract them, which adds or subtracts each element of the array.

      julia
      x + x
      5×3 Matrix{Float32}:
+ 1.13559   0.738356  0.685079
+ 0.197045  0.40229   1.17441
+ 1.5532    0.296496  0.170342
+ 1.44746   0.154041  1.67861
+ 0.809456  0.461908  1.35817
      julia
      x - x
      5×3 Matrix{Float32}:
+ 0.0  0.0  0.0
+ 0.0  0.0  0.0
+ 0.0  0.0  0.0
+ 0.0  0.0  0.0
+ 0.0  0.0  0.0

      Julia supports a feature called broadcasting, using the . syntax. This tiles small arrays (or single numbers) to fill bigger ones.

      julia
      x .+ 1
      5×3 Matrix{Float32}:
+ 1.56779  1.36918  1.34254
+ 1.09852  1.20114  1.58721
+ 1.7766   1.14825  1.08517
+ 1.72373  1.07702  1.8393
+ 1.40473  1.23095  1.67909

      We can see Julia tile the column vector 1:5 across all rows of the larger array.

      julia
      zeros(5, 5) .+ (1:5)
      5×5 Matrix{Float64}:
+ 1.0  1.0  1.0  1.0  1.0
+ 2.0  2.0  2.0  2.0  2.0
+ 3.0  3.0  3.0  3.0  3.0
+ 4.0  4.0  4.0  4.0  4.0
+ 5.0  5.0  5.0  5.0  5.0

      The x' syntax is used to transpose a column 1:5 into an equivalent row, and Julia will tile that across columns.

      julia
      zeros(5, 5) .+ (1:5)'
      5×5 Matrix{Float64}:
+ 1.0  2.0  3.0  4.0  5.0
+ 1.0  2.0  3.0  4.0  5.0
+ 1.0  2.0  3.0  4.0  5.0
+ 1.0  2.0  3.0  4.0  5.0
+ 1.0  2.0  3.0  4.0  5.0

      We can use this to make a times table.

      julia
      (1:5) .* (1:5)'
      5×5 Matrix{Int64}:
+ 1   2   3   4   5
+ 2   4   6   8  10
+ 3   6   9  12  15
+ 4   8  12  16  20
+ 5  10  15  20  25

      Finally, and importantly for machine learning, we can conveniently do things like matrix multiply.

      julia
      W = randn(5, 10)
+x = rand(10)
+W * x
      5-element Vector{Float64}:
+  1.2197981041108443
+ -2.62625877100596
+ -2.8573820474674845
+ -2.4319346874291314
+  1.0108668577150213

      Julia's arrays are very powerful, and you can learn more about what they can do here.

      CUDA Arrays ​

      CUDA functionality is provided separately by the CUDA.jl package. If you have a GPU and LuxCUDA is installed, Lux will provide CUDA capabilities. For additional details on backends see the manual section.

      You can manually add CUDA. Once CUDA is loaded you can move any array to the GPU with the cu function (or the gpu function exported by `Lux``), and it supports all of the above operations with the same syntax.

      julia
      using LuxCUDA, LuxAMDGPU
+
+if LuxCUDA.functional()
+    x_cu = cu(rand(5, 3))
+    @show x_cu
+elseif LuxAMDGPU.functional() # Similarly, for AMDGPU
+    x_amd = roc(rand(5, 3))
+    @show x_amd
+end
      5×3 CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}:
+ 0.857126  0.681728  0.73806
+ 0.191956  0.506485  0.622865
+ 0.857257  0.663036  0.239756
+ 0.54452   0.503186  0.27993
+ 0.833518  0.975649  0.967811

      (Im)mutability ​

      Lux as you might have read is Immutable by convention which means that the core library is built without any form of mutation and all functions are pure. However, we don't enforce it in any form. We do strongly recommend that users extending this framework for their respective applications don't mutate their arrays.

      julia
      x = reshape(1:8, 2, 4)
      2×4 reshape(::UnitRange{Int64}, 2, 4) with eltype Int64:
+ 1  3  5  7
+ 2  4  6  8

      To update this array, we should first copy the array.

      julia
      x_copy = copy(x)
+view(x_copy, :, 1) .= 0
+
+println("Original Array ", x)
+println("Mutated Array ", x_copy)
      Original Array [1 3 5 7; 2 4 6 8]
+Mutated Array [0 3 5 7; 0 4 6 8]

      Note that our current default AD engine (Zygote) is unable to differentiate through this mutation, however, for these specialized cases it is quite trivial to write custom backward passes. (This problem will be fixed once we move towards Enzyme.jl)

      Managing Randomness ​

      We rely on the Julia StdLib Random for managing the randomness in our execution. First, we create an PRNG (pseudorandom number generator) and seed it.

      julia
      rng = Xoshiro(0)     # Creates a Xoshiro PRNG with seed 0
      Random.Xoshiro(0xdb2fa90498613fdf, 0x48d73dc42d195740, 0x8c49bc52dc8a77ea, 0x1911b814c02405e8, 0x22a21880af5dc689)

      If we call any function that relies on rng and uses it via randn, rand, etc. rng will be mutated. As we have already established we care a lot about immutability, hence we should use Lux.replicate on PRNGs before using them.

      First, let us run a random number generator 3 times with the replicated rng.

      julia
      random_vectors = Vector{Vector{Float64}}(undef, 3)
+for i in 1:3
+    random_vectors[i] = rand(Lux.replicate(rng), 10)
+    println("Iteration $i ", random_vectors[i])
+end
+@assert random_vectors[1] ≈ random_vectors[2] ≈ random_vectors[3]
      Iteration 1 [0.4552384158732863, 0.5476424498276177, 0.7733535276924052, 0.9405848223512736, 0.02964765308691042, 0.74694291453392, 0.7468008914093891, 0.9766699015845924, 0.08694684883050086, 0.35149138733595564]
+Iteration 2 [0.4552384158732863, 0.5476424498276177, 0.7733535276924052, 0.9405848223512736, 0.02964765308691042, 0.74694291453392, 0.7468008914093891, 0.9766699015845924, 0.08694684883050086, 0.35149138733595564]
+Iteration 3 [0.4552384158732863, 0.5476424498276177, 0.7733535276924052, 0.9405848223512736, 0.02964765308691042, 0.74694291453392, 0.7468008914093891, 0.9766699015845924, 0.08694684883050086, 0.35149138733595564]

      As expected we get the same output. We can remove the replicate call and we will get different outputs.

      julia
      for i in 1:3
+    println("Iteration $i ", rand(rng, 10))
+end
      Iteration 1 [0.4552384158732863, 0.5476424498276177, 0.7733535276924052, 0.9405848223512736, 0.02964765308691042, 0.74694291453392, 0.7468008914093891, 0.9766699015845924, 0.08694684883050086, 0.35149138733595564]
+Iteration 2 [0.018743665453639813, 0.8601828553599953, 0.6556360448565952, 0.7746656838366666, 0.7817315740767116, 0.5553797706980106, 0.1261990389976131, 0.4488101521328277, 0.624383955429775, 0.05657739601024536]
+Iteration 3 [0.19597391412112541, 0.6830945313415872, 0.6776220912718907, 0.6456416023530093, 0.6340362477836592, 0.5595843665394066, 0.5675557670686644, 0.34351700231383653, 0.7237308297251812, 0.3691778381831775]

      Automatic Differentiation ​

      Julia has quite a few (maybe too many) AD tools. For the purpose of this tutorial, we will use:

      1. ForwardDiff.jl – For Jacobian-Vector Product (JVP)

      2. Zygote.jl – For Vector-Jacobian Product (VJP)

      Slight Detour: We have had several questions regarding if we will be considering any other AD system for the reverse-diff backend. For now we will stick to Zygote.jl, however once we have tested Lux extensively with Enzyme.jl, we will make the switch.

      Even though, theoretically, a VJP (Vector-Jacobian product - reverse autodiff) and a JVP (Jacobian-Vector product - forward-mode autodiff) are similar—they compute a product of a Jacobian and a vector—they differ by the computational complexity of the operation. In short, when you have a large number of parameters (hence a wide matrix), a JVP is less efficient computationally than a VJP, and, conversely, a JVP is more efficient when the Jacobian matrix is a tall matrix.

      julia
      using ComponentArrays, ForwardDiff, Zygote

      Gradients ​

      For our first example, consider a simple function computing f(x)=12xTx, where ∇f(x)=x

      julia
      f(x) = x' * x / 2
+∇f(x) = x  # `∇` can be typed as `\nabla<TAB>`
+v = randn(rng, Float32, 4)
      4-element Vector{Float32}:
+ -0.4051151
+ -0.4593922
+  0.92155594
+  1.1871622

      Let's use ForwardDiff and Zygote to compute the gradients.

      julia
      println("Actual Gradient: ", ∇f(v))
+println("Computed Gradient via Reverse Mode AD (Zygote): ", only(Zygote.gradient(f, v)))
+println("Computed Gradient via Forward Mode AD (ForwardDiff): ", ForwardDiff.gradient(f, v))
      Actual Gradient: Float32[-0.4051151, -0.4593922, 0.92155594, 1.1871622]
+Computed Gradient via Reverse Mode AD (Zygote): Float32[-0.4051151, -0.4593922, 0.92155594, 1.1871622]
+Computed Gradient via Forward Mode AD (ForwardDiff): Float32[-0.4051151, -0.4593922, 0.92155594, 1.1871622]

      Note that AD.gradient will only work for scalar valued outputs.

      Jacobian-Vector Product ​

      I will defer the discussion on forward-mode AD to https://book.sciml.ai/notes/08-Forward-Mode_Automatic_Differentiation_(AD)_via_High_Dimensional_Algebras/. Here let us just look at a mini example on how to use it.

      julia
      f(x) = x .* x ./ 2
+x = randn(rng, Float32, 5)
+v = ones(Float32, 5)
      5-element Vector{Float32}:
+ 1.0
+ 1.0
+ 1.0
+ 1.0
+ 1.0

      Construct the pushforward function. We will write out the function here but in practice we recommend using SparseDiffTools.auto_jacvec!

      First we need to create a Tag for ForwardDiff. It is enough to know that this is something that you must do. For more details, see the ForwardDiff Documentation!

      julia
      struct TestTag end

      Going in the details of what is function is doing is beyond the scope of this tutorial. But in short, it is constructing a new Dual Vector with the partials set to the input to the pushforward function. When this is propagated through the original function we get the value and the jvp

      julia
      function pushforward_forwarddiff(f, x)
+    T = eltype(x)
+    function pushforward(v)
+        v_ = reshape(v, axes(x))
+        y = ForwardDiff.Dual{
+            ForwardDiff.Tag{TestTag, T}, T, 1}.(x, ForwardDiff.Partials.(tuple.(v_)))
+        res = vec(f(y))
+        return ForwardDiff.value.(res), vec(ForwardDiff.partials.(res, 1))
+    end
+    return pushforward
+end
+
+pf_f = pushforward_forwarddiff(f, x)
      (::Main.var"##225".var"#pushforward#1"{typeof(Main.var"##225".f), Vector{Float32}, DataType}) (generic function with 1 method)

      Compute the jvp.

      julia
      val, jvp = pf_f(v)
+println("Computed Value: f(", x, ") = ", val)
+println("JVP: ", jvp[1])
      Computed Value: f(Float32[-0.877497, 1.1953009, -0.057005208, 0.25055695, 0.09351656]) = Float32[0.3850005, 0.71437216, 0.0016247969, 0.031389393, 0.0043726736]
+JVP: -0.877497

      Vector-Jacobian Product ​

      Using the same function and inputs, let us compute the VJP.

      julia
      val, pb_f = Zygote.pullback(f, x)
      (Float32[0.3850005, 0.71437216, 0.0016247969, 0.031389393, 0.0043726736], Zygote.var"#75#76"{Zygote.Pullback{Tuple{typeof(Main.var"##225".f), Vector{Float32}}, Tuple{Zygote.var"#3796#back#1207"{Zygote.var"#1203#1206"{Vector{Float32}, Vector{Float32}}}, Zygote.var"#3860#back#1233"{Zygote.ZBack{ChainRules.var"#slash_pullback_scalar#1558"{Vector{Float32}, Int64}}}, Zygote.Pullback{Tuple{typeof(Base.Broadcast.materialize), Vector{Float32}}, Tuple{}}}}}(∂(f)))

      Compute the vjp.

      julia
      vjp = only(pb_f(v))
+println("Computed Value: f(", x, ") = ", val)
+println("VJP: ", vjp[1])
      Computed Value: f(Float32[-0.877497, 1.1953009, -0.057005208, 0.25055695, 0.09351656]) = Float32[0.3850005, 0.71437216, 0.0016247969, 0.031389393, 0.0043726736]
+VJP: -0.877497

      Linear Regression ​

      Finally, now let us consider a linear regression problem. From a set of data-points {(xi,yi),i∈{1,…,k},xi∈Rn,yi∈Rm}, we try to find a set of parameters W and b, s.t. fW,b(x)=Wx+b, which minimizes the mean squared error:

      L(W,b)⟶∑i=1k12∥yi−fW,b(xi)∥22

      We can write f from scratch, but to demonstrate Lux, let us use the Dense layer.

      julia
      model = Dense(10 => 5)
+
+rng = Random.default_rng()
+Random.seed!(rng, 0)
      Random.TaskLocalRNG()

      Let us initialize the parameters and states (in this case it is empty) for the model.

      julia
      ps, st = Lux.setup(rng, model)
+ps = ps |> ComponentArray
      ComponentVector{Float32}(weight = Float32[-0.5583162 0.3457679 0.50863314 0.60294497 0.23095794 0.16602759 5.5791984f-6 0.61324424 -0.35419345 0.039559156; -0.05661944 -0.4899126 0.31236076 0.47100115 -0.5062956 -0.20445547 -0.03762182 0.5370978 0.22614014 0.27704597; 0.5198015 0.55730057 -0.34535396 -0.21587563 -0.12729146 -0.51019937 0.46597028 0.2918885 0.20849374 -0.4068233; 0.06026341 -0.11202827 0.31218112 0.14536527 -0.3413506 0.40088427 -0.48716235 -0.15096173 0.42526972 -0.3576447; 0.23414856 -0.5949539 -0.26137677 0.21756552 0.34443143 0.25046515 -0.049256783 -0.48404032 0.08254115 -0.5224755], bias = Float32[0.0; 0.0; 0.0; 0.0; 0.0;;])

      Set problem dimensions.

      julia
      n_samples = 20
+x_dim = 10
+y_dim = 5
      5

      Generate random ground truth W and b.

      julia
      W = randn(rng, Float32, y_dim, x_dim)
+b = randn(rng, Float32, y_dim)
      5-element Vector{Float32}:
+  0.68468636
+ -0.57578707
+  0.0594993
+ -0.9436797
+  1.5164032

      Generate samples with additional noise.

      julia
      x_samples = randn(rng, Float32, x_dim, n_samples)
+y_samples = W * x_samples .+ b .+ 0.01f0 .* randn(rng, Float32, y_dim, n_samples)
+println("x shape: ", size(x_samples), "; y shape: ", size(y_samples))
      x shape: (10, 20); y shape: (5, 20)

      For updating our parameters let's use Optimisers.jl. We will use Stochastic Gradient Descent (SGD) with a learning rate of 0.01.

      julia
      using Optimisers
+
+opt = Optimisers.Descent(0.01f0)
      Descent(0.01f0)

      Initialize the initial state of the optimiser

      julia
      opt_state = Optimisers.setup(opt, ps)
      Leaf(Descent(0.01), nothing)

