diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 3f5135d08b..0244d2a756 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-01T09:17:07","documenter_version":"1.7.0"}} \ No newline at end of file +{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-01T09:17:48","documenter_version":"1.7.0"}} \ No newline at end of file diff --git a/dev/objects.inv b/dev/objects.inv index 4ae484d064..67ffa37681 100644 Binary files a/dev/objects.inv and b/dev/objects.inv differ diff --git a/dev/reference/destructure/index.html b/dev/reference/destructure/index.html index 289dc1e06d..e5c3fa9989 100644 --- a/dev/reference/destructure/index.html +++ b/dev/reference/destructure/index.html @@ -106,7 +106,7 @@ L2 (generic function with 1 method) julia> L2(m2) isa Float32 -truesource

Save and Load

Flux.state — Function
state(x)

Return an object with the same nested structure as x according to Functors.children, but made only of basic containers (e.g. named tuples, tuples, arrays, and dictionaries).

Besides trainable and non-trainable arrays, the state will contain leaf nodes that are not arrays, such as numbers, symbols, strings, and nothing values. The leaf types that end up in the state could increase in the future.

This method is particularly useful for saving and loading models, since the state contain only simple data types that can be easily serialized.

The state can be passed to loadmodel! to restore the model.

Examples

Copy the state into another model

julia> m1 = Chain(Dense(1, 2, tanh; init=ones), Dense(2, 1; init=ones));
+true
source

Save and Load

Flux.state — Function
state(x)

Return an object with the same nested structure as x according to Functors.children, but made only of basic containers (e.g. named tuples, tuples, arrays, and dictionaries).

Besides trainable and non-trainable arrays, the state will contain leaf nodes that are not arrays, such as numbers, symbols, strings, and nothing values. The leaf types that end up in the state could increase in the future.

This method is particularly useful for saving and loading models, since the state contain only simple data types that can be easily serialized.

The state can be passed to loadmodel! to restore the model.

Examples

Copy the state into another model

julia> m1 = Chain(Dense(1, 2, tanh; init=ones), Dense(2, 1; init=ones));
 
 julia> s = Flux.state(m1)
 (layers = ((weight = [1.0; 1.0;;], bias = [0.0, 0.0], σ = ()), (weight = [1.0 1.0], bias = [0.0], σ = ())),)
@@ -132,7 +132,7 @@
 
 julia> JLD2.jldsave("checkpoint.jld2", model_state = s)
 
-julia> Flux.loadmodel!(m2, JLD2.load("checkpoint.jld2", "model_state"))
source
Flux.loadmodel! — Function
loadmodel!(dst, src)

Copy all the parameters (trainable and non-trainable) from src into dst.

Recursively walks dst and src together using Functors.children, and calling copyto! on parameter arrays or throwing an error when there is a mismatch. Non-array elements (such as activation functions) are not copied and need not match. Zero bias vectors and bias=false are considered equivalent (see extended help for more details).

See also Flux.state.

Examples

julia> dst = Chain(Dense(Flux.ones32(2, 5), Flux.ones32(2), tanh), Dense(2 => 1; bias = [1f0]))
+julia> Flux.loadmodel!(m2, JLD2.load("checkpoint.jld2", "model_state"))
source
Flux.loadmodel! — Function
loadmodel!(dst, src)

Copy all the parameters (trainable and non-trainable) from src into dst.

Recursively walks dst and src together using Functors.children, and calling copyto! on parameter arrays or throwing an error when there is a mismatch. Non-array elements (such as activation functions) are not copied and need not match. Zero bias vectors and bias=false are considered equivalent (see extended help for more details).

See also Flux.state.

Examples

julia> dst = Chain(Dense(Flux.ones32(2, 5), Flux.ones32(2), tanh), Dense(2 => 1; bias = [1f0]))
 Chain(
   Dense(5 => 2, tanh),                  # 12 parameters
   Dense(2 => 1),                        # 3 parameters
@@ -149,7 +149,7 @@
 false
 
 julia> iszero(dst[2].bias)
-true

Extended help

Throws an error when:

  • dst and src do not share the same fields (at any level)
  • the sizes of leaf nodes are mismatched between dst and src
  • copying non-array values to/from an array parameter (except inactive parameters described below)
  • dst is a "tied" parameter (i.e. refers to another parameter) and loaded into multiple times with mismatched source values

Inactive parameters can be encoded by using the boolean value false instead of an array. If dst == false and src is an all-zero array, no error will be raised (and no values copied); however, attempting to copy a non-zero array to an inactive parameter will throw an error. Likewise, copying a src value of false to any dst array is valid, but copying a src value of true will error.

source

KeyPath

Functors.KeyPath — Type
KeyPath(keys...)

A type for representing a path of keys to a value in a nested structure. Can be constructed with a sequence of keys, or by concatenating other KeyPaths. Keys can be of type Symbol, String, or Int.

For custom types, access through symbol keys is assumed to be done with getproperty. For consistency, the method Base.propertynames is used to get the viable property names.

For string and integer keys instead, the access is done with getindex.

See also getkeypath, haskeypath.

Examples

julia> kp = KeyPath(:b, 3)
+true

Extended help

Throws an error when:

  • dst and src do not share the same fields (at any level)
  • the sizes of leaf nodes are mismatched between dst and src
  • copying non-array values to/from an array parameter (except inactive parameters described below)
  • dst is a "tied" parameter (i.e. refers to another parameter) and loaded into multiple times with mismatched source values

Inactive parameters can be encoded by using the boolean value false instead of an array. If dst == false and src is an all-zero array, no error will be raised (and no values copied); however, attempting to copy a non-zero array to an inactive parameter will throw an error. Likewise, copying a src value of false to any dst array is valid, but copying a src value of true will error.

source

KeyPath

Functors.KeyPath — Type
KeyPath(keys...)

A type for representing a path of keys to a value in a nested structure. Can be constructed with a sequence of keys, or by concatenating other KeyPaths. Keys can be of type Symbol, String, or Int.

For custom types, access through symbol keys is assumed to be done with getproperty. For consistency, the method Base.propertynames is used to get the viable property names.

For string and integer keys instead, the access is done with getindex.

See also getkeypath, haskeypath.

Examples

julia> kp = KeyPath(:b, 3)
 KeyPath(:b, 3)
 
 julia> KeyPath(:a, kp, :c, 4) # construct mixing keys and keypaths
diff --git a/dev/reference/models/functors/index.html b/dev/reference/models/functors/index.html
index 184b5c449b..3b505a9bb8 100644
--- a/dev/reference/models/functors/index.html
+++ b/dev/reference/models/functors/index.html
@@ -23,7 +23,7 @@
   Dense(2 => 1, tanh),                  # 3 parameters
   Dense(1 => 1; bias=false),            # 1 parameters
   Dropout(0.4),
-)                   # Total: 3 arrays, 4 parameters, 240 bytes.
source
Functors.@functor — Macro
@functor T
+)                   # Total: 3 arrays, 4 parameters, 240 bytes.
source
Functors.@functor — Macro
@functor T
 @functor T (x,)

Adds methods to functor allowing recursion into objects of type T, and reconstruction. Assumes that T has a constructor accepting all of its fields, which is true unless you have provided an inner constructor which does not.

By default all fields of T are considered children; this can be restricted be restructed by providing a tuple of field names.