      Define the loss function

      julia
      function mse(model, ps, st, X, y)
+    y_pred, st_new = model(X, ps, st)
+    return sum(abs2, y_pred .- y), st_new
+end
+mse(weight, bias, X, y) = sum(abs2, weight * X .+ bias .- y)
+loss_function(ps, X, y) = mse(model, ps, st, X, y)
+
+println("Loss Value with ground true parameters: ", mse(W, b, x_samples, y_samples))
+
+for i in 1:100
+    # In actual code, don't use globals. But here I will simply for the sake of
+    # demonstration
+    global ps, st, opt_state
+    # Compute the gradient using the pullback API to update the states
+    (loss, st), pb_f = Zygote.pullback(loss_function, ps, x_samples, y_samples)
+    # We pass nothing as the seed for `st`, since we don't want to propagate any gradient
+    # for st
+    gs = pb_f((one(loss), nothing))[1]
+    # Update model parameters
+    # `Optimisers.update` can be used if mutation is not desired
+    opt_state, ps = Optimisers.update!(opt_state, ps, gs)
+    (i % 10 == 1 || i == 100) && println(lazy"Loss Value after $i iterations: $loss")
+end
      Loss Value with ground true parameters: 0.009175307
+┌ Warning: Assignment to `pb_f` in soft scope is ambiguous because a global variable by the same name exists: `pb_f` will be treated as a new local. Disambiguate by using `local pb_f` to suppress this warning or `global pb_f` to assign to the existing global variable.
+└ @ /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/docs/src/tutorials/beginner/1_Basics.md:15
+Loss Value after 1 iterations: 812.3374
+Loss Value after 11 iterations: 5.479181
+Loss Value after 21 iterations: 0.806523
+Loss Value after 31 iterations: 0.1775011
+Loss Value after 41 iterations: 0.046897847
+Loss Value after 51 iterations: 0.015412594
+Loss Value after 61 iterations: 0.007253055
+Loss Value after 71 iterations: 0.0050410302
+Loss Value after 81 iterations: 0.0044205473
+Loss Value after 91 iterations: 0.004241652
+Loss Value after 100 iterations: 0.0041917767

      Appendix ​

      julia
      using InteractiveUtils
+InteractiveUtils.versioninfo()
+if @isdefined(LuxCUDA) && CUDA.functional(); println(); CUDA.versioninfo(); end
+if @isdefined(LuxAMDGPU) && LuxAMDGPU.functional(); println(); AMDGPU.versioninfo(); end
      Julia Version 1.10.2
+Commit bd47eca2c8a (2024-03-01 10:14 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 48 × AMD EPYC 7402 24-Core Processor
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
+Threads: 48 default, 0 interactive, 24 GC (on 2 virtual cores)
+Environment:
+  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
+  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6
+  JULIA_PROJECT = /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/docs
+  JULIA_AMDGPU_LOGGING_ENABLED = true
+  JULIA_DEBUG = Literate
+  JULIA_CPU_THREADS = 2
+  JULIA_NUM_THREADS = 48
+  JULIA_LOAD_PATH = @:@v#.#:@stdlib
+  JULIA_CUDA_HARD_MEMORY_LIMIT = 25%
+
+CUDA runtime 12.3, artifact installation
+CUDA driver 12.4
+NVIDIA driver 550.54.15
+
+CUDA libraries: 
+- CUBLAS: 12.3.4
+- CURAND: 10.3.4
+- CUFFT: 11.0.12
+- CUSOLVER: 11.5.4
+- CUSPARSE: 12.2.0
+- CUPTI: 21.0.0
+- NVML: 12.0.0+550.54.15
+
+Julia packages: 
+- CUDA: 5.2.0
+- CUDA_Driver_jll: 0.7.0+1
+- CUDA_Runtime_jll: 0.11.1+0
+
+Toolchain:
+- Julia: 1.10.2
+- LLVM: 15.0.7
+
+Environment:
+- JULIA_CUDA_HARD_MEMORY_LIMIT: 25%
+
+1 device:
+  0: NVIDIA A100-PCIE-40GB MIG 1g.5gb (sm_80, 4.518 GiB / 4.750 GiB available)
+┌ Warning: LuxAMDGPU is loaded but the AMDGPU is not functional.
+└ @ LuxAMDGPU ~/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6/packages/LuxAMDGPU/sGa0S/src/LuxAMDGPU.jl:19

      This page was generated using Literate.jl.

      + + + + \ No newline at end of file diff --git a/v0.5.30/tutorials/beginner/2_PolynomialFitting.html b/v0.5.30/tutorials/beginner/2_PolynomialFitting.html new file mode 100644 index 000000000..23cee6c27 --- /dev/null +++ b/v0.5.30/tutorials/beginner/2_PolynomialFitting.html @@ -0,0 +1,139 @@ + + + + + + Fitting a Polynomial using MLP | Lux.jl Documentation + + + + + + + + + + + + + +
      Lux.jl Documentation

      Appearance


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      Scientific Computing

      SciML.ai

      Machine Learning

      Structure Preserving

      GeometricML.jl

      Machine Learning

      Physical Systems

      MeshGraphNets.jl

      Graph Neural Nets

      Fitting a Polynomial using MLP ​

      In this tutorial we will fit a MultiLayer Perceptron (MLP) on data generated from a polynomial.

      Package Imports ​

      julia
      using Lux, ADTypes, LuxAMDGPU, LuxCUDA, Optimisers, Printf, Random, Statistics, Zygote
+using CairoMakie

      Dataset ​

      Generate 128 datapoints from the polynomial y=x2−2x.

      julia
      function generate_data(rng::AbstractRNG)
+    x = reshape(collect(range(-2.0f0, 2.0f0, 128)), (1, 128))
+    y = evalpoly.(x, ((0, -2, 1),)) .+ randn(rng, (1, 128)) .* 0.1f0
+    return (x, y)
+end
      generate_data (generic function with 1 method)

      Initialize the random number generator and fetch the dataset.

      julia
      rng = MersenneTwister()
+Random.seed!(rng, 12345)
+
+(x, y) = generate_data(rng)
      (Float32[-2.0 -1.968504 -1.9370079 -1.9055119 -1.8740157 -1.8425196 -1.8110236 -1.7795275 -1.7480315 -1.7165354 -1.6850394 -1.6535434 -1.6220472 -1.5905511 -1.5590551 -1.527559 -1.496063 -1.464567 -1.4330709 -1.4015749 -1.3700787 -1.3385826 -1.3070866 -1.2755905 -1.2440945 -1.2125984 -1.1811024 -1.1496063 -1.1181102 -1.0866141 -1.0551181 -1.023622 -0.992126 -0.96062994 -0.92913383 -0.8976378 -0.86614174 -0.8346457 -0.8031496 -0.77165353 -0.7401575 -0.70866144 -0.6771653 -0.6456693 -0.61417323 -0.5826772 -0.5511811 -0.51968503 -0.48818898 -0.4566929 -0.42519686 -0.39370078 -0.36220473 -0.33070865 -0.2992126 -0.26771653 -0.23622048 -0.20472442 -0.17322835 -0.14173229 -0.11023622 -0.07874016 -0.047244094 -0.015748031 0.015748031 0.047244094 0.07874016 0.11023622 0.14173229 0.17322835 0.20472442 0.23622048 0.26771653 0.2992126 0.33070865 0.36220473 0.39370078 0.42519686 0.4566929 0.48818898 0.51968503 0.5511811 0.5826772 0.61417323 0.6456693 0.6771653 0.70866144 0.7401575 0.77165353 0.8031496 0.8346457 0.86614174 0.8976378 0.92913383 0.96062994 0.992126 1.023622 1.0551181 1.0866141 1.1181102 1.1496063 1.1811024 1.2125984 1.2440945 1.2755905 1.3070866 1.3385826 1.3700787 1.4015749 1.4330709 1.464567 1.496063 1.527559 1.5590551 1.5905511 1.6220472 1.6535434 1.6850394 1.7165354 1.7480315 1.7795275 1.8110236 1.8425196 1.8740157 1.9055119 1.9370079 1.968504 2.0], [8.11723579535073 7.8972862806322315 7.667572185253954 7.493641443881164 7.328542256257643 7.1081451188446065 6.754145700236098 6.73844851250885 6.698323804024227 6.3637494708272655 6.270117709011731 6.2419372753805 5.816280759896085 5.718319527208828 5.741347639508506 5.258118446989299 5.268165780092538 5.195746082529355 5.032704772846244 4.733409783966572 4.520239616672976 4.369386593776045 4.107888442446331 4.182845399340577 4.002249800810884 3.8969011895086174 3.910820824989613 3.646440085736948 3.3343752660206305 3.3980378243437745 3.1887817476268587 2.9930802717826603 3.018980452144523 2.690492107796345 2.8576513349182378 2.4778283273281008 2.452401424624867 2.401875695877283 2.2896425232872755 2.2812518842985035 1.9742292519472466 1.7663454774622869 1.7829663021691418 1.6248666914928798 1.635090436697959 1.4887378757184528 1.4396068206428336 1.5047223947023354 1.2439428212858357 1.1770575798169982 1.0519113712665473 0.8008025630753797 0.8011788202541421 0.7702484835053167 0.9010273188596704 0.48114290312426095 0.4605012716399809 0.42308333113261615 0.2890108900859864 0.3324716507588617 0.2126899641074972 0.2560113968739265 0.08350192481301627 0.046225582753114294 -0.16118930624459 -0.013928769802494537 -0.030805824695545894 -0.10629780224701328 -0.17643440564041185 -0.2494508100897751 -0.3322350480467481 -0.45414851684613733 -0.6965624404632386 -0.38861245182183696 -0.4708530312086873 -0.6274991143463677 -0.5617763080815885 -0.6438360803492721 -0.7565600800322707 -0.5662591600023589 -0.6591533520776037 -0.9166793344639054 -0.8520467822193756 -0.9507226194240974 -1.0248823046771698 -0.97772916365376 -0.8199294436184201 -0.9080088282844027 -0.9682665790685976 -1.031816361263047 -0.9296919748814573 -1.1145618706755287 -1.2139119971536336 -1.0157839085777947 -0.9417175810509869 -0.9783498813733602 -0.9123675448444001 -1.138088633455826 -1.1212038088290894 -0.911429094488635 -1.023486657428913 -0.9287179111905346 -1.0396518660677925 -1.0370046468920306 -0.9846375721966646 -0.833026219703481 -0.8200258902651266 -0.789500663251252 -0.9068267920931062 -0.7284236770750803 -0.7093213401368348 -0.7048862544448803 -0.6215870033126495 -0.5892481295457608 -0.8462913756395639 -0.5544688796856879 -0.5805399434794658 -0.5761396334948753 -0.5851955365208916 -0.5561461874821676 -0.1969227628706652 -0.34073487813889014 -0.2738635064414512 -0.1425063756241582 -0.18330825579933746 -0.054321035831595324 -0.21213293699653427 0.049985105882301])

      Let's visualize the dataset

      julia
      begin
+    fig = Figure()
+    ax = CairoMakie.Axis(fig[1, 1]; xlabel="x", ylabel="y")
+
+    l = lines!(ax, x[1, :], x -> evalpoly(x, (0, -2, 1)); linewidth=3, color=:blue)
+    s = scatter!(ax, x[1, :], y[1, :]; markersize=12, alpha=0.5,
+        color=:orange, strokecolor=:black, strokewidth=2)
+
+    axislegend(ax, [l, s], ["True Quadratic Function", "Data Points"])
+
+    fig
+end

      Neural Network ​

      For this problem, you should not be using a neural network. But let's still do that!

      julia
      model = Chain(Dense(1 => 16, relu), Dense(16 => 1))
      Chain(
+    layer_1 = Dense(1 => 16, relu),     # 32 parameters
+    layer_2 = Dense(16 => 1),           # 17 parameters
+)         # Total: 49 parameters,
+          #        plus 0 states.

      Optimizer ​

      We will use Adam from Optimisers.jl

      julia
      opt = Adam(0.03f0)
      Adam(0.03, (0.9, 0.999), 1.0e-8)

      Loss Function ​

      We will use the Lux.Training API so we need to ensure that our loss function takes 4 inputs – model, parameters, states and data. The function must return 3 values – loss, updated_state, and any computed statistics.

      julia
      function loss_function(model, ps, st, data)
+    y_pred, st = Lux.apply(model, data[1], ps, st)
+    mse_loss = mean(abs2, y_pred .- data[2])
+    return mse_loss, st, ()
+end
      loss_function (generic function with 1 method)

      Training ​

      First we will create a Lux.Experimental.TrainState which is essentially a convenience wrapper over parameters, states and optimizer states.

      julia
      tstate = Lux.Experimental.TrainState(rng, model, opt)
      Lux.Experimental.TrainState{Lux.Chain{@NamedTuple{layer_1::Lux.Dense{true, typeof(NNlib.relu), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_2::Lux.Dense{true, typeof(identity), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing}, @NamedTuple{layer_1::@NamedTuple{weight::CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, bias::CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}}, layer_2::@NamedTuple{weight::CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, bias::CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}}}, @NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}}, @NamedTuple{layer_1::@NamedTuple{weight::Optimisers.Leaf{Optimisers.Adam, Tuple{CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, Tuple{Float32, Float32}}}, bias::Optimisers.Leaf{Optimisers.Adam, Tuple{CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, Tuple{Float32, Float32}}}}, layer_2::@NamedTuple{weight::Optimisers.Leaf{Optimisers.Adam, Tuple{CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, Tuple{Float32, Float32}}}, bias::Optimisers.Leaf{Optimisers.Adam, Tuple{CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, Tuple{Float32, Float32}}}}}}(Chain(), (layer_1 = (weight = Float32[0.36222202; 0.23371002; -0.49825558; -0.18142056; -0.13757975; -0.50849473; 0.13773328; -0.035294008; 0.21778254; 0.04964345; -0.56594235; -0.45329624; -0.08787567; 0.5648949; 0.5260752; -0.07562564;;], bias = Float32[0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0;;]), layer_2 = (weight = Float32[-0.14330137 -0.39328107 -0.18253882 -0.55998546 -0.5919335 -0.3069779 -0.39085856 -0.4838621 0.3979575 0.5851314 0.24242708 0.35374007 0.10175798 0.29761198 -0.34761065 -0.05758927], bias = Float32[0.0;;])), (layer_1 = NamedTuple(), layer_2 = NamedTuple()), (layer_1 = (weight = Leaf(Adam(0.03, (0.9, 0.999), 1.0e-8), (Float32[0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0;;], Float32[0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0;;], (0.9, 0.999))), bias = Leaf(Adam(0.03, (0.9, 0.999), 1.0e-8), (Float32[0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0;;], Float32[0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0; 0.0;;], (0.9, 0.999)))), layer_2 = (weight = Leaf(Adam(0.03, (0.9, 0.999), 1.0e-8), (Float32[0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0], Float32[0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0], (0.9, 0.999))), bias = Leaf(Adam(0.03, (0.9, 0.999), 1.0e-8), (Float32[0.0;;], Float32[0.0;;], (0.9, 0.999))))), 0)

      Now we will use Zygote for our AD requirements.

      julia
      vjp_rule = AutoZygote()
      ADTypes.AutoZygote()

      Finally the training loop.

      julia
      function main(tstate::Lux.Experimental.TrainState, vjp, data, epochs)
+    data = data .|> gpu_device()
+    for epoch in 1:epochs
+        grads, loss, stats, tstate = Lux.Training.compute_gradients(
+            vjp, loss_function, data, tstate)
+        if epoch % 50 == 1 || epoch == epochs
+            @printf "Epoch: %3d \t Loss: %.5g\n" epoch loss
+        end
+        tstate = Lux.Training.apply_gradients(tstate, grads)
+    end
+    return tstate
+end
+
+dev_cpu = cpu_device()
+dev_gpu = gpu_device()
+
+tstate = main(tstate, vjp_rule, (x, y), 250)
+y_pred = dev_cpu(Lux.apply(tstate.model, dev_gpu(x), tstate.parameters, tstate.states)[1])
      Epoch:   1 	 Loss: 9.4373
+Epoch:  51 	 Loss: 0.086228
+Epoch: 101 	 Loss: 0.033642
+Epoch: 151 	 Loss: 0.021989
+Epoch: 201 	 Loss: 0.017344
+Epoch: 250 	 Loss: 0.013794

      Let's plot the results

      julia
      begin
+    fig = Figure()
+    ax = CairoMakie.Axis(fig[1, 1]; xlabel="x", ylabel="y")
+
+    l = lines!(ax, x[1, :], x -> evalpoly(x, (0, -2, 1)); linewidth=3)
+    s1 = scatter!(ax, x[1, :], y[1, :]; markersize=12, alpha=0.5,
+        color=:orange, strokecolor=:black, strokewidth=2)
+    s2 = scatter!(ax, x[1, :], y_pred[1, :]; markersize=12, alpha=0.5,
+        color=:green, strokecolor=:black, strokewidth=2)
+
+    axislegend(ax, [l, s1, s2], ["True Quadratic Function", "Actual Data", "Predictions"])
+
+    fig
+end

      Appendix ​

      julia
      using InteractiveUtils
+InteractiveUtils.versioninfo()
+if @isdefined(LuxCUDA) && CUDA.functional(); println(); CUDA.versioninfo(); end
+if @isdefined(LuxAMDGPU) && LuxAMDGPU.functional(); println(); AMDGPU.versioninfo(); end
      Julia Version 1.10.2
+Commit bd47eca2c8a (2024-03-01 10:14 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 48 × AMD EPYC 7402 24-Core Processor
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
+Threads: 48 default, 0 interactive, 24 GC (on 2 virtual cores)
+Environment:
+  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
+  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6
+  JULIA_PROJECT = /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/docs
+  JULIA_AMDGPU_LOGGING_ENABLED = true
+  JULIA_DEBUG = Literate
+  JULIA_CPU_THREADS = 2
+  JULIA_NUM_THREADS = 48
+  JULIA_LOAD_PATH = @:@v#.#:@stdlib
+  JULIA_CUDA_HARD_MEMORY_LIMIT = 25%
+
+CUDA runtime 12.3, artifact installation
+CUDA driver 12.4
+NVIDIA driver 550.54.15
+
+CUDA libraries: 
+- CUBLAS: 12.3.4
+- CURAND: 10.3.4
+- CUFFT: 11.0.12
+- CUSOLVER: 11.5.4
+- CUSPARSE: 12.2.0
+- CUPTI: 21.0.0
+- NVML: 12.0.0+550.54.15
+
+Julia packages: 
+- CUDA: 5.2.0
+- CUDA_Driver_jll: 0.7.0+1
+- CUDA_Runtime_jll: 0.11.1+0
+
+Toolchain:
+- Julia: 1.10.2
+- LLVM: 15.0.7
+
+Environment:
+- JULIA_CUDA_HARD_MEMORY_LIMIT: 25%
+
+1 device:
+  0: NVIDIA A100-PCIE-40GB MIG 1g.5gb (sm_80, 4.600 GiB / 4.750 GiB available)
+┌ Warning: LuxAMDGPU is loaded but the AMDGPU is not functional.
+└ @ LuxAMDGPU ~/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6/packages/LuxAMDGPU/sGa0S/src/LuxAMDGPU.jl:19

      This page was generated using Literate.jl.

      + + + + \ No newline at end of file diff --git a/v0.5.30/tutorials/beginner/3_SimpleRNN.html b/v0.5.30/tutorials/beginner/3_SimpleRNN.html new file mode 100644 index 000000000..001f6eef9 --- /dev/null +++ b/v0.5.30/tutorials/beginner/3_SimpleRNN.html @@ -0,0 +1,404 @@ + + + + + + Training a Simple LSTM | Lux.jl Documentation + + + + + + + + + + + + + +
      Lux.jl Documentation

      Appearance


      Trusted by

      Scientific Computing

      SciML.ai

      Machine Learning

      Structure Preserving

      GeometricML.jl

      Machine Learning

      Physical Systems

      MeshGraphNets.jl

      Graph Neural Nets

      Training a Simple LSTM ​

      In this tutorial we will go over using a recurrent neural network to classify clockwise and anticlockwise spirals. By the end of this tutorial you will be able to:

      1. Create custom Lux models.

      2. Become familiar with the Lux recurrent neural network API.

      3. Training using Optimisers.jl and Zygote.jl.

      Package Imports ​

      julia
      using ADTypes, Lux, LuxAMDGPU, LuxCUDA, JLD2, MLUtils, Optimisers, Zygote, Printf, Random,
+      Statistics

      Dataset ​

      We will use MLUtils to generate 500 (noisy) clockwise and 500 (noisy) anticlockwise spirals. Using this data we will create a MLUtils.DataLoader. Our dataloader will give us sequences of size 2 × seq_len × batch_size and we need to predict a binary value whether the sequence is clockwise or anticlockwise.

      julia
      function get_dataloaders(; dataset_size=1000, sequence_length=50)
+    # Create the spirals
+    data = [MLUtils.Datasets.make_spiral(sequence_length) for _ in 1:dataset_size]
+    # Get the labels
+    labels = vcat(repeat([0.0f0], dataset_size ÷ 2), repeat([1.0f0], dataset_size ÷ 2))
+    clockwise_spirals = [reshape(d[1][:, 1:sequence_length], :, sequence_length, 1)
+                         for d in data[1:(dataset_size ÷ 2)]]
+    anticlockwise_spirals = [reshape(
+                                 d[1][:, (sequence_length + 1):end], :, sequence_length, 1)
+                             for d in data[((dataset_size ÷ 2) + 1):end]]
+    x_data = Float32.(cat(clockwise_spirals..., anticlockwise_spirals...; dims=3))
+    # Split the dataset
+    (x_train, y_train), (x_val, y_val) = splitobs((x_data, labels); at=0.8, shuffle=true)
+    # Create DataLoaders
+    return (
+        # Use DataLoader to automatically minibatch and shuffle the data
+        DataLoader(collect.((x_train, y_train)); batchsize=128, shuffle=true),
+        # Don't shuffle the validation data
+        DataLoader(collect.((x_val, y_val)); batchsize=128, shuffle=false))
+end
      get_dataloaders (generic function with 1 method)

      Creating a Classifier ​

      We will be extending the Lux.AbstractExplicitContainerLayer type for our custom model since it will contain a lstm block and a classifier head.

      We pass the fieldnames lstm_cell and classifier to the type to ensure that the parameters and states are automatically populated and we don't have to define Lux.initialparameters and Lux.initialstates.

      To understand more about container layers, please look at Container Layer.

      julia
      struct SpiralClassifier{L, C} <:
+       Lux.AbstractExplicitContainerLayer{(:lstm_cell, :classifier)}
+    lstm_cell::L
+    classifier::C
+end

      We won't define the model from scratch but rather use the Lux.LSTMCell and Lux.Dense.

      julia
      function SpiralClassifier(in_dims, hidden_dims, out_dims)
+    return SpiralClassifier(
+        LSTMCell(in_dims => hidden_dims), Dense(hidden_dims => out_dims, sigmoid))
+end
      Main.var"##225".SpiralClassifier

      We can use default Lux blocks – Recurrence(LSTMCell(in_dims => hidden_dims) – instead of defining the following. But let's still do it for the sake of it.

      Now we need to define the behavior of the Classifier when it is invoked.

      julia
      function (s::SpiralClassifier)(
+        x::AbstractArray{T, 3}, ps::NamedTuple, st::NamedTuple) where {T}
+    # First we will have to run the sequence through the LSTM Cell
+    # The first call to LSTM Cell will create the initial hidden state
+    # See that the parameters and states are automatically populated into a field called
+    # `lstm_cell` We use `eachslice` to get the elements in the sequence without copying,
+    # and `Iterators.peel` to split out the first element for LSTM initialization.
+    x_init, x_rest = Iterators.peel(Lux._eachslice(x, Val(2)))
+    (y, carry), st_lstm = s.lstm_cell(x_init, ps.lstm_cell, st.lstm_cell)
+    # Now that we have the hidden state and memory in `carry` we will pass the input and
+    # `carry` jointly
+    for x in x_rest
+        (y, carry), st_lstm = s.lstm_cell((x, carry), ps.lstm_cell, st_lstm)
+    end
+    # After running through the sequence we will pass the output through the classifier
+    y, st_classifier = s.classifier(y, ps.classifier, st.classifier)
+    # Finally remember to create the updated state
+    st = merge(st, (classifier=st_classifier, lstm_cell=st_lstm))
+    return vec(y), st
+end

      Defining Accuracy, Loss and Optimiser ​

      Now let's define the binarycrossentropy loss. Typically it is recommended to use logitbinarycrossentropy since it is more numerically stable, but for the sake of simplicity we will use binarycrossentropy.

      julia
      function xlogy(x, y)
+    result = x * log(y)
+    return ifelse(iszero(x), zero(result), result)
+end
+
+function binarycrossentropy(y_pred, y_true)
+    y_pred = y_pred .+ eps(eltype(y_pred))
+    return mean(@. -xlogy(y_true, y_pred) - xlogy(1 - y_true, 1 - y_pred))
+end
+
+function compute_loss(model, ps, st, (x, y))
+    y_pred, st = model(x, ps, st)
+    return binarycrossentropy(y_pred, y), st, (; y_pred=y_pred)
+end
+
+matches(y_pred, y_true) = sum((y_pred .> 0.5f0) .== y_true)
+accuracy(y_pred, y_true) = matches(y_pred, y_true) / length(y_pred)
      accuracy (generic function with 1 method)

      Training the Model ​

      julia
      function main()
+    # Get the dataloaders
+    (train_loader, val_loader) = get_dataloaders()
+
+    # Create the model
+    model = SpiralClassifier(2, 8, 1)
+    rng = Xoshiro(0)
+
+    dev = gpu_device()
+    train_state = Lux.Experimental.TrainState(
+        rng, model, Adam(0.01f0); transform_variables=dev)
+
+    for epoch in 1:25
+        # Train the model
+        for (x, y) in train_loader
+            x = x |> dev
+            y = y |> dev
+
+            gs, loss, _, train_state = Lux.Experimental.compute_gradients(
+                AutoZygote(), compute_loss, (x, y), train_state)
+            train_state = Lux.Experimental.apply_gradients(train_state, gs)
+
+            @printf "Epoch [%3d]: Loss %4.5f\n" epoch loss
+        end
+
+        # Validate the model
+        st_ = Lux.testmode(train_state.states)
+        for (x, y) in val_loader
+            x = x |> dev
+            y = y |> dev
+            loss, st_, ret = compute_loss(model, train_state.parameters, st_, (x, y))
+            acc = accuracy(ret.y_pred, y)
+            @printf "Validation: Loss %4.5f Accuracy %4.5f\n" loss acc
+        end
+    end
+
+    return (train_state.parameters, train_state.states) |> cpu_device()
+end
+
+ps_trained, st_trained = main()
      Epoch [  1]: Loss 0.56263
+Epoch [  1]: Loss 0.50622
+Epoch [  1]: Loss 0.46754
+Epoch [  1]: Loss 0.45518
+Epoch [  1]: Loss 0.43237
+Epoch [  1]: Loss 0.40357
+Epoch [  1]: Loss 0.37433
+Validation: Loss 0.36939 Accuracy 1.00000
+Validation: Loss 0.38321 Accuracy 1.00000
+Epoch [  2]: Loss 0.37481
+Epoch [  2]: Loss 0.35556
+Epoch [  2]: Loss 0.32647
+Epoch [  2]: Loss 0.32097
+Epoch [  2]: Loss 0.29943
+Epoch [  2]: Loss 0.28412
+Epoch [  2]: Loss 0.26005
+Validation: Loss 0.25919 Accuracy 1.00000
+Validation: Loss 0.26821 Accuracy 1.00000
+Epoch [  3]: Loss 0.26588
+Epoch [  3]: Loss 0.24159
+Epoch [  3]: Loss 0.23038
+Epoch [  3]: Loss 0.22152
+Epoch [  3]: Loss 0.20744
+Epoch [  3]: Loss 0.20136
+Epoch [  3]: Loss 0.18646
+Validation: Loss 0.18102 Accuracy 1.00000
+Validation: Loss 0.18637 Accuracy 1.00000
+Epoch [  4]: Loss 0.17623
+Epoch [  4]: Loss 0.16670
+Epoch [  4]: Loss 0.16627
+Epoch [  4]: Loss 0.15707
+Epoch [  4]: Loss 0.15225
+Epoch [  4]: Loss 0.14029
+Epoch [  4]: Loss 0.13672
+Validation: Loss 0.12918 Accuracy 1.00000
+Validation: Loss 0.13293 Accuracy 1.00000
+Epoch [  5]: Loss 0.12726
+Epoch [  5]: Loss 0.12789
+Epoch [  5]: Loss 0.11814
+Epoch [  5]: Loss 0.10943
+Epoch [  5]: Loss 0.10736
+Epoch [  5]: Loss 0.10008
+Epoch [  5]: Loss 0.09878
+Validation: Loss 0.09405 Accuracy 1.00000
+Validation: Loss 0.09701 Accuracy 1.00000
+Epoch [  6]: Loss 0.09387
+Epoch [  6]: Loss 0.08977
+Epoch [  6]: Loss 0.08546
+Epoch [  6]: Loss 0.08282
+Epoch [  6]: Loss 0.07942
+Epoch [  6]: Loss 0.07283
+Epoch [  6]: Loss 0.07509
+Validation: Loss 0.06955 Accuracy 1.00000
+Validation: Loss 0.07227 Accuracy 1.00000
+Epoch [  7]: Loss 0.06925
+Epoch [  7]: Loss 0.06594
+Epoch [  7]: Loss 0.06383
+Epoch [  7]: Loss 0.05994
+Epoch [  7]: Loss 0.05758
+Epoch [  7]: Loss 0.05775
+Epoch [  7]: Loss 0.05475
+Validation: Loss 0.05197 Accuracy 1.00000
+Validation: Loss 0.05449 Accuracy 1.00000
+Epoch [  8]: Loss 0.05228
+Epoch [  8]: Loss 0.05002
+Epoch [  8]: Loss 0.04655
+Epoch [  8]: Loss 0.04395
+Epoch [  8]: Loss 0.04409
+Epoch [  8]: Loss 0.04332
+Epoch [  8]: Loss 0.04139
+Validation: Loss 0.03915 Accuracy 1.00000
+Validation: Loss 0.04145 Accuracy 1.00000
+Epoch [  9]: Loss 0.03956
+Epoch [  9]: Loss 0.03666
+Epoch [  9]: Loss 0.03553
+Epoch [  9]: Loss 0.03384
+Epoch [  9]: Loss 0.03446
+Epoch [  9]: Loss 0.03219
+Epoch [  9]: Loss 0.02961
+Validation: Loss 0.02991 Accuracy 1.00000
+Validation: Loss 0.03203 Accuracy 1.00000
+Epoch [ 10]: Loss 0.03070
+Epoch [ 10]: Loss 0.02812
+Epoch [ 10]: Loss 0.02747
+Epoch [ 10]: Loss 0.02620
+Epoch [ 10]: Loss 0.02516
+Epoch [ 10]: Loss 0.02568
+Epoch [ 10]: Loss 0.02363
+Validation: Loss 0.02351 Accuracy 1.00000
+Validation: Loss 0.02541 Accuracy 1.00000
+Epoch [ 11]: Loss 0.02379
+Epoch [ 11]: Loss 0.02360
+Epoch [ 11]: Loss 0.02179
+Epoch [ 11]: Loss 0.02033
+Epoch [ 11]: Loss 0.02039
+Epoch [ 11]: Loss 0.01950
+Epoch [ 11]: Loss 0.02115
+Validation: Loss 0.01913 Accuracy 1.00000
+Validation: Loss 0.02080 Accuracy 1.00000
+Epoch [ 12]: Loss 0.01892
+Epoch [ 12]: Loss 0.01786
+Epoch [ 12]: Loss 0.01832
+Epoch [ 12]: Loss 0.01683
+Epoch [ 12]: Loss 0.01617
+Epoch [ 12]: Loss 0.01823
+Epoch [ 12]: Loss 0.01779
+Validation: Loss 0.01608 Accuracy 1.00000
+Validation: Loss 0.01752 Accuracy 1.00000
+Epoch [ 13]: Loss 0.01481
+Epoch [ 13]: Loss 0.01561
+Epoch [ 13]: Loss 0.01593
+Epoch [ 13]: Loss 0.01432
+Epoch [ 13]: Loss 0.01573
+Epoch [ 13]: Loss 0.01389
+Epoch [ 13]: Loss 0.01494
+Validation: Loss 0.01388 Accuracy 1.00000
+Validation: Loss 0.01514 Accuracy 1.00000
+Epoch [ 14]: Loss 0.01335
+Epoch [ 14]: Loss 0.01329
+Epoch [ 14]: Loss 0.01391
+Epoch [ 14]: Loss 0.01310
+Epoch [ 14]: Loss 0.01329
+Epoch [ 14]: Loss 0.01209
+Epoch [ 14]: Loss 0.01129
+Validation: Loss 0.01222 Accuracy 1.00000
+Validation: Loss 0.01335 Accuracy 1.00000
+Epoch [ 15]: Loss 0.01293
+Epoch [ 15]: Loss 0.01176
+Epoch [ 15]: Loss 0.01128
+Epoch [ 15]: Loss 0.01138
+Epoch [ 15]: Loss 0.01119
+Epoch [ 15]: Loss 0.01150
+Epoch [ 15]: Loss 0.01013
+Validation: Loss 0.01094 Accuracy 1.00000
+Validation: Loss 0.01196 Accuracy 1.00000
+Epoch [ 16]: Loss 0.01111
+Epoch [ 16]: Loss 0.01155
+Epoch [ 16]: Loss 0.01045
+Epoch [ 16]: Loss 0.01038
+Epoch [ 16]: Loss 0.00986
+Epoch [ 16]: Loss 0.00926
+Epoch [ 16]: Loss 0.01058
+Validation: Loss 0.00990 Accuracy 1.00000
+Validation: Loss 0.01085 Accuracy 1.00000
+Epoch [ 17]: Loss 0.00961
+Epoch [ 17]: Loss 0.00939
+Epoch [ 17]: Loss 0.01024
+Epoch [ 17]: Loss 0.00949
+Epoch [ 17]: Loss 0.00934
+Epoch [ 17]: Loss 0.00900
+Epoch [ 17]: Loss 0.00861
+Validation: Loss 0.00904 Accuracy 1.00000
+Validation: Loss 0.00990 Accuracy 1.00000
+Epoch [ 18]: Loss 0.00919
+Epoch [ 18]: Loss 0.00851
+Epoch [ 18]: Loss 0.00921
+Epoch [ 18]: Loss 0.00895
+Epoch [ 18]: Loss 0.00814
+Epoch [ 18]: Loss 0.00790
+Epoch [ 18]: Loss 0.00914
+Validation: Loss 0.00831 Accuracy 1.00000
+Validation: Loss 0.00911 Accuracy 1.00000
+Epoch [ 19]: Loss 0.00879
+Epoch [ 19]: Loss 0.00821
+Epoch [ 19]: Loss 0.00771
+Epoch [ 19]: Loss 0.00754
+Epoch [ 19]: Loss 0.00763
+Epoch [ 19]: Loss 0.00819
+Epoch [ 19]: Loss 0.00725
+Validation: Loss 0.00767 Accuracy 1.00000
+Validation: Loss 0.00842 Accuracy 1.00000
+Epoch [ 20]: Loss 0.00766
+Epoch [ 20]: Loss 0.00682
+Epoch [ 20]: Loss 0.00756
+Epoch [ 20]: Loss 0.00719
+Epoch [ 20]: Loss 0.00725
+Epoch [ 20]: Loss 0.00777
+Epoch [ 20]: Loss 0.00760
+Validation: Loss 0.00713 Accuracy 1.00000
+Validation: Loss 0.00783 Accuracy 1.00000
+Epoch [ 21]: Loss 0.00663
+Epoch [ 21]: Loss 0.00737
+Epoch [ 21]: Loss 0.00708
+Epoch [ 21]: Loss 0.00655
+Epoch [ 21]: Loss 0.00692
+Epoch [ 21]: Loss 0.00675
+Epoch [ 21]: Loss 0.00652
+Validation: Loss 0.00664 Accuracy 1.00000
+Validation: Loss 0.00730 Accuracy 1.00000
+Epoch [ 22]: Loss 0.00615
+Epoch [ 22]: Loss 0.00571
+Epoch [ 22]: Loss 0.00629
+Epoch [ 22]: Loss 0.00674
+Epoch [ 22]: Loss 0.00678
+Epoch [ 22]: Loss 0.00690
+Epoch [ 22]: Loss 0.00588
+Validation: Loss 0.00621 Accuracy 1.00000
+Validation: Loss 0.00684 Accuracy 1.00000
+Epoch [ 23]: Loss 0.00587
+Epoch [ 23]: Loss 0.00625
+Epoch [ 23]: Loss 0.00642
+Epoch [ 23]: Loss 0.00557
+Epoch [ 23]: Loss 0.00585
+Epoch [ 23]: Loss 0.00597
+Epoch [ 23]: Loss 0.00643
+Validation: Loss 0.00583 Accuracy 1.00000
+Validation: Loss 0.00642 Accuracy 1.00000
+Epoch [ 24]: Loss 0.00560
+Epoch [ 24]: Loss 0.00568
+Epoch [ 24]: Loss 0.00568
+Epoch [ 24]: Loss 0.00549
+Epoch [ 24]: Loss 0.00585
+Epoch [ 24]: Loss 0.00556
+Epoch [ 24]: Loss 0.00554
+Validation: Loss 0.00549 Accuracy 1.00000
+Validation: Loss 0.00604 Accuracy 1.00000
+Epoch [ 25]: Loss 0.00557
+Epoch [ 25]: Loss 0.00522
+Epoch [ 25]: Loss 0.00536
+Epoch [ 25]: Loss 0.00513
+Epoch [ 25]: Loss 0.00540
+Epoch [ 25]: Loss 0.00509
+Epoch [ 25]: Loss 0.00569
+Validation: Loss 0.00517 Accuracy 1.00000
+Validation: Loss 0.00570 Accuracy 1.00000