Examples

julia> struct Foo; x; y; end
 
 julia> @functor Foo
@@ -193,7 +193,7 @@
 julia> m.bias
 2-element Vector{Float32}:
  0.0
- 0.0
source
Flux.gpu — Method
gpu(m)

Copies m to the current GPU device (using current GPU backend), if one is available. If no GPU is available, it does nothing (but prints a warning the first time).

On arrays, this calls CUDA's cu, which also changes arrays with Float64 elements to Float32 while copying them to the device (same for AMDGPU). To act on arrays within a struct, the struct type must be marked with @functor.

Use cpu to copy back to ordinary Arrays. See also f32 and f16 to change element type only.

See the CUDA.jl docs to help identify the current device.

Example

julia> m = Dense(rand(2, 3))  # constructed with Float64 weight matrix
+ 0.0
source
Flux.gpu — Method
gpu(m)

Copies m to the current GPU device (using current GPU backend), if one is available. If no GPU is available, it does nothing (but prints a warning the first time).

On arrays, this calls CUDA's cu, which also changes arrays with Float64 elements to Float32 while copying them to the device (same for AMDGPU). To act on arrays within a struct, the struct type must be marked with @functor.

Use cpu to copy back to ordinary Arrays. See also f32 and f16 to change element type only.

See the CUDA.jl docs to help identify the current device.

Example

julia> m = Dense(rand(2, 3))  # constructed with Float64 weight matrix
 Dense(3 => 2)       # 8 parameters
 
 julia> typeof(m.weight)
@@ -203,7 +203,7 @@
 Dense(3 => 2)       # 8 parameters
 
 julia> typeof(m_gpu.weight)
-CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}
source
Flux.gpu — Method
gpu(data::DataLoader)
+CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}
source
Flux.gpu — Method
gpu(data::DataLoader)
 cpu(data::DataLoader)

Transforms a given DataLoader to apply gpu or cpu to each batch of data, when iterated over. (If no GPU is available, this does nothing.)

Example

julia> dl = Flux.DataLoader((x = ones(2,10), y='a':'j'), batchsize=3)
 4-element DataLoader(::NamedTuple{(:x, :y), Tuple{Matrix{Float64}, StepRange{Char, Int64}}}, batchsize=3)
   with first element:
@@ -223,4 +223,4 @@
  1.0  1.0  1.0

For large datasets, this is preferred over moving all the data to the GPU before creating the DataLoader, like this:

julia> Flux.DataLoader((x = ones(2,10), y=2:11) |> gpu, batchsize=3)
 4-element DataLoader(::NamedTuple{(:x, :y), Tuple{CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, UnitRange{Int64}}}, batchsize=3)
   with first element:
-  (; x = 2×3 CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, y = 3-element UnitRange{Int64})
Warning

This only works if gpu is applied directly to the DataLoader. While gpu acts recursively on Flux models and many basic Julia structs, it will not work on (say) a tuple of DataLoaders.

source
+ (; x = 2×3 CUDA.CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, y = 3-element UnitRange{Int64})
Warning

This only works if gpu is applied directly to the DataLoader. While gpu acts recursively on Flux models and many basic Julia structs, it will not work on (say) a tuple of DataLoaders.

source
diff --git a/dev/reference/models/layers/index.html b/dev/reference/models/layers/index.html index 00183bb707..391c933eef 100644 --- a/dev/reference/models/layers/index.html +++ b/dev/reference/models/layers/index.html @@ -23,7 +23,7 @@ julia> Flux.trainables(model2) # no trainable bias 1-element Vector{AbstractArray}: - [1.0 1.0 … 1.0 1.0; 1.0 1.0 … 1.0 1.0]source
Flux.Bilinear — Type
Bilinear((in1, in2) => out, σ=identity; bias=true, init=glorot_uniform)
+ [1.0 1.0 … 1.0 1.0; 1.0 1.0 … 1.0 1.0]
source
Flux.Bilinear — Type
Bilinear((in1, in2) => out, σ=identity; bias=true, init=glorot_uniform)
 Bilinear(W::AbstractArray, [bias, σ])

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

z[i] = σ(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.

If the second input y is not given, it is taken to be equal to x, i.e. B(x) == B(x, x)

The two inputs may also be provided as a tuple, B((x, y)) == B(x, y), which is accepted as the input to a Chain.

If the two input sizes are the same, in1 == in2, then you may write Bilinear(in => out, σ).

The initialisation works as for Dense layer, with W = init(out, in1, in2). By default the bias vector is zeros(Float32, out), option bias=false will switch off trainable bias. Either of these may be provided explicitly.

Examples

julia> x, y = randn(Float32, 5, 32), randn(Float32, 5, 32);
 
 julia> B = Flux.Bilinear((5, 5) => 7)
@@ -44,7 +44,7 @@
 (3, 32)
 
 julia> Flux.Bilinear(rand(4,8,16), false, tanh)  # first dim of weight is the output
-Bilinear((8, 16) => 4, tanh; bias=false)  # 512 parameters
source
Flux.Scale — Type
Scale(size::Integer..., σ=identity; bias=true, init=ones32)
+Bilinear((8, 16) => 4, tanh; bias=false)  # 512 parameters
source
Flux.Scale — Type
Scale(size::Integer..., σ=identity; bias=true, init=ones32)
 Scale(scale::AbstractArray, [bias, σ])

Create an element-wise layer, whose forward pass is given by:

y = σ.(scale .* x .+ bias)

This uses .* instead of matrix multiplication * of Dense.

The learnable scale & bias are initialised init(size...) and zeros32(size...), with init=ones32 by default. You may specify the function init, turn off trainable bias with bias=false, or provide the array(s) explicitly.

Used by LayerNorm with affine=true.

Examples

julia> a = Flux.Scale(2)
 Scale(2)            # 4 parameters
 
@@ -68,7 +68,7 @@
 
 julia> Flux.trainables(b)
 1-element Vector{AbstractArray}:
- Float32[1.0 2.0 3.0 4.0]
source

Perhaps Scale isn't quite fully connected, but it may be thought of as Dense(Diagonal(s.weights), s.bias), and LinearAlgebra's Diagonal is a matrix which just happens to contain many zeros.

Convolution Models

These layers are used to build convolutional neural networks (CNNs).

They all expect images in what is called WHCN order: a batch of 32 colour images, each 50 x 50 pixels, will have size(x) == (50, 50, 3, 32). A single grayscale image might instead have size(x) == (28, 28, 1, 1).

Besides images, 2D data, they also work with 1D data, where for instance stereo sound recording with 1000 samples might have size(x) == (1000, 2, 1). They will also work with 3D data, ndims(x) == 5, where again the last two dimensions are channel and batch.

To understand how strides and padding work, the article by Dumoulin & Visin has great illustrations.

Flux.Conv — Type
Conv(filter, in => out, σ = identity;
+ Float32[1.0 2.0 3.0 4.0]
source

Perhaps Scale isn't quite fully connected, but it may be thought of as Dense(Diagonal(s.weights), s.bias), and LinearAlgebra's Diagonal is a matrix which just happens to contain many zeros.

Convolution Models

These layers are used to build convolutional neural networks (CNNs).

They all expect images in what is called WHCN order: a batch of 32 colour images, each 50 x 50 pixels, will have size(x) == (50, 50, 3, 32). A single grayscale image might instead have size(x) == (28, 28, 1, 1).

Besides images, 2D data, they also work with 1D data, where for instance stereo sound recording with 1000 samples might have size(x) == (1000, 2, 1). They will also work with 3D data, ndims(x) == 5, where again the last two dimensions are channel and batch.

To understand how strides and padding work, the article by Dumoulin & Visin has great illustrations.