      Saving the Model ​

      We can save the model using JLD2 (and any other serialization library of your choice) Note that we transfer the model to CPU before saving. Additionally, we recommend that you don't save the model

      julia
      @save "trained_model.jld2" {compress = true} ps_trained st_trained

      Let's try loading the model

      julia
      @load "trained_model.jld2" ps_trained st_trained
      2-element Vector{Symbol}:
+ :ps_trained
+ :st_trained

      Appendix ​

      julia
      using InteractiveUtils
+InteractiveUtils.versioninfo()
+if @isdefined(LuxCUDA) && CUDA.functional(); println(); CUDA.versioninfo(); end
+if @isdefined(LuxAMDGPU) && LuxAMDGPU.functional(); println(); AMDGPU.versioninfo(); end
      Julia Version 1.10.2
+Commit bd47eca2c8a (2024-03-01 10:14 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 48 × AMD EPYC 7402 24-Core Processor
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
+Threads: 48 default, 0 interactive, 24 GC (on 2 virtual cores)
+Environment:
+  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
+  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6
+  JULIA_PROJECT = /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/docs
+  JULIA_AMDGPU_LOGGING_ENABLED = true
+  JULIA_DEBUG = Literate
+  JULIA_CPU_THREADS = 2
+  JULIA_NUM_THREADS = 48
+  JULIA_LOAD_PATH = @:@v#.#:@stdlib
+  JULIA_CUDA_HARD_MEMORY_LIMIT = 25%
+
+CUDA runtime 12.3, artifact installation
+CUDA driver 12.4
+NVIDIA driver 550.54.15
+
+CUDA libraries: 
+- CUBLAS: 12.3.4
+- CURAND: 10.3.4
+- CUFFT: 11.0.12
+- CUSOLVER: 11.5.4
+- CUSPARSE: 12.2.0
+- CUPTI: 21.0.0
+- NVML: 12.0.0+550.54.15
+
+Julia packages: 
+- CUDA: 5.2.0
+- CUDA_Driver_jll: 0.7.0+1
+- CUDA_Runtime_jll: 0.11.1+0
+
+Toolchain:
+- Julia: 1.10.2
+- LLVM: 15.0.7
+
+Environment:
+- JULIA_CUDA_HARD_MEMORY_LIMIT: 25%
+
+1 device:
+  0: NVIDIA A100-PCIE-40GB MIG 1g.5gb (sm_80, 4.141 GiB / 4.750 GiB available)
+┌ Warning: LuxAMDGPU is loaded but the AMDGPU is not functional.
+└ @ LuxAMDGPU ~/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6/packages/LuxAMDGPU/sGa0S/src/LuxAMDGPU.jl:19

      This page was generated using Literate.jl.

      + + + + \ No newline at end of file diff --git a/v0.5.30/tutorials/beginner/4_SimpleChains.html b/v0.5.30/tutorials/beginner/4_SimpleChains.html new file mode 100644 index 000000000..2a25f1eb6 --- /dev/null +++ b/v0.5.30/tutorials/beginner/4_SimpleChains.html @@ -0,0 +1,138 @@ + + + + + + MNIST Classification with SimpleChains | Lux.jl Documentation + + + + + + + + + + + + + +
      Lux.jl Documentation

      Appearance


      Trusted by

      Scientific Computing

      SciML.ai

      Machine Learning

      Structure Preserving

      GeometricML.jl

      Machine Learning

      Physical Systems

      MeshGraphNets.jl

      Graph Neural Nets

      MNIST Classification with SimpleChains ​

      SimpleChains.jl is an excellent framework for training small neural networks. In this tutorial we will demonstrate how to use the same API as Lux.jl to train a model using SimpleChains.jl. We will use the tutorial from SimpleChains.jl as a reference.

      Package Imports ​

      julia
      using Lux, ADTypes, MLUtils, Optimisers, Zygote, OneHotArrays, Random, Statistics, Printf
+import MLDatasets: MNIST
+import SimpleChains: static

      Loading MNIST ​

      julia
      function loadmnist(batchsize, train_split)
+    # Load MNIST
+    N = 2000
+    dataset = MNIST(; split=:train)
+    imgs = dataset.features[:, :, 1:N]
+    labels_raw = dataset.targets[1:N]
+
+    # Process images into (H,W,C,BS) batches
+    x_data = Float32.(reshape(imgs, size(imgs, 1), size(imgs, 2), 1, size(imgs, 3)))
+    y_data = onehotbatch(labels_raw, 0:9)
+    (x_train, y_train), (x_test, y_test) = splitobs((x_data, y_data); at=train_split)
+
+    return (
+        # Use DataLoader to automatically minibatch and shuffle the data
+        DataLoader(collect.((x_train, y_train)); batchsize, shuffle=true),
+        # Don't shuffle the test data
+        DataLoader(collect.((x_test, y_test)); batchsize, shuffle=false))
+end
      loadmnist (generic function with 1 method)

      Define the Model ​

      julia
      lux_model = Chain(Conv((5, 5), 1 => 6, relu), MaxPool((2, 2)),
+    Conv((5, 5), 6 => 16, relu), MaxPool((2, 2)), FlattenLayer(3),
+    Chain(Dense(256 => 128, relu), Dense(128 => 84, relu), Dense(84 => 10)))
      Chain(
+    layer_1 = Conv((5, 5), 1 => 6, relu),  # 156 parameters
+    layer_2 = MaxPool((2, 2)),
+    layer_3 = Conv((5, 5), 6 => 16, relu),  # 2_416 parameters
+    layer_4 = MaxPool((2, 2)),
+    layer_5 = FlattenLayer(),
+    layer_6 = Dense(256 => 128, relu),  # 32_896 parameters
+    layer_7 = Dense(128 => 84, relu),   # 10_836 parameters
+    layer_8 = Dense(84 => 10),          # 850 parameters
+)         # Total: 47_154 parameters,
+          #        plus 0 states.

      We now need to convert the lux_model to SimpleChains.jl. We need to do this by defining the ToSimpleChainsAdaptor and providing the input dimensions.

      julia
      adaptor = ToSimpleChainsAdaptor((static(28), static(28), static(1)))
+simple_chains_model = adaptor(lux_model)
      SimpleChainsLayer()  # 47_154 parameters

      Helper Functions ​

      julia
      logitcrossentropy(y_pred, y) = mean(-sum(y .* logsoftmax(y_pred); dims=1))
+
+function loss(model, ps, st, (x, y))
+    y_pred, st = model(x, ps, st)
+    return logitcrossentropy(y_pred, y), st, (;)
+end
+
+function accuracy(model, ps, st, dataloader)
+    total_correct, total = 0, 0
+    st = Lux.testmode(st)
+    for (x, y) in dataloader
+        target_class = onecold(y)
+        predicted_class = onecold(Array(first(model(x, ps, st))))
+        total_correct += sum(target_class .== predicted_class)
+        total += length(target_class)
+    end
+    return total_correct / total
+end
      accuracy (generic function with 1 method)

      Define the Training Loop ​

      julia
      function train(model; rng=Xoshiro(0), kwargs...)
+    train_dataloader, test_dataloader = loadmnist(128, 0.9)
+
+    train_state = Lux.Experimental.TrainState(
+        rng, model, Adam(3.0f-4); transform_variables=identity)
+
+    ### Lets train the model
+    nepochs = 10
+    for epoch in 1:nepochs
+        stime = time()
+        for (x, y) in train_dataloader
+            (gs, _, _, train_state) = Lux.Experimental.compute_gradients(
+                AutoZygote(), loss, (x, y), train_state)
+            train_state = Lux.Experimental.apply_gradients(train_state, gs)
+        end
+        ttime = time() - stime
+
+        tr_acc = accuracy(
+            model, train_state.parameters, train_state.states, train_dataloader) * 100
+        te_acc = accuracy(
+            model, train_state.parameters, train_state.states, test_dataloader) * 100
+
+        @printf "[%2d/%2d] \t Time %.2fs \t Training Accuracy: %.2f%% \t Test Accuracy: %.2f%%\n" epoch nepochs ttime tr_acc te_acc
+    end
+end
      train (generic function with 1 method)

      Finally Training the Model ​

      First we will train the Lux model

      julia
      train(lux_model)
      [ 1/10] 	 Time 84.57s 	 Training Accuracy: 24.11% 	 Test Accuracy: 24.00%
+[ 2/10] 	 Time 48.82s 	 Training Accuracy: 46.89% 	 Test Accuracy: 47.50%
+[ 3/10] 	 Time 48.37s 	 Training Accuracy: 68.06% 	 Test Accuracy: 67.50%
+[ 4/10] 	 Time 48.83s 	 Training Accuracy: 74.33% 	 Test Accuracy: 72.50%
+[ 5/10] 	 Time 48.44s 	 Training Accuracy: 80.61% 	 Test Accuracy: 79.00%
+[ 6/10] 	 Time 44.90s 	 Training Accuracy: 82.83% 	 Test Accuracy: 82.50%
+[ 7/10] 	 Time 47.44s 	 Training Accuracy: 84.72% 	 Test Accuracy: 83.00%
+[ 8/10] 	 Time 49.94s 	 Training Accuracy: 85.61% 	 Test Accuracy: 84.00%
+[ 9/10] 	 Time 49.01s 	 Training Accuracy: 85.83% 	 Test Accuracy: 84.50%
+[10/10] 	 Time 48.72s 	 Training Accuracy: 87.61% 	 Test Accuracy: 85.50%

      Now we will train the SimpleChains model

      julia
      train(simple_chains_model)
      [ 1/10] 	 Time 885.21s 	 Training Accuracy: 29.78% 	 Test Accuracy: 27.00%
+[ 2/10] 	 Time 15.95s 	 Training Accuracy: 40.83% 	 Test Accuracy: 38.00%
+[ 3/10] 	 Time 15.94s 	 Training Accuracy: 60.06% 	 Test Accuracy: 55.50%
+[ 4/10] 	 Time 15.94s 	 Training Accuracy: 66.33% 	 Test Accuracy: 62.00%
+[ 5/10] 	 Time 15.94s 	 Training Accuracy: 74.28% 	 Test Accuracy: 71.00%
+[ 6/10] 	 Time 15.95s 	 Training Accuracy: 80.33% 	 Test Accuracy: 76.00%
+[ 7/10] 	 Time 15.94s 	 Training Accuracy: 82.94% 	 Test Accuracy: 81.00%
+[ 8/10] 	 Time 15.96s 	 Training Accuracy: 83.61% 	 Test Accuracy: 80.50%
+[ 9/10] 	 Time 15.95s 	 Training Accuracy: 85.61% 	 Test Accuracy: 82.00%
+[10/10] 	 Time 15.94s 	 Training Accuracy: 87.06% 	 Test Accuracy: 84.00%

      On my local machine we see a 3-4x speedup when using SimpleChains.jl. The conditions of the server this documentation is being built on is not ideal for CPU benchmarking hence, the speedup may not be as significant and even there might be regressions.

      Appendix ​

      julia
      using InteractiveUtils
+InteractiveUtils.versioninfo()
+if @isdefined(LuxCUDA) && CUDA.functional(); println(); CUDA.versioninfo(); end
+if @isdefined(LuxAMDGPU) && LuxAMDGPU.functional(); println(); AMDGPU.versioninfo(); end
      Julia Version 1.10.2
+Commit bd47eca2c8a (2024-03-01 10:14 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 48 × AMD EPYC 7402 24-Core Processor
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
+Threads: 48 default, 0 interactive, 24 GC (on 2 virtual cores)
+Environment:
+  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
+  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6
+  JULIA_PROJECT = /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/docs
+  JULIA_AMDGPU_LOGGING_ENABLED = true
+  JULIA_DEBUG = Literate
+  JULIA_CPU_THREADS = 2
+  JULIA_NUM_THREADS = 48
+  JULIA_LOAD_PATH = @:@v#.#:@stdlib
+  JULIA_CUDA_HARD_MEMORY_LIMIT = 25%

      This page was generated using Literate.jl.

      + + + + \ No newline at end of file diff --git a/v0.5.30/tutorials/index.html b/v0.5.30/tutorials/index.html new file mode 100644 index 000000000..2fc83cd9f --- /dev/null +++ b/v0.5.30/tutorials/index.html @@ -0,0 +1,24 @@ + + + + + + Lux.jl Documentation + + + + + + + + + + + + + +
      Lux.jl Documentation

      Appearance

      Tutorials

      Beginners Tutorials

      Julia & Lux for the Uninitiated

      Julia & Lux for the Uninitiated

      A tutorial on how to get started with Julia and Lux for those who have never used Julia before.

      Fitting a Polynomial using MLP

      Fitting a Polynomial using MLP

      Learn the Basics of Lux by fitting a Multi-Layer Perceptron to a Polynomial.

      Training a Simple LSTM

      Training a Simple LSTM

      Learn the API for defining Recurrent Models in Lux.

      Use SimpleChains.jl as a Backend

      Use SimpleChains.jl as a Backend

      Learn how to train small neural networks really fast

      Intermediate Tutorials

      MNIST Classification using Neural ODE

      MNIST Classification using Neural ODE

      Train a Neural ODE to classify MNIST Images.

      Bayesian Neural Networks

      Bayesian Neural Networks

      Figure out how to use Probabilistic Programming Frameworks like Turing with Lux.

      Training a HyperNetwork

      Training a HyperNetwork

      In this tutorial we will train a hypernetwork to work on multiple datasets by predicting neural network parameters.

      Advanced Tutorials

      Neural ODE to Model Gravitational Waveforms

      Neural ODE to Model Gravitational Waveforms

      Training a Neural ODE to fit simulated data of gravitational waveforms.

      + + + + \ No newline at end of file diff --git a/v0.5.30/tutorials/intermediate/1_NeuralODE.html b/v0.5.30/tutorials/intermediate/1_NeuralODE.html new file mode 100644 index 000000000..99ea29b6d --- /dev/null +++ b/v0.5.30/tutorials/intermediate/1_NeuralODE.html @@ -0,0 +1,276 @@ + + + + + + MNIST Classification using Neural ODEs | Lux.jl Documentation + + + + + + + + + + + + + +
      Lux.jl Documentation

      Appearance


      Trusted by

      Scientific Computing

      SciML.ai

      Machine Learning

      Structure Preserving

      GeometricML.jl

      Machine Learning

      Physical Systems

      MeshGraphNets.jl

      Graph Neural Nets

      MNIST Classification using Neural ODEs ​

      To understand Neural ODEs, users should look up these lecture notes. We recommend users to directly use DiffEqFlux.jl, instead of implementing Neural ODEs from scratch.

      Package Imports ​

      julia
      using Lux, ComponentArrays, SciMLSensitivity, LuxAMDGPU, LuxCUDA, Optimisers,
+      OrdinaryDiffEq, Random, Statistics, Zygote, OneHotArrays, InteractiveUtils, Printf
+import MLDatasets: MNIST
+import MLUtils: DataLoader, splitobs
+
+CUDA.allowscalar(false)

      Loading MNIST ​

      julia
      function loadmnist(batchsize, train_split)
+    # Load MNIST: Only 1500 for demonstration purposes
+    N = 1500
+    dataset = MNIST(; split=:train)
+    imgs = dataset.features[:, :, 1:N]
+    labels_raw = dataset.targets[1:N]
+
+    # Process images into (H,W,C,BS) batches
+    x_data = Float32.(reshape(imgs, size(imgs, 1), size(imgs, 2), 1, size(imgs, 3)))
+    y_data = onehotbatch(labels_raw, 0:9)
+    (x_train, y_train), (x_test, y_test) = splitobs((x_data, y_data); at=train_split)
+
+    return (
+        # Use DataLoader to automatically minibatch and shuffle the data
+        DataLoader(collect.((x_train, y_train)); batchsize, shuffle=true),
+        # Don't shuffle the test data
+        DataLoader(collect.((x_test, y_test)); batchsize, shuffle=false))
+end
      loadmnist (generic function with 1 method)

      Define the Neural ODE Layer ​

      The NeuralODE is a ContainerLayer, which stores a model. The parameters and states of the NeuralODE are same as those of the underlying model.

      julia
      struct NeuralODE{M <: Lux.AbstractExplicitLayer, So, T, K} <:
+       Lux.AbstractExplicitContainerLayer{(:model,)}
+    model::M
+    solver::So
+    tspan::T
+    kwargs::K
+end
+
+function NeuralODE(
+        model::Lux.AbstractExplicitLayer; solver=Tsit5(), tspan=(0.0f0, 1.0f0), kwargs...)
+    return NeuralODE(model, solver, tspan, kwargs)
+end
      Main.var"##225".NeuralODE

      OrdinaryDiffEq.jl can deal with non-Vector Inputs! However, certain discrete sensitivities like ReverseDiffAdjoint can't handle non-Vector inputs. Hence, we need to convert the input and output of the ODE solver to a Vector.

      julia
      function (n::NeuralODE)(x, ps, st)
+    function dudt(u, p, t)
+        u_, st = n.model(reshape(u, size(x)), p, st)
+        return vec(u_)
+    end
+    prob = ODEProblem{false}(ODEFunction{false}(dudt), vec(x), n.tspan, ps)
+    return solve(prob, n.solver; n.kwargs...), st
+end
+
+@views diffeqsol_to_array(l::Int, x::ODESolution) = reshape(last(x.u), (l, :))
+@views diffeqsol_to_array(l::Int, x::AbstractMatrix) = reshape(x[:, end], (l, :))
      diffeqsol_to_array (generic function with 2 methods)

      Create and Initialize the Neural ODE Layer ​

      julia
      function create_model(model_fn=NeuralODE; dev=gpu_device(), use_named_tuple::Bool=false,
+        sensealg=InterpolatingAdjoint(; autojacvec=ZygoteVJP()))
+    # Construct the Neural ODE Model
+    model = Chain(FlattenLayer(),
+        Dense(784 => 20, tanh),
+        model_fn(Chain(Dense(20 => 10, tanh), Dense(10 => 10, tanh), Dense(10 => 20, tanh));
+            save_everystep=false, reltol=1.0f-3,
+            abstol=1.0f-3, save_start=false, sensealg),
+        Base.Fix1(diffeqsol_to_array, 20),
+        Dense(20 => 10))
+
+    rng = Random.default_rng()
+    Random.seed!(rng, 0)
+
+    ps, st = Lux.setup(rng, model)
+    ps = (use_named_tuple ? ps : ComponentArray(ps)) |> dev
+    st = st |> dev
+
+    return model, ps, st
+end
      create_model (generic function with 2 methods)

      Define Utility Functions ​

      julia
      logitcrossentropy(y_pred, y) = mean(-sum(y .* logsoftmax(y_pred); dims=1))
+
+function loss(x, y, model, ps, st)
+    y_pred, st = model(x, ps, st)
+    return logitcrossentropy(y_pred, y), st
+end
+
+function accuracy(model, ps, st, dataloader; dev=gpu_device())
+    total_correct, total = 0, 0
+    st = Lux.testmode(st)
+    cpu_dev = cpu_device()
+    for (x, y) in dataloader
+        target_class = onecold(y)
+        predicted_class = onecold(cpu_dev(first(model(dev(x), ps, st))))
+        total_correct += sum(target_class .== predicted_class)
+        total += length(target_class)
+    end
+    return total_correct / total
+end
      accuracy (generic function with 1 method)

      Training ​

      julia
      function train(model_function; cpu::Bool=false, kwargs...)
+    dev = cpu ? cpu_device() : gpu_device()
+    model, ps, st = create_model(model_function; dev, kwargs...)
+
+    # Training
+    train_dataloader, test_dataloader = loadmnist(128, 0.9)
+
+    opt = Adam(0.001f0)
+    st_opt = Optimisers.setup(opt, ps)
+
+    ### Warmup the Model
+    img = dev(train_dataloader.data[1][:, :, :, 1:1])
+    lab = dev(train_dataloader.data[2][:, 1:1])
+    loss(img, lab, model, ps, st)
+    (l, _), back = pullback(p -> loss(img, lab, model, p, st), ps)
+    back((one(l), nothing))
+
+    ### Lets train the model
+    nepochs = 9
+    for epoch in 1:nepochs
+        stime = time()
+        for (x, y) in train_dataloader
+            x = dev(x)
+            y = dev(y)
+            (l, st), back = pullback(p -> loss(x, y, model, p, st), ps)
+            ### We need to add `nothing`s equal to the number of returned values - 1
+            gs = back((one(l), nothing))[1]
+            st_opt, ps = Optimisers.update(st_opt, ps, gs)
+        end
+        ttime = time() - stime
+
+        tr_acc = accuracy(model, ps, st, train_dataloader; dev)
+        te_acc = accuracy(model, ps, st, test_dataloader; dev)
+        @printf "[%d/%d] \t Time %.2fs \t Training Accuracy: %.5f%% \t Test Accuracy: %.5f%%\n" epoch nepochs ttime tr_acc te_acc
+    end
+end
+
+train(NeuralODE)
      [1/9] 	 Time 3.31s 	 Training Accuracy: 0.50741% 	 Test Accuracy: 0.45333%
+[2/9] 	 Time 0.30s 	 Training Accuracy: 0.70741% 	 Test Accuracy: 0.66667%
+[3/9] 	 Time 0.44s 	 Training Accuracy: 0.77852% 	 Test Accuracy: 0.71333%
+[4/9] 	 Time 0.27s 	 Training Accuracy: 0.81037% 	 Test Accuracy: 0.75333%
+[5/9] 	 Time 0.30s 	 Training Accuracy: 0.82667% 	 Test Accuracy: 0.78000%
+[6/9] 	 Time 0.33s 	 Training Accuracy: 0.84148% 	 Test Accuracy: 0.78667%
+[7/9] 	 Time 0.34s 	 Training Accuracy: 0.85481% 	 Test Accuracy: 0.80667%
+[8/9] 	 Time 0.35s 	 Training Accuracy: 0.86815% 	 Test Accuracy: 0.82000%
+[9/9] 	 Time 0.34s 	 Training Accuracy: 0.87407% 	 Test Accuracy: 0.84000%

      We can also change the sensealg and train the model! GaussAdjoint allows you to use any arbitrary parameter structure and not just a flat vector (ComponentArray).

      julia
      train(NeuralODE; sensealg=GaussAdjoint(; autojacvec=ZygoteVJP()), use_named_tuple=true)
      [1/9] 	 Time 2.41s 	 Training Accuracy: 0.49630% 	 Test Accuracy: 0.38000%
+[2/9] 	 Time 0.32s 	 Training Accuracy: 0.70593% 	 Test Accuracy: 0.65333%
+[3/9] 	 Time 0.25s 	 Training Accuracy: 0.78296% 	 Test Accuracy: 0.72000%
+[4/9] 	 Time 0.33s 	 Training Accuracy: 0.80889% 	 Test Accuracy: 0.74000%
+[5/9] 	 Time 0.36s 	 Training Accuracy: 0.82370% 	 Test Accuracy: 0.76667%
+[6/9] 	 Time 0.37s 	 Training Accuracy: 0.84074% 	 Test Accuracy: 0.78667%
+[7/9] 	 Time 0.37s 	 Training Accuracy: 0.85630% 	 Test Accuracy: 0.81333%
+[8/9] 	 Time 0.34s 	 Training Accuracy: 0.86370% 	 Test Accuracy: 0.82000%
+[9/9] 	 Time 0.28s 	 Training Accuracy: 0.87704% 	 Test Accuracy: 0.82667%

      But remember some AD backends like ReverseDiff is not GPU compatible. For a model this size, you will notice that training time is significantly lower for training on CPU than on GPU.

      julia
      train(NeuralODE; sensealg=InterpolatingAdjoint(; autojacvec=ReverseDiffVJP()), cpu=true)
      [1/9] 	 Time 1.04s 	 Training Accuracy: 0.50963% 	 Test Accuracy: 0.43333%
+[2/9] 	 Time 0.26s 	 Training Accuracy: 0.69630% 	 Test Accuracy: 0.66000%
+[3/9] 	 Time 0.24s 	 Training Accuracy: 0.77926% 	 Test Accuracy: 0.71333%
+[4/9] 	 Time 0.24s 	 Training Accuracy: 0.80741% 	 Test Accuracy: 0.76667%
+[5/9] 	 Time 0.25s 	 Training Accuracy: 0.82519% 	 Test Accuracy: 0.78000%
+[6/9] 	 Time 0.25s 	 Training Accuracy: 0.84074% 	 Test Accuracy: 0.78667%
+[7/9] 	 Time 0.25s 	 Training Accuracy: 0.85333% 	 Test Accuracy: 0.80667%
+[8/9] 	 Time 0.25s 	 Training Accuracy: 0.86593% 	 Test Accuracy: 0.81333%
+[9/9] 	 Time 0.25s 	 Training Accuracy: 0.87704% 	 Test Accuracy: 0.82000%

      For completeness, let's also test out discrete sensitivities!