Flux.Conv — Type
Conv(filter, in => out, σ = identity;
      stride = 1, pad = 0, dilation = 1, groups = 1, [bias, init])

Standard convolutional layer. filter is a tuple of integers specifying the size of the convolutional kernel; in and out specify the number of input and output channels.

Image data should be stored in WHCN order (width, height, channels, batch). In other words, a 100×100 RGB image would be a 100×100×3×1 array, and a batch of 50 would be a 100×100×3×50 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 is the number of input channels, and size(x, ndims(x)) is (as always) the number of observations in a batch. Then:

  • filter should be a tuple of N integers.
  • Keywords stride and dilation should each be either single integer, or a tuple with N integers.
  • Keyword 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.
  • Keyword groups is expected to be an Int. It specifies the number of groups to divide a convolution into.

Keywords to control initialization of the layer:

  • init - Function used to generate initial weights. Defaults to glorot_uniform.
  • bias - The initial bias vector is all zero by default. Trainable bias can be disabled entirely by setting this to false, or another vector can be provided such as bias = randn(Float32, out).

See also ConvTranspose, DepthwiseConv, CrossCor.

Examples

julia> xs = rand32(100, 100, 3, 50); # a batch of 50 RGB images
 
 julia> layer = Conv((5,5), 3 => 7, relu; bias = false)
@@ -87,7 +87,7 @@
 (130, 100, 7, 50)
 
 julia> Conv((5,5), 3 => 7; stride = 2, dilation = 4)(xs) |> size
-(42, 42, 7, 50)
source
Flux.Conv — Method
Conv(weight::AbstractArray, [bias, activation; stride, pad, dilation])

Constructs a convolutional layer with the given weight and bias. Accepts the same keywords and has the same defaults as Conv(k::NTuple{N,Integer}, ch::Pair{<:Integer,<:Integer}, σ; ...).

julia> weight = rand(3, 4, 5);
+(42, 42, 7, 50)
source
Flux.Conv — Method
Conv(weight::AbstractArray, [bias, activation; stride, pad, dilation])

Constructs a convolutional layer with the given weight and bias. Accepts the same keywords and has the same defaults as Conv(k::NTuple{N,Integer}, ch::Pair{<:Integer,<:Integer}, σ; ...).

julia> weight = rand(3, 4, 5);
 
 julia> bias = zeros(5);
 
@@ -98,7 +98,7 @@
 (98, 5, 64)
 
 julia> Flux.params(layer) |> length
-2
source
Flux.ConvTranspose — Type
ConvTranspose(filter, in => out, σ=identity; stride=1, pad=0, outpad=0, dilation=1, [bias, init])

Standard convolutional transpose layer. filter is a tuple of integers specifying the size of the convolutional kernel, while in and out specify the number of input and output channels.

Note that pad=SamePad() here tries to ensure size(output,d) == size(x,d) * stride.

To conserve Conv inversability when stride > 1, outpad can be used to increase the size of the output in the desired dimensions. Whereas pad is used to zero-pad the input, outpad only affects the output shape.

Parameters are controlled by additional keywords, with defaults init=glorot_uniform and bias=true.

See also Conv for more detailed description of keywords.

Examples

julia> xs = rand32(100, 100, 3, 50);  # a batch of 50 RGB images
+2
source
Flux.ConvTranspose — Type
ConvTranspose(filter, in => out, σ=identity; stride=1, pad=0, outpad=0, dilation=1, [bias, init])

Standard convolutional transpose layer. filter is a tuple of integers specifying the size of the convolutional kernel, while in and out specify the number of input and output channels.

Note that pad=SamePad() here tries to ensure size(output,d) == size(x,d) * stride.

To conserve Conv inversability when stride > 1, outpad can be used to increase the size of the output in the desired dimensions. Whereas pad is used to zero-pad the input, outpad only affects the output shape.

Parameters are controlled by additional keywords, with defaults init=glorot_uniform and bias=true.

See also Conv for more detailed description of keywords.

Examples

julia> xs = rand32(100, 100, 3, 50);  # a batch of 50 RGB images
 
 julia> layer = ConvTranspose((5,5), 3 => 7, relu)
 ConvTranspose((5, 5), 3 => 7, relu)  # 532 parameters
@@ -113,7 +113,7 @@
 (204, 204, 7, 50)
 
 julia> ConvTranspose((5,5), 3 => 7, stride=3, pad=SamePad())(xs) |> size
-(300, 300, 7, 50)
source
Flux.ConvTranspose — Method
ConvTranspose(weight::AbstractArray, [bias, activation; stride, pad, outpad, dilation, groups])

Constructs a ConvTranspose layer with the given weight and bias. Accepts the same keywords and has the same defaults as ConvTranspose(k::NTuple{N,Integer}, ch::Pair{<:Integer,<:Integer}, σ; ...).

Examples

julia> weight = rand(3, 4, 5);
+(300, 300, 7, 50)
source
Flux.ConvTranspose — Method
ConvTranspose(weight::AbstractArray, [bias, activation; stride, pad, outpad, dilation, groups])

Constructs a ConvTranspose layer with the given weight and bias. Accepts the same keywords and has the same defaults as ConvTranspose(k::NTuple{N,Integer}, ch::Pair{<:Integer,<:Integer}, σ; ...).

Examples

julia> weight = rand(3, 4, 5);
 
 julia> bias = zeros(4);
 
@@ -124,7 +124,7 @@
 (102, 4, 64)
 
 julia> Flux.params(layer) |> length
-2
source
Flux.CrossCor — Type
CrossCor(filter, in => out, σ=identity; stride=1, pad=0, dilation=1, [bias, init])

Standard cross correlation layer. filter is a tuple of integers specifying the size of the convolutional kernel; in and out specify the number of input and output channels.

Parameters are controlled by additional keywords, with defaults init=glorot_uniform and bias=true.

See also Conv for more detailed description of keywords.

Examples

julia> xs = rand(Float32, 100, 100, 3, 50);  # a batch of 50 RGB images
+2
source
Flux.CrossCor — Type
CrossCor(filter, in => out, σ=identity; stride=1, pad=0, dilation=1, [bias, init])

Standard cross correlation layer. filter is a tuple of integers specifying the size of the convolutional kernel; in and out specify the number of input and output channels.

Parameters are controlled by additional keywords, with defaults init=glorot_uniform and bias=true.

See also Conv for more detailed description of keywords.

Examples

julia> xs = rand(Float32, 100, 100, 3, 50);  # a batch of 50 RGB images
 
 julia> layer = CrossCor((5,5), 3 => 6, relu; bias=false)
 CrossCor((5, 5), 3 => 6, relu, bias=false)  # 450 parameters
@@ -133,7 +133,7 @@
 (96, 96, 6, 50)
 
 julia> CrossCor((5,5), 3 => 7, stride=3, pad=(2,0))(xs) |> size
-(34, 32, 7, 50)
source
Flux.CrossCor — Method
CrossCor(weight::AbstractArray, [bias, activation; stride, pad, dilation])

Constructs a CrossCor layer with the given weight and bias. Accepts the same keywords and has the same defaults as CrossCor(k::NTuple{N,Integer}, ch::Pair{<:Integer,<:Integer}, σ; ...).

Examples

julia> weight = rand(3, 4, 5);
+(34, 32, 7, 50)
source
Flux.CrossCor — Method
CrossCor(weight::AbstractArray, [bias, activation; stride, pad, dilation])

Constructs a CrossCor layer with the given weight and bias. Accepts the same keywords and has the same defaults as CrossCor(k::NTuple{N,Integer}, ch::Pair{<:Integer,<:Integer}, σ; ...).