      julia
      train(NeuralODE; sensealg=ReverseDiffAdjoint(), cpu=true)
      [1/9] 	 Time 7.18s 	 Training Accuracy: 0.50963% 	 Test Accuracy: 0.43333%
+[2/9] 	 Time 6.91s 	 Training Accuracy: 0.69630% 	 Test Accuracy: 0.66000%
+[3/9] 	 Time 6.87s 	 Training Accuracy: 0.77926% 	 Test Accuracy: 0.71333%
+[4/9] 	 Time 7.30s 	 Training Accuracy: 0.80741% 	 Test Accuracy: 0.76667%
+[5/9] 	 Time 8.68s 	 Training Accuracy: 0.82519% 	 Test Accuracy: 0.78000%
+[6/9] 	 Time 9.59s 	 Training Accuracy: 0.84074% 	 Test Accuracy: 0.78667%
+[7/9] 	 Time 9.60s 	 Training Accuracy: 0.85333% 	 Test Accuracy: 0.80667%
+[8/9] 	 Time 9.82s 	 Training Accuracy: 0.86593% 	 Test Accuracy: 0.81333%
+[9/9] 	 Time 9.71s 	 Training Accuracy: 0.87704% 	 Test Accuracy: 0.82000%

      Alternate Implementation using Stateful Layer ​

      Starting v0.5.5, Lux provides a Lux.Experimental.StatefulLuxLayer which can be used to avoid the Boxing of st.

      julia
      struct StatefulNeuralODE{M <: Lux.AbstractExplicitLayer, So, T, K} <:
+       Lux.AbstractExplicitContainerLayer{(:model,)}
+    model::M
+    solver::So
+    tspan::T
+    kwargs::K
+end
+
+function StatefulNeuralODE(
+        model::Lux.AbstractExplicitLayer; solver=Tsit5(), tspan=(0.0f0, 1.0f0), kwargs...)
+    return StatefulNeuralODE(model, solver, tspan, kwargs)
+end
+
+function (n::StatefulNeuralODE)(x, ps, st)
+    st_model = Lux.StatefulLuxLayer(n.model, ps, st)
+    dudt(u, p, t) = st_model(u, p)
+    prob = ODEProblem{false}(ODEFunction{false}(dudt), x, n.tspan, ps)
+    return solve(prob, n.solver; n.kwargs...), st_model.st
+end

      Train the new Stateful Neural ODE ​

      julia
      train(StatefulNeuralODE)
      [1/9] 	 Time 1.33s 	 Training Accuracy: 0.49852% 	 Test Accuracy: 0.40667%
+[2/9] 	 Time 0.32s 	 Training Accuracy: 0.70296% 	 Test Accuracy: 0.66667%
+[3/9] 	 Time 0.35s 	 Training Accuracy: 0.78074% 	 Test Accuracy: 0.71333%
+[4/9] 	 Time 0.54s 	 Training Accuracy: 0.80741% 	 Test Accuracy: 0.76000%
+[5/9] 	 Time 0.31s 	 Training Accuracy: 0.82000% 	 Test Accuracy: 0.78000%
+[6/9] 	 Time 0.32s 	 Training Accuracy: 0.84444% 	 Test Accuracy: 0.79333%
+[7/9] 	 Time 0.37s 	 Training Accuracy: 0.85704% 	 Test Accuracy: 0.82000%
+[8/9] 	 Time 0.38s 	 Training Accuracy: 0.87037% 	 Test Accuracy: 0.80667%
+[9/9] 	 Time 0.39s 	 Training Accuracy: 0.88000% 	 Test Accuracy: 0.82667%

      We might not see a significant difference in the training time, but let us investigate the type stabilities of the layers.

      Type Stability ​

      julia
      model, ps, st = create_model(NeuralODE)
+
+model_stateful, ps_stateful, st_stateful = create_model(StatefulNeuralODE)
+
+x = gpu_device()(ones(Float32, 28, 28, 1, 3));

      NeuralODE is not type stable due to the boxing of st

      julia
      @code_warntype model(x, ps, st)
      MethodInstance for (::Lux.Chain{@NamedTuple{layer_1::Lux.FlattenLayer{Nothing}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Main.var"##225".NeuralODE{Lux.Chain{@NamedTuple{layer_1::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing}, OrdinaryDiffEq.Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, Tuple{Float32, Float32}, Base.Pairs{Symbol, Any, NTuple{5, Symbol}, @NamedTuple{save_everystep::Bool, reltol::Float32, abstol::Float32, save_start::Bool, sensealg::SciMLSensitivity.InterpolatingAdjoint{0, true, Val{:central}, SciMLSensitivity.ZygoteVJP}}}}, layer_4::Lux.WrappedFunction{Base.Fix1{typeof(Main.var"##225".diffeqsol_to_array), Int64}}, layer_5::Lux.Dense{true, typeof(identity), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing})(::CUDA.CuArray{Float32, 4, CUDA.Mem.DeviceBuffer}, ::ComponentArrays.ComponentVector{Float32, CUDA.CuArray{Float32, 1, CUDA.Mem.DeviceBuffer}, Tuple{ComponentArrays.Axis{(layer_1 = 1:0, layer_2 = ViewAxis(1:15700, Axis(weight = ViewAxis(1:15680, ShapedAxis((20, 784))), bias = ViewAxis(15681:15700, ShapedAxis((20, 1))))), layer_3 = ViewAxis(15701:16240, Axis(layer_1 = ViewAxis(1:210, Axis(weight = ViewAxis(1:200, ShapedAxis((10, 20))), bias = ViewAxis(201:210, ShapedAxis((10, 1))))), layer_2 = ViewAxis(211:320, Axis(weight = ViewAxis(1:100, ShapedAxis((10, 10))), bias = ViewAxis(101:110, ShapedAxis((10, 1))))), layer_3 = ViewAxis(321:540, Axis(weight = ViewAxis(1:200, ShapedAxis((20, 10))), bias = ViewAxis(201:220, ShapedAxis((20, 1))))))), layer_4 = 16241:16240, layer_5 = ViewAxis(16241:16450, Axis(weight = ViewAxis(1:200, ShapedAxis((10, 20))), bias = ViewAxis(201:210, ShapedAxis((10, 1))))))}}}, ::@NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}, layer_3::@NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}, layer_3::@NamedTuple{}}, layer_4::@NamedTuple{}, layer_5::@NamedTuple{}})
+  from (c::Lux.Chain)(x, ps, st::NamedTuple) @ Lux /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/src/layers/containers.jl:477
+Arguments
+  c::Lux.Chain{@NamedTuple{layer_1::Lux.FlattenLayer{Nothing}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Main.var"##225".NeuralODE{Lux.Chain{@NamedTuple{layer_1::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing}, OrdinaryDiffEq.Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, Tuple{Float32, Float32}, Base.Pairs{Symbol, Any, NTuple{5, Symbol}, @NamedTuple{save_everystep::Bool, reltol::Float32, abstol::Float32, save_start::Bool, sensealg::SciMLSensitivity.InterpolatingAdjoint{0, true, Val{:central}, SciMLSensitivity.ZygoteVJP}}}}, layer_4::Lux.WrappedFunction{Base.Fix1{typeof(Main.var"##225".diffeqsol_to_array), Int64}}, layer_5::Lux.Dense{true, typeof(identity), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing}
+  x::CUDA.CuArray{Float32, 4, CUDA.Mem.DeviceBuffer}
+  ps::ComponentArrays.ComponentVector{Float32, CUDA.CuArray{Float32, 1, CUDA.Mem.DeviceBuffer}, Tuple{ComponentArrays.Axis{(layer_1 = 1:0, layer_2 = ViewAxis(1:15700, Axis(weight = ViewAxis(1:15680, ShapedAxis((20, 784))), bias = ViewAxis(15681:15700, ShapedAxis((20, 1))))), layer_3 = ViewAxis(15701:16240, Axis(layer_1 = ViewAxis(1:210, Axis(weight = ViewAxis(1:200, ShapedAxis((10, 20))), bias = ViewAxis(201:210, ShapedAxis((10, 1))))), layer_2 = ViewAxis(211:320, Axis(weight = ViewAxis(1:100, ShapedAxis((10, 10))), bias = ViewAxis(101:110, ShapedAxis((10, 1))))), layer_3 = ViewAxis(321:540, Axis(weight = ViewAxis(1:200, ShapedAxis((20, 10))), bias = ViewAxis(201:220, ShapedAxis((20, 1))))))), layer_4 = 16241:16240, layer_5 = ViewAxis(16241:16450, Axis(weight = ViewAxis(1:200, ShapedAxis((10, 20))), bias = ViewAxis(201:210, ShapedAxis((10, 1))))))}}}
+  st::Core.Const((layer_1 = NamedTuple(), layer_2 = NamedTuple(), layer_3 = (layer_1 = NamedTuple(), layer_2 = NamedTuple(), layer_3 = NamedTuple()), layer_4 = NamedTuple(), layer_5 = NamedTuple()))
+Body::TUPLE{CUDA.CUARRAY{FLOAT32, 2, CUDA.MEM.DEVICEBUFFER}, NAMEDTUPLE{(:LAYER_1, :LAYER_2, :LAYER_3, :LAYER_4, :LAYER_5), <:TUPLE{@NAMEDTUPLE{}, @NAMEDTUPLE{}, ANY, @NAMEDTUPLE{}, @NAMEDTUPLE{}}}}
+1 ─ %1 = Base.getproperty(c, :layers)::@NamedTuple{layer_1::Lux.FlattenLayer{Nothing}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Main.var"##225".NeuralODE{Lux.Chain{@NamedTuple{layer_1::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing}, OrdinaryDiffEq.Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, Tuple{Float32, Float32}, Base.Pairs{Symbol, Any, NTuple{5, Symbol}, @NamedTuple{save_everystep::Bool, reltol::Float32, abstol::Float32, save_start::Bool, sensealg::SciMLSensitivity.InterpolatingAdjoint{0, true, Val{:central}, SciMLSensitivity.ZygoteVJP}}}}, layer_4::Lux.WrappedFunction{Base.Fix1{typeof(Main.var"##225".diffeqsol_to_array), Int64}}, layer_5::Lux.Dense{true, typeof(identity), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}
+│   %2 = Lux.applychain(%1, x, ps, st)::TUPLE{CUDA.CUARRAY{FLOAT32, 2, CUDA.MEM.DEVICEBUFFER}, NAMEDTUPLE{(:LAYER_1, :LAYER_2, :LAYER_3, :LAYER_4, :LAYER_5), <:TUPLE{@NAMEDTUPLE{}, @NAMEDTUPLE{}, ANY, @NAMEDTUPLE{}, @NAMEDTUPLE{}}}}
+└──      return %2

      We avoid the problem entirely by using StatefulNeuralODE

      julia
      @code_warntype model_stateful(x, ps_stateful, st_stateful)
      MethodInstance for (::Lux.Chain{@NamedTuple{layer_1::Lux.FlattenLayer{Nothing}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Main.var"##225".StatefulNeuralODE{Lux.Chain{@NamedTuple{layer_1::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing}, OrdinaryDiffEq.Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, Tuple{Float32, Float32}, Base.Pairs{Symbol, Any, NTuple{5, Symbol}, @NamedTuple{save_everystep::Bool, reltol::Float32, abstol::Float32, save_start::Bool, sensealg::SciMLSensitivity.InterpolatingAdjoint{0, true, Val{:central}, SciMLSensitivity.ZygoteVJP}}}}, layer_4::Lux.WrappedFunction{Base.Fix1{typeof(Main.var"##225".diffeqsol_to_array), Int64}}, layer_5::Lux.Dense{true, typeof(identity), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing})(::CUDA.CuArray{Float32, 4, CUDA.Mem.DeviceBuffer}, ::ComponentArrays.ComponentVector{Float32, CUDA.CuArray{Float32, 1, CUDA.Mem.DeviceBuffer}, Tuple{ComponentArrays.Axis{(layer_1 = 1:0, layer_2 = ViewAxis(1:15700, Axis(weight = ViewAxis(1:15680, ShapedAxis((20, 784))), bias = ViewAxis(15681:15700, ShapedAxis((20, 1))))), layer_3 = ViewAxis(15701:16240, Axis(layer_1 = ViewAxis(1:210, Axis(weight = ViewAxis(1:200, ShapedAxis((10, 20))), bias = ViewAxis(201:210, ShapedAxis((10, 1))))), layer_2 = ViewAxis(211:320, Axis(weight = ViewAxis(1:100, ShapedAxis((10, 10))), bias = ViewAxis(101:110, ShapedAxis((10, 1))))), layer_3 = ViewAxis(321:540, Axis(weight = ViewAxis(1:200, ShapedAxis((20, 10))), bias = ViewAxis(201:220, ShapedAxis((20, 1))))))), layer_4 = 16241:16240, layer_5 = ViewAxis(16241:16450, Axis(weight = ViewAxis(1:200, ShapedAxis((10, 20))), bias = ViewAxis(201:210, ShapedAxis((10, 1))))))}}}, ::@NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}, layer_3::@NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}, layer_3::@NamedTuple{}}, layer_4::@NamedTuple{}, layer_5::@NamedTuple{}})
+  from (c::Lux.Chain)(x, ps, st::NamedTuple) @ Lux /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/src/layers/containers.jl:477
+Arguments
+  c::Lux.Chain{@NamedTuple{layer_1::Lux.FlattenLayer{Nothing}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Main.var"##225".StatefulNeuralODE{Lux.Chain{@NamedTuple{layer_1::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing}, OrdinaryDiffEq.Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, Tuple{Float32, Float32}, Base.Pairs{Symbol, Any, NTuple{5, Symbol}, @NamedTuple{save_everystep::Bool, reltol::Float32, abstol::Float32, save_start::Bool, sensealg::SciMLSensitivity.InterpolatingAdjoint{0, true, Val{:central}, SciMLSensitivity.ZygoteVJP}}}}, layer_4::Lux.WrappedFunction{Base.Fix1{typeof(Main.var"##225".diffeqsol_to_array), Int64}}, layer_5::Lux.Dense{true, typeof(identity), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing}
+  x::CUDA.CuArray{Float32, 4, CUDA.Mem.DeviceBuffer}
+  ps::ComponentArrays.ComponentVector{Float32, CUDA.CuArray{Float32, 1, CUDA.Mem.DeviceBuffer}, Tuple{ComponentArrays.Axis{(layer_1 = 1:0, layer_2 = ViewAxis(1:15700, Axis(weight = ViewAxis(1:15680, ShapedAxis((20, 784))), bias = ViewAxis(15681:15700, ShapedAxis((20, 1))))), layer_3 = ViewAxis(15701:16240, Axis(layer_1 = ViewAxis(1:210, Axis(weight = ViewAxis(1:200, ShapedAxis((10, 20))), bias = ViewAxis(201:210, ShapedAxis((10, 1))))), layer_2 = ViewAxis(211:320, Axis(weight = ViewAxis(1:100, ShapedAxis((10, 10))), bias = ViewAxis(101:110, ShapedAxis((10, 1))))), layer_3 = ViewAxis(321:540, Axis(weight = ViewAxis(1:200, ShapedAxis((20, 10))), bias = ViewAxis(201:220, ShapedAxis((20, 1))))))), layer_4 = 16241:16240, layer_5 = ViewAxis(16241:16450, Axis(weight = ViewAxis(1:200, ShapedAxis((10, 20))), bias = ViewAxis(201:210, ShapedAxis((10, 1))))))}}}
+  st::Core.Const((layer_1 = NamedTuple(), layer_2 = NamedTuple(), layer_3 = (layer_1 = NamedTuple(), layer_2 = NamedTuple(), layer_3 = NamedTuple()), layer_4 = NamedTuple(), layer_5 = NamedTuple()))
+Body::Tuple{CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, @NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}, layer_3::@NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}, layer_3::@NamedTuple{}}, layer_4::@NamedTuple{}, layer_5::@NamedTuple{}}}
+1 ─ %1 = Base.getproperty(c, :layers)::@NamedTuple{layer_1::Lux.FlattenLayer{Nothing}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Main.var"##225".StatefulNeuralODE{Lux.Chain{@NamedTuple{layer_1::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_2::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}, layer_3::Lux.Dense{true, typeof(NNlib.tanh_fast), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}, Nothing}, OrdinaryDiffEq.Tsit5{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, Tuple{Float32, Float32}, Base.Pairs{Symbol, Any, NTuple{5, Symbol}, @NamedTuple{save_everystep::Bool, reltol::Float32, abstol::Float32, save_start::Bool, sensealg::SciMLSensitivity.InterpolatingAdjoint{0, true, Val{:central}, SciMLSensitivity.ZygoteVJP}}}}, layer_4::Lux.WrappedFunction{Base.Fix1{typeof(Main.var"##225".diffeqsol_to_array), Int64}}, layer_5::Lux.Dense{true, typeof(identity), typeof(WeightInitializers.glorot_uniform), typeof(WeightInitializers.zeros32)}}
+│   %2 = Lux.applychain(%1, x, ps, st)::Tuple{CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, @NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}, layer_3::@NamedTuple{layer_1::@NamedTuple{}, layer_2::@NamedTuple{}, layer_3::@NamedTuple{}}, layer_4::@NamedTuple{}, layer_5::@NamedTuple{}}}
+└──      return %2

      Note, that we still recommend using this layer internally and not exposing this as the default API to the users.