Examples

julia> weight = rand(3, 4, 5);
 
 julia> bias = zeros(5);
 
@@ -141,7 +141,7 @@
 CrossCor((3,), 4 => 5, relu)  # 65 parameters
 
 julia> layer(randn(100, 4, 64)) |> size
-(98, 5, 64)
source
Flux.DepthwiseConv — Function
DepthwiseConv(filter, in => out, σ=identity; stride=1, pad=0, dilation=1, [bias, init])
+(98, 5, 64)
source
Flux.DepthwiseConv — Function
DepthwiseConv(filter, in => out, σ=identity; stride=1, pad=0, dilation=1, [bias, init])
 DepthwiseConv(weight::AbstractArray, [bias, activation; stride, pad, dilation])

Return a depthwise convolutional layer, that is a Conv layer with number of groups equal to the number of input channels.

See Conv for a description of the arguments.

Examples

julia> xs = rand(Float32, 100, 100, 3, 50);  # a batch of 50 RGB images
 
 julia> layer = DepthwiseConv((5,5), 3 => 6, relu; bias=false)
@@ -151,7 +151,7 @@
 (96, 96, 6, 50)
 
 julia> DepthwiseConv((5, 5), 3 => 9, stride=2, pad=2)(xs) |> size
-(50, 50, 9, 50)
source
Flux.SamePad — Type
SamePad()

Passed as an option to convolutional layers (and friends), this causes the padding to be chosen such that the input and output sizes agree (on the first N dimensions, the kernel or window) when stride==1. When stride≠1, the output size equals ceil(input_size/stride).

See also Conv, MaxPool.

Examples

julia> xs = rand32(100, 100, 3, 50);  # a batch of images
+(50, 50, 9, 50)
source
Flux.SamePad — Type
SamePad()

Passed as an option to convolutional layers (and friends), this causes the padding to be chosen such that the input and output sizes agree (on the first N dimensions, the kernel or window) when stride==1. When stride≠1, the output size equals ceil(input_size/stride).

See also Conv, MaxPool.

Examples

julia> xs = rand32(100, 100, 3, 50);  # a batch of images
 
 julia> layer = Conv((2,2), 3 => 7, pad=SamePad())
 Conv((2, 2), 3 => 7, pad=(1, 0, 1, 0))  # 91 parameters
@@ -169,7 +169,7 @@
 Conv((5, 5), 3 => 7, pad=2, stride=2)  # 532 parameters
 
 julia> layer3(xs) |> size  # output size = `ceil(input_size/stride)` = 50
-(50, 50, 7, 50)
source
Flux.flatten — Function

flatten(x)

Same as MLUtils.flatten, which should be prefered to this method existing only for backward compatibility.

source

MultiHeadAttention

The basic blocks needed to implement Transformer architectures. See also the functional counterparts documented in NNlib's Attention section.

Flux.MultiHeadAttention — Type
MultiHeadAttention(dims; [nheads, bias, init, dropout_prob])

The multi-head dot-product attention layer used in Transformer architectures [1].

Returns the transformed input sequence and the attention scores.

[1] Vaswani et al. "Attention is all you need." Advances in Neural Information Processing Systems. 2017.

Arguments

  • dims: The embedding dimensions of inputs, intermediate tensors and outputs. In the most general case, it is given as a) (q_in_dim, k_in_dim, v_in_dim) => (qk_dim, v_dim) => out_dim. Can take also simpler forms as b) dims::Int; c) in_dim::Int => (qk_dim, v_dim) => out_dim; d) in_dim::Int => qkv_dim => out_dim.
  • nheads: number of heads. Default 8.
  • init: weight initializer for the Dense layers. Default glorot_uniform.
  • bias : whether pointwise QKVO dense transforms use bias. Default false.
  • dropout_prob: dropout probability for the attention scores. Default 0.0.

Forward

(mha::MultiHeadAttention)(q_in, k_in, v_in, [bias]; [mask])

The arguments of the forward pass are:

  • q_in: Input query array of size (q_in_dim, q_len, batch_size).
  • k_in: Input key array of size (k_in_dim, kv_len, batch_size).
  • v_in: Input value array of size (v_in_dim, kv_len, batch_size).
  • bias: Bias array broadcastable to size (kv_len, q_len, nheads, batch_size). It will be added to the attention scores before the softmax. Default nothing.
  • mask: Input array broadcastable to size (kv_len, q_len, nheads, batch_size). The mask is applied to the attention scores just before the softmax. See NNlib.make_causal_mask for creating causal masks. Default nothing.

Alternative calling signatures are mha(q_in), equivalent to mha(q_in, q_in, q_in) (self-attention), and mha(q_in, k_in), equivalent to mha(q_in, k_in, k_in) (key and value are the same).

See also NNlib.dot_product_attention.

Examples

mha = MultiHeadAttention(64, nheads = 8)
+(50, 50, 7, 50)
source
Flux.flatten — Function

flatten(x)

Same as MLUtils.flatten, which should be prefered to this method existing only for backward compatibility.

source

MultiHeadAttention

The basic blocks needed to implement Transformer architectures. See also the functional counterparts documented in NNlib's Attention section.

Flux.MultiHeadAttention — Type
MultiHeadAttention(dims; [nheads, bias, init, dropout_prob])

The multi-head dot-product attention layer used in Transformer architectures [1].

Returns the transformed input sequence and the attention scores.

[1] Vaswani et al. "Attention is all you need." Advances in Neural Information Processing Systems. 2017.

Arguments

  • dims: The embedding dimensions of inputs, intermediate tensors and outputs. In the most general case, it is given as a) (q_in_dim, k_in_dim, v_in_dim) => (qk_dim, v_dim) => out_dim. Can take also simpler forms as b) dims::Int; c) in_dim::Int => (qk_dim, v_dim) => out_dim; d) in_dim::Int => qkv_dim => out_dim.
  • nheads: number of heads. Default 8.
  • init: weight initializer for the Dense layers. Default glorot_uniform.
  • bias : whether pointwise QKVO dense transforms use bias. Default false.
  • dropout_prob: dropout probability for the attention scores. Default 0.0.

Forward

(mha::MultiHeadAttention)(q_in, k_in, v_in, [bias]; [mask])

The arguments of the forward pass are:

  • q_in: Input query array of size (q_in_dim, q_len, batch_size).
  • k_in: Input key array of size (k_in_dim, kv_len, batch_size).
  • v_in: Input value array of size (v_in_dim, kv_len, batch_size).
  • bias: Bias array broadcastable to size (kv_len, q_len, nheads, batch_size). It will be added to the attention scores before the softmax. Default nothing.
  • mask: Input array broadcastable to size (kv_len, q_len, nheads, batch_size). The mask is applied to the attention scores just before the softmax. See NNlib.make_causal_mask for creating causal masks. Default nothing.

Alternative calling signatures are mha(q_in), equivalent to mha(q_in, q_in, q_in) (self-attention), and mha(q_in, k_in), equivalent to mha(q_in, k_in, k_in) (key and value are the same).

See also NNlib.dot_product_attention.

Examples

mha = MultiHeadAttention(64, nheads = 8)
 q = rand(Float32, (64, 10, 32))
 k = rand(Float32, (64, 20, 32))
 v = rand(Float32, (64, 20, 32))
@@ -180,13 +180,13 @@
 mha = MultiHeadAttention(64 => 1024 => 1024, nheads = 8)
 y, α = mha(q) # self-attention
 # [y] = [1024, 10, 32]
-# [α] = [10, 10, 8, 32]
source

Pooling

These layers are commonly used after a convolution layer, and reduce the size of its output. They have no trainable parameters.

Flux.AdaptiveMaxPool — Type
AdaptiveMaxPool(out::NTuple)

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

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).

See also MaxPool, AdaptiveMeanPool.

Examples

julia> xs = rand(Float32, 100, 100, 3, 50);  # batch of 50 RGB images
+# [α] = [10, 10, 8, 32]
source

Pooling

These layers are commonly used after a convolution layer, and reduce the size of its output. They have no trainable parameters.

Flux.AdaptiveMaxPool — Type
AdaptiveMaxPool(out::NTuple)

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

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).

See also MaxPool, AdaptiveMeanPool.

Examples

julia> xs = rand(Float32, 100, 100, 3, 50);  # batch of 50 RGB images
 
 julia> AdaptiveMaxPool((25, 25))(xs) |> size
 (25, 25, 3, 50)
 
 julia> MaxPool((4,4))(xs) ≈ AdaptiveMaxPool((25, 25))(xs)
-true
source
Flux.MaxPool — Type
MaxPool(window::NTuple; pad=0, stride=window)

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

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

By default the window size is also the stride in each dimension. The keyword pad accepts the same options as for the Conv layer, including SamePad().

See also Conv, MeanPool, AdaptiveMaxPool, GlobalMaxPool.

Examples

julia> xs = rand(Float32, 100, 100, 3, 50);  # batch of 50 RGB images
+true
source
Flux.MaxPool — Type
MaxPool(window::NTuple; pad=0, stride=window)

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

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

By default the window size is also the stride in each dimension. The keyword pad accepts the same options as for the Conv layer, including SamePad().

See also Conv, MeanPool, AdaptiveMaxPool, GlobalMaxPool.

Examples

julia> xs = rand(Float32, 100, 100, 3, 50);  # batch of 50 RGB images
 
 julia> m = Chain(Conv((5, 5), 3 => 7, pad=SamePad()), MaxPool((5, 5), pad=SamePad()))
 Chain(
@@ -204,7 +204,7 @@
 MaxPool((5,), pad=2, stride=3)
 
 julia> layer(rand(Float32, 100, 7, 50)) |> size
-(34, 7, 50)
source
Flux.GlobalMaxPool — Type
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.

See also MaxPool, GlobalMeanPool.

julia> xs = rand(Float32, 100, 100, 3, 50);
+(34, 7, 50)
source
Flux.GlobalMaxPool — Type
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.

See also MaxPool, GlobalMeanPool.

julia> xs = rand(Float32, 100, 100, 3, 50);
 
 julia> m = Chain(Conv((3,3), 3 => 7), GlobalMaxPool());
 
@@ -212,13 +212,13 @@
 (1, 1, 7, 50)
 
 julia> GlobalMaxPool()(rand(3,5,7)) |> size  # preserves 2 dimensions
-(1, 5, 7)
source
Flux.AdaptiveMeanPool — Type
AdaptiveMeanPool(out::NTuple)

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

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).

See also MaxPool, AdaptiveMaxPool.

Examples

julia> xs = rand(Float32, 100, 100, 3, 50);  # batch of 50 RGB images
+(1, 5, 7)
source
Flux.AdaptiveMeanPool — Type
AdaptiveMeanPool(out::NTuple)

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

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).

See also MaxPool, AdaptiveMaxPool.

Examples

julia> xs = rand(Float32, 100, 100, 3, 50);  # batch of 50 RGB images
 
 julia> AdaptiveMeanPool((25, 25))(xs) |> size
 (25, 25, 3, 50)
 
 julia> MeanPool((4,4))(xs) ≈ AdaptiveMeanPool((25, 25))(xs)
-true
source
Flux.MeanPool — Type
MeanPool(window::NTuple; pad=0, stride=window)

Mean pooling layer, averaging all pixels in a block of size window.

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

By default the window size is also the stride in each dimension. The keyword pad accepts the same options as for the Conv layer, including SamePad().

See also Conv, MaxPool, AdaptiveMeanPool.

Examples

julia> xs = rand(Float32, 100, 100, 3, 50);
+true
source
Flux.MeanPool — Type
MeanPool(window::NTuple; pad=0, stride=window)

Mean pooling layer, averaging all pixels in a block of size window.

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

By default the window size is also the stride in each dimension. The keyword pad accepts the same options as for the Conv layer, including SamePad().

See also Conv, MaxPool, AdaptiveMeanPool.

Examples

julia> xs = rand(Float32, 100, 100, 3, 50);
 
 julia> m = Chain(Conv((5,5), 3 => 7), MeanPool((5,5), pad=SamePad()))
 Chain(
@@ -230,12 +230,12 @@
 (96, 96, 7, 50)
 
 julia> m(xs) |> size
-(20, 20, 7, 50)
source
Flux.GlobalMeanPool — Type
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.

julia> xs = rand(Float32, 100, 100, 3, 50);
+(20, 20, 7, 50)
source
Flux.GlobalMeanPool — Type
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.

julia> xs = rand(Float32, 100, 100, 3, 50);
 
 julia> m = Chain(Conv((3,3), 3 => 7), GlobalMeanPool());
 
 julia> m(xs) |> size
-(1, 1, 7, 50)
source

Upsampling

The opposite of pooling, these layers increase the size of an array. They have no trainable parameters.

Flux.Upsample — Type
Upsample(mode = :nearest; [scale, size]) 
+(1, 1, 7, 50)
source

Upsampling

The opposite of pooling, these layers increase the size of an array. They have no trainable parameters.

Flux.Upsample — Type
Upsample(mode = :nearest; [scale, size]) 
 Upsample(scale, mode = :nearest)

An upsampling layer. One of two keywords must be given:

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.

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

Examples

julia> m = Upsample(scale = (2, 3))
 Upsample(:nearest, scale = (2, 3))
 
@@ -246,7 +246,7 @@
 Upsample(:bilinear, size = (4, 5))
 
 julia> m(ones(2, 2, 1, 1)) |> size
-(4, 5, 1, 1)
source
Flux.PixelShuffle — Type
PixelShuffle(r::Int)

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

See NNlib.pixel_shuffle.

Examples

julia> p = PixelShuffle(2);
+(4, 5, 1, 1)
source
Flux.PixelShuffle — Type
PixelShuffle(r::Int)

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

See NNlib.pixel_shuffle.

Examples

julia> p = PixelShuffle(2);
 
 julia> xs = [2row + col + channel/10 for row in 1:2, col in 1:2, channel in 1:4, n in 1:1]
 2×2×4×1 Array{Float64, 4}:
@@ -298,7 +298,7 @@
  4.1  4.3  5.1  5.3  6.1  6.3
  4.2  4.4  5.2  5.4  6.2  6.4
  7.1  7.3  8.1  8.3  9.1  9.3
- 7.2  7.4  8.2  8.4  9.2  9.4
source

Embedding Vectors

These layers accept an index, and return a vector (or several indices, and several vectors). The possible embedding vectors are learned parameters.

Flux.Embedding — Type
Embedding(in => out; init=randn32)

A lookup table that stores embeddings of dimension out for a vocabulary of size in, as a trainable matrix.

This layer is often used to store word embeddings and retrieve them using indices. The input to the layer can be a vocabulary index in 1:in, an array of indices, or the corresponding onehot encoding.