      Appendix ​

      julia
      using InteractiveUtils
+InteractiveUtils.versioninfo()
+if @isdefined(LuxCUDA) && CUDA.functional(); println(); CUDA.versioninfo(); end
+if @isdefined(LuxAMDGPU) && LuxAMDGPU.functional(); println(); AMDGPU.versioninfo(); end
      Julia Version 1.10.2
+Commit bd47eca2c8a (2024-03-01 10:14 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 48 × AMD EPYC 7402 24-Core Processor
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
+Threads: 48 default, 0 interactive, 24 GC (on 2 virtual cores)
+Environment:
+  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
+  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6
+  JULIA_PROJECT = /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/docs
+  JULIA_AMDGPU_LOGGING_ENABLED = true
+  JULIA_DEBUG = Literate
+  JULIA_CPU_THREADS = 2
+  JULIA_NUM_THREADS = 48
+  JULIA_LOAD_PATH = @:@v#.#:@stdlib
+  JULIA_CUDA_HARD_MEMORY_LIMIT = 25%
+
+CUDA runtime 12.3, artifact installation
+CUDA driver 12.4
+NVIDIA driver 550.54.15
+
+CUDA libraries: 
+- CUBLAS: 12.3.4
+- CURAND: 10.3.4
+- CUFFT: 11.0.12
+- CUSOLVER: 11.5.4
+- CUSPARSE: 12.2.0
+- CUPTI: 21.0.0
+- NVML: 12.0.0+550.54.15
+
+Julia packages: 
+- CUDA: 5.2.0
+- CUDA_Driver_jll: 0.7.0+1
+- CUDA_Runtime_jll: 0.11.1+0
+
+Toolchain:
+- Julia: 1.10.2
+- LLVM: 15.0.7
+
+Environment:
+- JULIA_CUDA_HARD_MEMORY_LIMIT: 25%
+
+1 device:
+  0: NVIDIA A100-PCIE-40GB MIG 1g.5gb (sm_80, 3.443 GiB / 4.750 GiB available)
+┌ Warning: LuxAMDGPU is loaded but the AMDGPU is not functional.
+└ @ LuxAMDGPU ~/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6/packages/LuxAMDGPU/sGa0S/src/LuxAMDGPU.jl:19

      This page was generated using Literate.jl.

      + + + + \ No newline at end of file diff --git a/v0.5.30/tutorials/intermediate/2_BayesianNN.html b/v0.5.30/tutorials/intermediate/2_BayesianNN.html new file mode 100644 index 000000000..cbb63726c --- /dev/null +++ b/v0.5.30/tutorials/intermediate/2_BayesianNN.html @@ -0,0 +1,220 @@ + + + + + + Bayesian Neural Network | Lux.jl Documentation + + + + + + + + + + + + + +
      Lux.jl Documentation

      Appearance


      Trusted by

      Scientific Computing

      SciML.ai

      Machine Learning

      Structure Preserving

      GeometricML.jl

      Machine Learning

      Physical Systems

      MeshGraphNets.jl

      Graph Neural Nets

      Bayesian Neural Network ​

      We borrow this tutorial from the official Turing Docs. We will show how the explicit parameterization of Lux enables first-class composability with packages which expect flattened out parameter vectors.

      We will use Turing.jl with Lux.jl to implement implementing a classification algorithm. Lets start by importing the relevant libraries.

      julia
      # Import libraries
+using Lux, Turing, CairoMakie, Random, Tracker, Functors, LinearAlgebra
+
+# Sampling progress
+Turing.setprogress!(true);
      [ Info: [Turing]: progress logging is enabled globally
+[ Info: [AdvancedVI]: global PROGRESS is set as true

      Generating data ​

      Our goal here is to use a Bayesian neural network to classify points in an artificial dataset. The code below generates data points arranged in a box-like pattern and displays a graph of the dataset we'll be working with.

      julia
      # Number of points to generate
+N = 80
+M = round(Int, N / 4)
+rng = Random.default_rng()
+Random.seed!(rng, 1234)
+
+# Generate artificial data
+x1s = rand(rng, Float32, M) * 4.5f0;
+x2s = rand(rng, Float32, M) * 4.5f0;
+xt1s = Array([[x1s[i] + 0.5f0; x2s[i] + 0.5f0] for i in 1:M])
+x1s = rand(rng, Float32, M) * 4.5f0;
+x2s = rand(rng, Float32, M) * 4.5f0;
+append!(xt1s, Array([[x1s[i] - 5.0f0; x2s[i] - 5.0f0] for i in 1:M]))
+
+x1s = rand(rng, Float32, M) * 4.5f0;
+x2s = rand(rng, Float32, M) * 4.5f0;
+xt0s = Array([[x1s[i] + 0.5f0; x2s[i] - 5.0f0] for i in 1:M])
+x1s = rand(rng, Float32, M) * 4.5f0;
+x2s = rand(rng, Float32, M) * 4.5f0;
+append!(xt0s, Array([[x1s[i] - 5.0f0; x2s[i] + 0.5f0] for i in 1:M]))
+
+# Store all the data for later
+xs = [xt1s; xt0s]
+ts = [ones(2 * M); zeros(2 * M)]
+
+# Plot data points
+
+function plot_data()
+    x1 = first.(xt1s)
+    y1 = last.(xt1s)
+    x2 = first.(xt0s)
+    y2 = last.(xt0s)
+
+    fig = Figure()
+    ax = CairoMakie.Axis(fig[1, 1]; xlabel="x", ylabel="y")
+
+    scatter!(ax, x1, y1; markersize=16, color=:red, strokecolor=:black, strokewidth=2)
+    scatter!(ax, x2, y2; markersize=16, color=:blue, strokecolor=:black, strokewidth=2)
+
+    return fig
+end
+
+plot_data()

      Building the Neural Network ​

      The next step is to define a feedforward neural network where we express our parameters as distributions, and not single points as with traditional neural networks. For this we will use Dense to define liner layers and compose them via Chain, both are neural network primitives from Lux. The network nn we will create will have two hidden layers with tanh activations and one output layer with sigmoid activation, as shown below.

      The nn is an instance that acts as a function and can take data, parameters and current state as inputs and output predictions. We will define distributions on the neural network parameters.

      julia
      # Construct a neural network using Lux
+nn = Chain(Dense(2 => 3, tanh), Dense(3 => 2, tanh), Dense(2 => 1, sigmoid))
+
+# Initialize the model weights and state
+ps, st = Lux.setup(rng, nn)
+
+Lux.parameterlength(nn) # number of paraemters in NN
      20

      The probabilistic model specification below creates a parameters variable, which has IID normal variables. The parameters represents all parameters of our neural net (weights and biases).

      julia
      # Create a regularization term and a Gaussian prior variance term.
+alpha = 0.09
+sig = sqrt(1.0 / alpha)
      3.3333333333333335

      Construct named tuple from a sampled parameter vector. We could also use ComponentArrays here and simply broadcast to avoid doing this. But let's do it this way to avoid dependencies.

      julia
      function vector_to_parameters(ps_new::AbstractVector, ps::NamedTuple)
+    @assert length(ps_new) == Lux.parameterlength(ps)
+    i = 1
+    function get_ps(x)
+        z = reshape(view(ps_new, i:(i + length(x) - 1)), size(x))
+        i += length(x)
+        return z
+    end
+    return fmap(get_ps, ps)
+end
      vector_to_parameters (generic function with 1 method)

      To interface with external libraries it is often desirable to use the StatefulLuxLayer to automatically handle the neural network states.

      julia
      const model = StatefulLuxLayer(nn, st)
+
+# Specify the probabilistic model.
+@model function bayes_nn(xs, ts)
+    # Sample the parameters
+    nparameters = Lux.parameterlength(nn)
+    parameters ~ MvNormal(zeros(nparameters), Diagonal(abs2.(sig .* ones(nparameters))))
+
+    # Forward NN to make predictions
+    preds = Lux.apply(model, xs, vector_to_parameters(parameters, ps))
+
+    # Observe each prediction.
+    for i in eachindex(ts)
+        ts[i] ~ Bernoulli(preds[i])
+    end
+end
      bayes_nn (generic function with 2 methods)

      Inference can now be performed by calling sample. We use the HMC sampler here.

      julia
      # Perform inference.
+N = 5000
+ch = sample(bayes_nn(reduce(hcat, xs), ts), HMC(0.05, 4; adtype=AutoTracker()), N)
      Chains MCMC chain (5000×30×1 Array{Float64, 3}):
+
+Iterations        = 1:1:5000
+Number of chains  = 1
+Samples per chain = 5000
+Wall duration     = 24.99 seconds
+Compute duration  = 24.99 seconds
+parameters        = parameters[1], parameters[2], parameters[3], parameters[4], parameters[5], parameters[6], parameters[7], parameters[8], parameters[9], parameters[10], parameters[11], parameters[12], parameters[13], parameters[14], parameters[15], parameters[16], parameters[17], parameters[18], parameters[19], parameters[20]
+internals         = lp, n_steps, is_accept, acceptance_rate, log_density, hamiltonian_energy, hamiltonian_energy_error, numerical_error, step_size, nom_step_size
+
+Summary Statistics
+      parameters      mean       std      mcse   ess_bulk   ess_tail      rhat   ess_per_sec
+          Symbol   Float64   Float64   Float64    Float64    Float64   Float64       Float64
+
+   parameters[1]   -0.5133    1.8835    0.5330    13.1888    25.0326    1.4853        0.5277
+   parameters[2]   -5.3361    2.4104    0.6377    15.5139    36.9602    1.0376        0.6208
+   parameters[3]    0.3151    0.6835    0.1441    27.6358    50.3442    1.1216        1.1058
+   parameters[4]    1.9624    3.7648    1.1478    11.5629    25.5317    2.0118        0.4627
+   parameters[5]   -0.0914    0.6013    0.0858    52.3129    54.6520    1.1223        2.0932
+   parameters[6]    4.9348    2.3882    0.6909    12.4651    22.5599    1.8704        0.4988
+   parameters[7]   -1.6494    2.7707    0.8306    11.9136    35.7353    1.9059        0.4767
+   parameters[8]   -0.3367    1.5561    0.3957    15.3027    35.5527    1.2732        0.6123
+   parameters[9]   -0.6247    1.7715    0.4439    16.1582    41.0067    1.0886        0.6465
+  parameters[10]   -0.0485    2.6496    0.7711    12.0002    18.2390    1.6173        0.4802
+  parameters[11]   -2.7777    2.4100    0.6937    13.2493    54.0054    1.2589        0.5301
+  parameters[12]    1.7397    2.7286    0.8144    12.5350    30.6674    1.3093        0.5016
+  parameters[13]   -1.3065    3.0122    0.9212    11.3718    29.5307    1.8415        0.4550
+  parameters[14]    2.1359    1.7145    0.4376    16.0168    29.9135    1.1185        0.6409
+  parameters[15]   -2.2917    1.1075    0.2143    27.1032    53.9717    1.0339        1.0845
+  parameters[16]   -1.8241    1.7783    0.4754    14.8255    44.7465    1.2380        0.5932
+  parameters[17]   -2.9541    1.0941    0.1964    32.4857    49.3634    1.0550        1.2998
+  parameters[18]   -2.9283    3.1083    0.9424    13.4337    49.1159    1.4880        0.5375
+  parameters[19]   -5.8506    1.2702    0.1981    41.3283    64.0949    1.0032        1.6537
+  parameters[20]   -3.6909    1.8615    0.5266    13.1481    52.3750    1.6064        0.5261
+
+Quantiles
+      parameters      2.5%     25.0%     50.0%     75.0%     97.5%
+          Symbol   Float64   Float64   Float64   Float64   Float64
+
+   parameters[1]   -2.9584   -2.1586   -0.3884    0.5613    4.2684
+   parameters[2]   -9.8741   -7.2592   -4.9623   -3.2715   -1.7035
+   parameters[3]   -0.6888   -0.1073    0.1721    0.5713    2.2193
+   parameters[4]   -5.7669   -1.4891    3.0249    5.1736    7.8110
+   parameters[5]   -1.2037   -0.4726   -0.1166    0.2270    1.2686
+   parameters[6]    1.5300    2.9517    4.4678    6.7396   10.5049
+   parameters[7]   -5.8618   -4.2435   -1.3364    0.6954    3.0399
+   parameters[8]   -3.2162   -1.3171   -0.3432    0.4455    3.4264
+   parameters[9]   -4.2319   -1.6828   -0.5051    0.6070    2.9411
+  parameters[10]   -6.1276   -1.8893    0.2035    1.6808    4.6669
+  parameters[11]   -6.8391   -4.9499   -2.5672   -0.5826    1.1874
+  parameters[12]   -3.4081   -0.4600    2.2126    3.9338    5.8529
+  parameters[13]   -6.1325   -3.7644   -2.1160    1.6571    3.6084
+  parameters[14]   -1.1205    1.0660    1.9677    3.1250    5.5755
+  parameters[15]   -4.6287   -3.0619   -2.1911   -1.5340   -0.1136
+  parameters[16]   -5.3259   -3.0340   -1.9008   -0.9440    1.7702
+  parameters[17]   -5.6472   -3.5470   -2.8160   -2.2108   -1.0283
+  parameters[18]   -6.7277   -5.2922   -4.2915    0.7602    2.7335
+  parameters[19]   -8.5012   -6.5957   -5.8670   -5.0328   -3.3450
+  parameters[20]   -6.7333   -5.1577   -3.8273   -2.2208   -0.3195

      Now we extract the parameter samples from the sampled chain as θ (this is of size 5000 x 20 where 5000 is the number of iterations and 20 is the number of parameters). We'll use these primarily to determine how good our model's classifier is.

      julia
      # Extract all weight and bias parameters.
+θ = MCMCChains.group(ch, :parameters).value;

      Prediction Visualization ​

      julia
      # A helper to run the nn through data `x` using parameters `θ`
+nn_forward(x, θ) = model(x, vector_to_parameters(θ, ps))
+
+# Plot the data we have.
+fig = plot_data()
+
+# Find the index that provided the highest log posterior in the chain.
+_, i = findmax(ch[:lp])
+
+# Extract the max row value from i.
+i = i.I[1]
+
+# Plot the posterior distribution with a contour plot
+x1_range = collect(range(-6; stop=6, length=25))
+x2_range = collect(range(-6; stop=6, length=25))
+Z = [nn_forward([x1, x2], θ[i, :])[1] for x1 in x1_range, x2 in x2_range]
+contour!(x1_range, x2_range, Z; linewidth=3, colormap=:seaborn_bright)
+fig

      The contour plot above shows that the MAP method is not too bad at classifying our data. Now we can visualize our predictions.

      p(x~|X,α)=∫θp(x~|θ)p(θ|X,α)≈∑θ∼p(θ|X,α)fθ(x~)

      The nn_predict function takes the average predicted value from a network parameterized by weights drawn from the MCMC chain.

      julia
      # Return the average predicted value across multiple weights.
+nn_predict(x, θ, num) = mean([first(nn_forward(x, view(θ, i, :))) for i in 1:10:num])
      nn_predict (generic function with 1 method)

      Next, we use the nn_predict function to predict the value at a sample of points where the x1 and x2 coordinates range between -6 and 6. As we can see below, we still have a satisfactory fit to our data, and more importantly, we can also see where the neural network is uncertain about its predictions much easier–-those regions between cluster boundaries.