For indices x, the result is of size (out, size(x)...), allowing several batch dimensions. For one-hot ohx, the result is of size (out, size(ohx)[2:end]...).

Examples

julia> emb = Embedding(26 => 4, init=Flux.identity_init(gain=22))
+ 7.2  7.4  8.2  8.4  9.2  9.4
source

Embedding Vectors

These layers accept an index, and return a vector (or several indices, and several vectors). The possible embedding vectors are learned parameters.

Flux.Embedding — Type
Embedding(in => out; init=randn32)

A lookup table that stores embeddings of dimension out for a vocabulary of size in, as a trainable matrix.

This layer is often used to store word embeddings and retrieve them using indices. The input to the layer can be a vocabulary index in 1:in, an array of indices, or the corresponding onehot encoding.

For indices x, the result is of size (out, size(x)...), allowing several batch dimensions. For one-hot ohx, the result is of size (out, size(ohx)[2:end]...).

Examples

julia> emb = Embedding(26 => 4, init=Flux.identity_init(gain=22))
 Embedding(26 => 4)  # 104 parameters
 
 julia> emb(2)  # one column of e.weight (here not random!)
@@ -319,7 +319,7 @@
 true
 
 julia> emb(rand(1:26, (10, 1, 12))) |> size  # three batch dimensions
-(4, 10, 1, 12)
source
Flux.EmbeddingBag — Type
EmbeddingBag(in => out, reduction=mean; init=Flux.randn32)

A lookup table that stores embeddings of dimension out for a vocabulary of size in. Differs from Embedding in that, instead of acting on a single vocabulary index, it always acts a vector of indices which it calls a "bag". Their individual embedding vectors are reduced to one, using mean or some other function.

Instead of acting on one "bag", such as x::Vector{Int}, the layer can also act on several:

  • Acting on a vector of "bags", it produces a matrix whose columns are the reduced vectors. More generally on x::Array{Vector{Int}}, its output is of size (out, size(x)...).

  • Any higher-rank array of integers is interpreted as a collection of "bags" each along the first dimension. Thus the output is mapslices(e, x; dims=1) when e::EmbeddingBag and x::Array{Int,N}. This method is more efficient, but requires that all "bags" have the same length.

  • A vector of "bags" may also be produced by splitting a vector of indices at specified points. For this case the layer takes two inputs, both vectors of integers. See details below.

The "bag" may equivalently be represented as a OneHotMatrix. A collection of these, or one higher-rank OneHotArray, again produce a stack of embeddings. See details below.

Examples

julia> vocab_size = 26;  # embed into 3 dimensions, with non-random vectors:
+(4, 10, 1, 12)
source
Flux.EmbeddingBag — Type
EmbeddingBag(in => out, reduction=mean; init=Flux.randn32)

A lookup table that stores embeddings of dimension out for a vocabulary of size in. Differs from Embedding in that, instead of acting on a single vocabulary index, it always acts a vector of indices which it calls a "bag". Their individual embedding vectors are reduced to one, using mean or some other function.

Instead of acting on one "bag", such as x::Vector{Int}, the layer can also act on several:

  • Acting on a vector of "bags", it produces a matrix whose columns are the reduced vectors. More generally on x::Array{Vector{Int}}, its output is of size (out, size(x)...).

  • Any higher-rank array of integers is interpreted as a collection of "bags" each along the first dimension. Thus the output is mapslices(e, x; dims=1) when e::EmbeddingBag and x::Array{Int,N}. This method is more efficient, but requires that all "bags" have the same length.

  • A vector of "bags" may also be produced by splitting a vector of indices at specified points. For this case the layer takes two inputs, both vectors of integers. See details below.

The "bag" may equivalently be represented as a OneHotMatrix. A collection of these, or one higher-rank OneHotArray, again produce a stack of embeddings. See details below.

Examples

julia> vocab_size = 26;  # embed into 3 dimensions, with non-random vectors:
 
 julia> eb = EmbeddingBag(vocab_size => 3, init=Flux.identity_init(gain=100))
 EmbeddingBag(26 => 3)  # 78 parameters
@@ -368,7 +368,7 @@
 3×2 Matrix{Float32}:
  33.3333    0.0
  66.6667    0.0
-  0.0     100.0
source

Dataflow Layers, or Containers

The basic Chain(F, G, H) applies the layers it contains in sequence, equivalent to H ∘ G ∘ F. Flux has some other layers which contain layers, but connect them up in a more complicated way: SkipConnection allows ResNet's residual connection.

Flux.Chain — Type
Chain(layers...)
+  0.0     100.0
source

Dataflow Layers, or Containers

The basic Chain(F, G, H) applies the layers it contains in sequence, equivalent to H ∘ G ∘ F. Flux has some other layers which contain layers, but connect them up in a more complicated way: SkipConnection allows ResNet's residual connection.

Flux.Chain — Type
Chain(layers...)
 Chain(name = layer, ...)

Collects multiple layers / functions to be called in sequence on a given input. Supports indexing and slicing, m[2] or m[1:end-1], and if names are given, m[:name] == m[1] etc.

Examples

julia> m = Chain(x -> x^2, x -> x+1);
 
 julia> m(5) == 26
@@ -385,12 +385,12 @@
                   dec = Dense(5 => 2));
 
 julia> m2(x) == (m2[:dec] ∘ m2[:enc])(x)
-true

For large models, there is a special type-unstable path which can reduce compilation times. This can be used by supplying a vector of layers Chain([layer1, layer2, ...]). This feature is somewhat experimental, beware!

source
Flux.activations — Function
activations(c::Chain, input)

Like calling a Chain, but saves the result of each layer as an output.

Examples

julia> using Flux: activations
+true

For large models, there is a special type-unstable path which can reduce compilation times. This can be used by supplying a vector of layers Chain([layer1, layer2, ...]). This feature is somewhat experimental, beware!

source
Flux.activations — Function
activations(c::Chain, input)

Like calling a Chain, but saves the result of each layer as an output.

Examples

julia> using Flux: activations
 
 julia> c = Chain(x -> x + 1, x -> x * 2, x -> x ^ 3);
 
 julia> activations(c, 1)
-(2, 4, 64)
source
Flux.Maxout — Type
Maxout(layers...)
+(2, 4, 64)
source
Flux.Maxout — Type
Maxout(layers...)
 Maxout(f, n_alts)

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

Instead of defining layers individually, you can provide a zero-argument function which constructs them, and the number to construct.

Maxout over linear dense layers satisfies the universal approximation theorem. See Goodfellow, Warde-Farley, Mirza, Courville & Bengio "Maxout Networks" https://arxiv.org/abs/1302.4389.

See also Parallel to reduce with other operators.

Examples

julia> m = Maxout(x -> abs2.(x), x -> x .* 3);
 
 julia> m([-2 -1 0 1 2])
@@ -405,7 +405,7 @@
 )                   # Total: 6 arrays, 126 parameters, 816 bytes.
 
 julia> Flux.outputsize(m3, (5, 11))
-(7, 11)
source
Flux.SkipConnection — Type
SkipConnection(layer, connection)

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, +). Here is a more complicated example:

julia> m = Conv((3,3), 4 => 7, pad=(1,1));
+(7, 11)
source
Flux.SkipConnection — Type
SkipConnection(layer, connection)

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, +). Here is a more complicated example:

julia> m = Conv((3,3), 4 => 7, pad=(1,1));
 
 julia> x = ones(Float32, 5, 5, 4, 10);
 
@@ -415,7 +415,7 @@
 julia> sm = SkipConnection(m, (mx, x) -> cat(mx, x, dims=3));
 
 julia> size(sm(x)) == (5, 5, 11, 10)
-true

See also Parallel, Maxout.

source
Flux.Parallel — Type
Parallel(connection, layers...)
+true

See also Parallel, Maxout.

source
Flux.Parallel — Type
Parallel(connection, layers...)
 Parallel(connection; name = layer, ...)

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

Called with one input x, this is equivalent to connection([l(x) for l in layers]...). If called with multiple inputs, one is passed to each layer, thus Parallel(+, f, g)(x, y) = f(x) + g(y).

Like Chain, its sub-layers may be given names using the keyword constructor. These can be accessed by indexing: m[1] == m[:name] is the first layer.

See also SkipConnection which is Parallel with one identity, and Maxout which reduces by broadcasting max.

Examples

julia> model = Chain(Dense(3 => 5),
                      Parallel(vcat, Dense(5 => 4), Chain(Dense(5 => 7), Dense(7 => 4))),
                      Dense(8 => 17));
@@ -437,7 +437,7 @@
 (2,)
 
 julia> model2[:β] == model2[2]
-true
source
Flux.PairwiseFusion — Type
PairwiseFusion(connection, layers...)

Arguments

  • connection: A function taking 2 inputs and combining them into a single output
  • layers: The layers whose outputs are combined

Inputs

This layer behaves differently based on input type:

  1. If input x is a tuple of length N (or the input is xs with N x's), matching the number of layers,

then each layer receives a new input x[i] combined with the previous output y[i-1] using connection. Thus (y1, y2, y3) = PairwiseFusion(connection, layer1, layer2, layer3)((x1, x2, x3)) may be drawn as:

x1 → layer1 → y1 ↘
+true
source
Flux.PairwiseFusion — Type
PairwiseFusion(connection, layers...)

Arguments

  • connection: A function taking 2 inputs and combining them into a single output
  • layers: The layers whose outputs are combined

Inputs

This layer behaves differently based on input type:

  1. If input x is a tuple of length N (or the input is xs with N x's), matching the number of layers,

then each layer receives a new input x[i] combined with the previous output y[i-1] using connection. Thus (y1, y2, y3) = PairwiseFusion(connection, layer1, layer2, layer3)((x1, x2, x3)) may be drawn as:

x1 → layer1 → y1 ↘
                   connection → layer2 → y2 ↘
               x2 ↗                          connection → layer3 → y3
                                         x3 ↗

... or written as:

y1 = layer1(x1)
@@ -445,7 +445,7 @@
 y3 = layer3(connection(y2, x3))
  1. With just one input, each layer receives the same x combined with the previous output. Thus y = PairwiseFusion(connection, layers...)(x) obeys:
y[1] == layers[1](x)
 for i in 2:length(layers)
     y[i] == connection(layers[i](y[i-1]), x)
-end

Returns

A tuple of length N with the output of each fusion ((y1, y2, ..., yN) in the example above).

source

Recurrent Models

Much like the core layers above, but can be used to process sequence data (as well as other kinds of structured data).

Flux.RNN — Function
RNN(in => out, σ = tanh)

The most basic recurrent layer; essentially acts as a Dense layer, but with the output fed back into the input each time step.

The arguments in and out describe the size of the feature vectors passed as input and as output. That is, it accepts a vector of length in or a batch of vectors represented as a in x B matrix and outputs a vector of length out or a batch of vectors of size out x B.

This constructor is syntactic sugar for Recur(RNNCell(a...)), and so RNNs are stateful. Note that the state shape can change depending on the inputs, and so it is good to reset! the model between inference calls if the batch size changes. See the examples below.

Examples

julia> r = RNN(3 => 5)
+end

Returns

A tuple of length N with the output of each fusion ((y1, y2, ..., yN) in the example above).

source

Recurrent Models

Much like the core layers above, but can be used to process sequence data (as well as other kinds of structured data).

Flux.RNN — Function
RNN(in => out, σ = tanh)

The most basic recurrent layer; essentially acts as a Dense layer, but with the output fed back into the input each time step.

The arguments in and out describe the size of the feature vectors passed as input and as output. That is, it accepts a vector of length in or a batch of vectors represented as a in x B matrix and outputs a vector of length out or a batch of vectors of size out x B.

This constructor is syntactic sugar for Recur(RNNCell(a...)), and so RNNs are stateful. Note that the state shape can change depending on the inputs, and so it is good to reset! the model between inference calls if the batch size changes. See the examples below.

Examples

julia> r = RNN(3 => 5)
 Recur(
   RNNCell(3 => 5, tanh),                # 50 parameters
 )         # Total: 4 trainable arrays, 50 parameters,
@@ -484,7 +484,7 @@
 julia> r = Flux.Recur(Flux.RNNCell(tanh, rand(5, 4), Tridiagonal(rand(5, 5)), rand(5), rand(5, 1)))
 
 julia> r(rand(4, 10)) |> size # batch size of 10
-(5, 10)
source
Flux.LSTM — Function
LSTM(in => out)

Long Short Term Memory recurrent layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.

The arguments in and out describe the size of the feature vectors passed as input and as output. That is, it accepts a vector of length in or a batch of vectors represented as a in x B matrix and outputs a vector of length out or a batch of vectors of size out x B.

This constructor is syntactic sugar for Recur(LSTMCell(a...)), and so LSTMs are stateful. Note that the state shape can change depending on the inputs, and so it is good to reset! the model between inference calls if the batch size changes. See the examples below.

See this article for a good overview of the internals.

Examples

julia> l = LSTM(3 => 5)
+(5, 10)
source
Flux.LSTM — Function
LSTM(in => out)

Long Short Term Memory recurrent layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.

The arguments in and out describe the size of the feature vectors passed as input and as output. That is, it accepts a vector of length in or a batch of vectors represented as a in x B matrix and outputs a vector of length out or a batch of vectors of size out x B.

This constructor is syntactic sugar for Recur(LSTMCell(a...)), and so LSTMs are stateful. Note that the state shape can change depending on the inputs, and so it is good to reset! the model between inference calls if the batch size changes. See the examples below.

See this article for a good overview of the internals.

Examples

julia> l = LSTM(3 => 5)
 Recur(
   LSTMCell(3 => 5),                     # 190 parameters
 )         # Total: 5 trainable arrays, 190 parameters,
@@ -496,7 +496,7 @@
 julia> Flux.reset!(l);
 
 julia> l(rand(Float32, 3, 10)) |> size # batch size of 10
-(5, 10)
Batch size changes

Failing to call reset! when the input batch size changes can lead to unexpected behavior. See the example in RNN.

Note:

LSTMCells can be constructed directly by specifying the non-linear function, the Wi and Wh internal matrices, a bias vector b, and a learnable initial state state0. The Wi and Wh matrices do not need to be the same type. See the example in RNN.

source
Flux.GRU — Function
GRU(in => out)

Gated Recurrent Unit layer. Behaves like an RNN but generally exhibits a longer memory span over sequences. This implements the variant proposed in v1 of the referenced paper.

The integer arguments in and out describe the size of the feature vectors passed as input and as output. That is, it accepts a vector of length in or a batch of vectors represented as a in x B matrix and outputs a vector of length out or a batch of vectors of size out x B.

This constructor is syntactic sugar for Recur(GRUCell(a...)), and so GRUs are stateful. Note that the state shape can change depending on the inputs, and so it is good to reset! the model between inference calls if the batch size changes. See the examples below.