      Plot the average prediction.

      julia
      fig = plot_data()
+
+n_end = 1500
+x1_range = collect(range(-6; stop=6, length=25))
+x2_range = collect(range(-6; stop=6, length=25))
+Z = [nn_predict([x1, x2], θ, n_end)[1] for x1 in x1_range, x2 in x2_range]
+contour!(x1_range, x2_range, Z; linewidth=3, colormap=:seaborn_bright)
+fig

      Suppose we are interested in how the predictive power of our Bayesian neural network evolved between samples. In that case, the following graph displays an animation of the contour plot generated from the network weights in samples 1 to 5,000.

      julia
      fig = plot_data()
+Z = [first(nn_forward([x1, x2], θ[1, :])) for x1 in x1_range, x2 in x2_range]
+c = contour!(x1_range, x2_range, Z; linewidth=3, colormap=:seaborn_bright)
+record(fig, "results.gif", 1:250:size(θ, 1)) do i
+    fig.current_axis[].title = "Iteration: $i"
+    Z = [first(nn_forward([x1, x2], θ[i, :])) for x1 in x1_range, x2 in x2_range]
+    c[3] = Z
+    return fig
+end
      "results.gif"

      Appendix ​

      julia
      using InteractiveUtils
+InteractiveUtils.versioninfo()
+if @isdefined(LuxCUDA) && CUDA.functional(); println(); CUDA.versioninfo(); end
+if @isdefined(LuxAMDGPU) && LuxAMDGPU.functional(); println(); AMDGPU.versioninfo(); end
      Julia Version 1.10.2
+Commit bd47eca2c8a (2024-03-01 10:14 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 48 × AMD EPYC 7402 24-Core Processor
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
+Threads: 48 default, 0 interactive, 24 GC (on 2 virtual cores)
+Environment:
+  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
+  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6
+  JULIA_PROJECT = /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/docs
+  JULIA_AMDGPU_LOGGING_ENABLED = true
+  JULIA_DEBUG = Literate
+  JULIA_CPU_THREADS = 2
+  JULIA_NUM_THREADS = 48
+  JULIA_LOAD_PATH = @:@v#.#:@stdlib
+  JULIA_CUDA_HARD_MEMORY_LIMIT = 25%

      This page was generated using Literate.jl.

      + + + + \ No newline at end of file diff --git a/v0.5.30/tutorials/intermediate/3_HyperNet.html b/v0.5.30/tutorials/intermediate/3_HyperNet.html new file mode 100644 index 000000000..4fafbb14e --- /dev/null +++ b/v0.5.30/tutorials/intermediate/3_HyperNet.html @@ -0,0 +1,229 @@ + + + + + + Training a HyperNetwork on MNIST and FashionMNIST | Lux.jl Documentation + + + + + + + + + + + + + +
      Lux.jl Documentation

      Appearance


      Trusted by

      Scientific Computing

      SciML.ai

      Machine Learning

      Structure Preserving

      GeometricML.jl

      Machine Learning

      Physical Systems

      MeshGraphNets.jl

      Graph Neural Nets

      Training a HyperNetwork on MNIST and FashionMNIST ​

      Package Imports ​

      julia
      using Lux, ADTypes, ComponentArrays, LuxAMDGPU, LuxCUDA, MLDatasets, MLUtils, OneHotArrays,
+      Optimisers, Printf, Random, Setfield, Statistics, Zygote
+
+CUDA.allowscalar(false)

      Loading Datasets ​

      julia
      function load_dataset(::Type{dset}, n_train::Int, n_eval::Int, batchsize::Int) where {dset}
+    imgs, labels = dset(:train)[1:n_train]
+    x_train, y_train = reshape(imgs, 28, 28, 1, n_train), onehotbatch(labels, 0:9)
+
+    imgs, labels = dset(:test)[1:n_eval]
+    x_test, y_test = reshape(imgs, 28, 28, 1, n_eval), onehotbatch(labels, 0:9)
+
+    return (DataLoader((x_train, y_train); batchsize=min(batchsize, n_train), shuffle=true),
+        DataLoader((x_test, y_test); batchsize=min(batchsize, n_eval), shuffle=false))
+end
+
+function load_datasets(n_train=1024, n_eval=32, batchsize=256)
+    return load_dataset.((MNIST, FashionMNIST), n_train, n_eval, batchsize)
+end
      load_datasets (generic function with 4 methods)

      Implement a HyperNet Layer ​

      julia
      struct HyperNet{W <: Lux.AbstractExplicitLayer, C <: Lux.AbstractExplicitLayer, A} <:
+       Lux.AbstractExplicitContainerLayer{(:weight_generator, :core_network)}
+    weight_generator::W
+    core_network::C
+    ca_axes::A
+end
+
+function HyperNet(w::Lux.AbstractExplicitLayer, c::Lux.AbstractExplicitLayer)
+    ca_axes = Lux.initialparameters(Random.default_rng(), c) |> ComponentArray |> getaxes
+    return HyperNet(w, c, ca_axes)
+end
+
+function Lux.initialparameters(rng::AbstractRNG, h::HyperNet)
+    return (weight_generator=Lux.initialparameters(rng, h.weight_generator),)
+end
+
+function (hn::HyperNet)(x, ps, st::NamedTuple)
+    ps_new, st_ = hn.weight_generator(x, ps.weight_generator, st.weight_generator)
+    @set! st.weight_generator = st_
+    return ComponentArray(vec(ps_new), hn.ca_axes), st
+end
+
+function (hn::HyperNet)((x, y)::T, ps, st::NamedTuple) where {T <: Tuple}
+    ps_ca, st = hn(x, ps, st)
+    pred, st_ = hn.core_network(y, ps_ca, st.core_network)
+    @set! st.core_network = st_
+    return pred, st
+end

      Create and Initialize the HyperNet ​

      julia
      function create_model()
+    # Doesn't need to be a MLP can have any Lux Layer
+    core_network = Chain(FlattenLayer(), Dense(784, 256, relu), Dense(256, 10))
+    weight_generator = Chain(Embedding(2 => 32), Dense(32, 64, relu),
+        Dense(64, Lux.parameterlength(core_network)))
+
+    model = HyperNet(weight_generator, core_network)
+    return model
+end
      create_model (generic function with 1 method)

      Define Utility Functions ​

      julia
      logitcrossentropy(y_pred, y) = mean(-sum(y .* logsoftmax(y_pred); dims=1))
+
+function loss(model, ps, st, (data_idx, x, y))
+    y_pred, st = model((data_idx, x), ps, st)
+    return logitcrossentropy(y_pred, y), st, (;)
+end
+
+function accuracy(model, ps, st, dataloader, data_idx, gdev=gpu_device())
+    total_correct, total = 0, 0
+    st = Lux.testmode(st)
+    cpu_dev = cpu_device()
+    for (x, y) in dataloader
+        x = x |> gdev
+        y = y |> gdev
+        target_class = onecold(cpu_dev(y))
+        predicted_class = onecold(cpu_dev(model((data_idx, x), ps, st)[1]))
+        total_correct += sum(target_class .== predicted_class)
+        total += length(target_class)
+    end
+    return total_correct / total
+end
      accuracy (generic function with 2 methods)

      Training ​

      julia
      function train()
+    model = create_model()
+    dataloaders = load_datasets()
+
+    dev = gpu_device()
+
+    rng = Xoshiro(0)
+
+    train_state = Lux.Experimental.TrainState(
+        rng, model, Adam(3.0f-4); transform_variables=dev)
+
+    ### Lets train the model
+    nepochs = 10
+    for epoch in 1:nepochs, data_idx in 1:2
+        train_dataloader, test_dataloader = dataloaders[data_idx]
+
+        stime = time()
+        for (x, y) in train_dataloader
+            x = x |> dev
+            y = y |> dev
+            (gs, _, _, train_state) = Lux.Experimental.compute_gradients(
+                AutoZygote(), loss, (data_idx, x, y), train_state)
+            train_state = Lux.Experimental.apply_gradients(train_state, gs)
+        end
+        ttime = time() - stime
+
+        train_acc = round(
+            accuracy(model, train_state.parameters, train_state.states,
+                train_dataloader, data_idx, dev) * 100;
+            digits=2)
+        test_acc = round(
+            accuracy(model, train_state.parameters, train_state.states,
+                test_dataloader, data_idx, dev) * 100;
+            digits=2)
+
+        data_name = data_idx == 1 ? "MNIST" : "FashionMNIST"
+
+        @printf "[%3d/%3d] \t %12s \t Time %.5fs \t Training Accuracy: %.2f%% \t Test Accuracy: %.2f%%\n" epoch nepochs data_name ttime train_acc test_acc
+    end
+
+    println()
+
+    for data_idx in 1:2
+        train_dataloader, test_dataloader = dataloaders[data_idx]
+        train_acc = round(
+            accuracy(model, train_state.parameters, train_state.states,
+                train_dataloader, data_idx, dev) * 100;
+            digits=2)
+        test_acc = round(
+            accuracy(model, train_state.parameters, train_state.states,
+                test_dataloader, data_idx, dev) * 100;
+            digits=2)
+
+        data_name = data_idx == 1 ? "MNIST" : "FashionMNIST"
+
+        @printf "[FINAL] \t %12s \t Training Accuracy: %.2f%% \t Test Accuracy: %.2f%%\n" data_name train_acc test_acc
+    end
+end
+
+train()
      [  1/ 10] 	        MNIST 	 Time 62.70427s 	 Training Accuracy: 76.27% 	 Test Accuracy: 78.12%
+[  1/ 10] 	 FashionMNIST 	 Time 0.17746s 	 Training Accuracy: 54.98% 	 Test Accuracy: 50.00%
+[  2/ 10] 	        MNIST 	 Time 0.03860s 	 Training Accuracy: 75.49% 	 Test Accuracy: 71.88%
+[  2/ 10] 	 FashionMNIST 	 Time 0.05287s 	 Training Accuracy: 56.45% 	 Test Accuracy: 65.62%
+[  3/ 10] 	        MNIST 	 Time 0.03839s 	 Training Accuracy: 81.84% 	 Test Accuracy: 78.12%
+[  3/ 10] 	 FashionMNIST 	 Time 0.03281s 	 Training Accuracy: 62.21% 	 Test Accuracy: 56.25%
+[  4/ 10] 	        MNIST 	 Time 0.03007s 	 Training Accuracy: 82.62% 	 Test Accuracy: 81.25%
+[  4/ 10] 	 FashionMNIST 	 Time 0.03060s 	 Training Accuracy: 66.41% 	 Test Accuracy: 56.25%
+[  5/ 10] 	        MNIST 	 Time 0.03625s 	 Training Accuracy: 81.54% 	 Test Accuracy: 81.25%
+[  5/ 10] 	 FashionMNIST 	 Time 0.02937s 	 Training Accuracy: 65.72% 	 Test Accuracy: 71.88%
+[  6/ 10] 	        MNIST 	 Time 0.03049s 	 Training Accuracy: 90.53% 	 Test Accuracy: 90.62%
+[  6/ 10] 	 FashionMNIST 	 Time 0.02975s 	 Training Accuracy: 69.14% 	 Test Accuracy: 62.50%
+[  7/ 10] 	        MNIST 	 Time 0.04204s 	 Training Accuracy: 92.68% 	 Test Accuracy: 90.62%
+[  7/ 10] 	 FashionMNIST 	 Time 0.02972s 	 Training Accuracy: 75.10% 	 Test Accuracy: 68.75%
+[  8/ 10] 	        MNIST 	 Time 0.03066s 	 Training Accuracy: 93.85% 	 Test Accuracy: 90.62%
+[  8/ 10] 	 FashionMNIST 	 Time 0.03352s 	 Training Accuracy: 74.02% 	 Test Accuracy: 71.88%
+[  9/ 10] 	        MNIST 	 Time 0.02887s 	 Training Accuracy: 94.53% 	 Test Accuracy: 93.75%
+[  9/ 10] 	 FashionMNIST 	 Time 0.03016s 	 Training Accuracy: 76.76% 	 Test Accuracy: 71.88%
+[ 10/ 10] 	        MNIST 	 Time 0.02880s 	 Training Accuracy: 94.73% 	 Test Accuracy: 87.50%
+[ 10/ 10] 	 FashionMNIST 	 Time 0.02935s 	 Training Accuracy: 80.08% 	 Test Accuracy: 65.62%
+
+[FINAL] 	        MNIST 	 Training Accuracy: 91.70% 	 Test Accuracy: 78.12%
+[FINAL] 	 FashionMNIST 	 Training Accuracy: 80.08% 	 Test Accuracy: 65.62%

      Appendix ​

      julia
      using InteractiveUtils
+InteractiveUtils.versioninfo()
+if @isdefined(LuxCUDA) && CUDA.functional(); println(); CUDA.versioninfo(); end
+if @isdefined(LuxAMDGPU) && LuxAMDGPU.functional(); println(); AMDGPU.versioninfo(); end
      Julia Version 1.10.2
+Commit bd47eca2c8a (2024-03-01 10:14 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 48 × AMD EPYC 7402 24-Core Processor
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
+Threads: 48 default, 0 interactive, 24 GC (on 2 virtual cores)
+Environment:
+  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64
+  JULIA_DEPOT_PATH = /root/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6
+  JULIA_PROJECT = /var/lib/buildkite-agent/builds/gpuci-1/julialang/lux-dot-jl/docs
+  JULIA_AMDGPU_LOGGING_ENABLED = true
+  JULIA_DEBUG = Literate
+  JULIA_CPU_THREADS = 2
+  JULIA_NUM_THREADS = 48
+  JULIA_LOAD_PATH = @:@v#.#:@stdlib
+  JULIA_CUDA_HARD_MEMORY_LIMIT = 25%
+
+CUDA runtime 12.3, artifact installation
+CUDA driver 12.4
+NVIDIA driver 550.54.15
+
+CUDA libraries: 
+- CUBLAS: 12.3.4
+- CURAND: 10.3.4
+- CUFFT: 11.0.12
+- CUSOLVER: 11.5.4
+- CUSPARSE: 12.2.0
+- CUPTI: 21.0.0
+- NVML: 12.0.0+550.54.15
+
+Julia packages: 
+- CUDA: 5.2.0
+- CUDA_Driver_jll: 0.7.0+1
+- CUDA_Runtime_jll: 0.11.1+0
+
+Toolchain:
+- Julia: 1.10.2
+- LLVM: 15.0.7
+
+Environment:
+- JULIA_CUDA_HARD_MEMORY_LIMIT: 25%
+
+1 device:
+  0: NVIDIA A100-PCIE-40GB MIG 1g.5gb (sm_80, 3.443 GiB / 4.750 GiB available)
+┌ Warning: LuxAMDGPU is loaded but the AMDGPU is not functional.
+└ @ LuxAMDGPU ~/.cache/julia-buildkite-plugin/depots/01872db4-8c79-43af-ab7d-12abac4f24f6/packages/LuxAMDGPU/sGa0S/src/LuxAMDGPU.jl:19

      This page was generated using Literate.jl.

      + + + + \ No newline at end of file diff --git a/versions.js b/versions.js index 3862e532d..235ec52e6 100644 --- a/versions.js +++ b/versions.js @@ -5,5 +5,5 @@ var DOC_VERSIONS = [ "v0.3", "dev", ]; -var DOCUMENTER_NEWEST = "v0.5.29"; +var DOCUMENTER_NEWEST = "v0.5.30"; var DOCUMENTER_STABLE = "stable";

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