See this article for a good overview of the internals.

Examples

julia> g = GRU(3 => 5)
+(5, 10)
Batch size changes

Failing to call reset! when the input batch size changes can lead to unexpected behavior. See the example in RNN.

Note:

LSTMCells can be constructed directly by specifying the non-linear function, the Wi and Wh internal matrices, a bias vector b, and a learnable initial state state0. The Wi and Wh matrices do not need to be the same type. See the example in RNN.

source
Flux.GRU — Function
GRU(in => out)

Gated Recurrent Unit layer. Behaves like an RNN but generally exhibits a longer memory span over sequences. This implements the variant proposed in v1 of the referenced paper.

The integer arguments in and out describe the size of the feature vectors passed as input and as output. That is, it accepts a vector of length in or a batch of vectors represented as a in x B matrix and outputs a vector of length out or a batch of vectors of size out x B.

This constructor is syntactic sugar for Recur(GRUCell(a...)), and so GRUs are stateful. Note that the state shape can change depending on the inputs, and so it is good to reset! the model between inference calls if the batch size changes. See the examples below.

See this article for a good overview of the internals.

Examples

julia> g = GRU(3 => 5)
 Recur(
   GRUCell(3 => 5),                      # 140 parameters
 )         # Total: 4 trainable arrays, 140 parameters,
@@ -508,7 +508,7 @@
 julia> Flux.reset!(g);
 
 julia> g(rand(Float32, 3, 10)) |> size # batch size of 10
-(5, 10)
Batch size changes

Failing to call reset! when the input batch size changes can lead to unexpected behavior. See the example in RNN.

Note:

GRUCells can be constructed directly by specifying the non-linear function, the Wi and Wh internal matrices, a bias vector b, and a learnable initial state state0. The Wi and Wh matrices do not need to be the same type. See the example in RNN.

source
Flux.GRUv3 — Function
GRUv3(in => out)

Gated Recurrent Unit layer. Behaves like an RNN but generally exhibits a longer memory span over sequences. This implements the variant proposed in v3 of the referenced paper.

The arguments in and out describe the size of the feature vectors passed as input and as output. That is, it accepts a vector of length in or a batch of vectors represented as a in x B matrix and outputs a vector of length out or a batch of vectors of size out x B.

This constructor is syntactic sugar for Recur(GRUv3Cell(a...)), and so GRUv3s are stateful. Note that the state shape can change depending on the inputs, and so it is good to reset! the model between inference calls if the batch size changes. See the examples below.

See this article for a good overview of the internals.

Examples

julia> g = GRUv3(3 => 5)
+(5, 10)
Batch size changes

Failing to call reset! when the input batch size changes can lead to unexpected behavior. See the example in RNN.

Note:

GRUCells can be constructed directly by specifying the non-linear function, the Wi and Wh internal matrices, a bias vector b, and a learnable initial state state0. The Wi and Wh matrices do not need to be the same type. See the example in RNN.

source
Flux.GRUv3 — Function
GRUv3(in => out)

Gated Recurrent Unit layer. Behaves like an RNN but generally exhibits a longer memory span over sequences. This implements the variant proposed in v3 of the referenced paper.

The arguments in and out describe the size of the feature vectors passed as input and as output. That is, it accepts a vector of length in or a batch of vectors represented as a in x B matrix and outputs a vector of length out or a batch of vectors of size out x B.

This constructor is syntactic sugar for Recur(GRUv3Cell(a...)), and so GRUv3s are stateful. Note that the state shape can change depending on the inputs, and so it is good to reset! the model between inference calls if the batch size changes. See the examples below.

See this article for a good overview of the internals.

Examples

julia> g = GRUv3(3 => 5)
 Recur(
   GRUv3Cell(3 => 5),                    # 140 parameters
 )         # Total: 5 trainable arrays, 140 parameters,
@@ -520,7 +520,7 @@
 julia> Flux.reset!(g);
 
 julia> g(rand(Float32, 3, 10)) |> size # batch size of 10
-(5, 10)
Batch size changes

Failing to call reset! when the input batch size changes can lead to unexpected behavior. See the example in RNN.

Note:

GRUv3Cells can be constructed directly by specifying the non-linear function, the Wi, Wh, and Wh_h internal matrices, a bias vector b, and a learnable initial state state0. The Wi, Wh, and Wh_h matrices do not need to be the same type. See the example in RNN.

source
Flux.Recur — Type
Recur(cell)

Recur takes a recurrent cell and makes it stateful, managing the hidden state in the background. cell should be a model of the form:

h, y = cell(h, x...)

For example, here's a recurrent network that keeps a running total of its inputs:

Examples

julia> accum(h, x) = (h + x, x)
+(5, 10)
Batch size changes

Failing to call reset! when the input batch size changes can lead to unexpected behavior. See the example in RNN.

Note:

GRUv3Cells can be constructed directly by specifying the non-linear function, the Wi, Wh, and Wh_h internal matrices, a bias vector b, and a learnable initial state state0. The Wi, Wh, and Wh_h matrices do not need to be the same type. See the example in RNN.

source
Flux.Recur — Type
Recur(cell)

Recur takes a recurrent cell and makes it stateful, managing the hidden state in the background. cell should be a model of the form:

h, y = cell(h, x...)

For example, here's a recurrent network that keeps a running total of its inputs:

Examples

julia> accum(h, x) = (h + x, x)
 accum (generic function with 1 method)
 
 julia> rnn = Flux.Recur(accum, 0)
@@ -571,7 +571,7 @@
 
 julia> rnn.state
 1×1 Matrix{Int64}:
- 60
source
Flux.reset! — Function
reset!(rnn)

Reset the hidden state of a recurrent layer back to its original value.

Assuming you have a Recur layer rnn, this is roughly equivalent to:

rnn.state = hidden(rnn.cell)

Examples

julia> r = Flux.RNNCell(relu, ones(1,1), zeros(1,1), ones(1,1), zeros(1,1));  # users should use the RNN wrapper struct instead
+ 60
source
Flux.reset! — Function
reset!(rnn)

Reset the hidden state of a recurrent layer back to its original value.

Assuming you have a Recur layer rnn, this is roughly equivalent to:

rnn.state = hidden(rnn.cell)

Examples

julia> r = Flux.RNNCell(relu, ones(1,1), zeros(1,1), ones(1,1), zeros(1,1));  # users should use the RNN wrapper struct instead
 
 julia> y = Flux.Recur(r, ones(1,1));
 
@@ -593,7 +593,7 @@
 
 julia> y.state
 1×1 Matrix{Float64}:
- 0.0
source

Normalisation & Regularisation

These layers don't affect the structure of the network but may improve training times or reduce overfitting. Some of them contain trainable parameters, while others do not.

Flux.BatchNorm — Type
BatchNorm(channels::Integer, λ=identity;
+ 0.0
source

Normalisation & Regularisation

These layers don't affect the structure of the network but may improve training times or reduce overfitting. Some of them contain trainable parameters, while others do not.

Flux.BatchNorm — Type
BatchNorm(channels::Integer, λ=identity;
           initβ=zeros32, initγ=ones32,
           affine=true, track_stats=true, active=nothing,
           eps=1f-5, momentum= 0.1f0)

Batch Normalization layer. channels should be the size of the channel dimension in your data (see below).

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.

BatchNorm computes the mean and variance for each D_1×...×D_{N-2}×1×D_N input slice and normalises the input accordingly.

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

After normalisation, elementwise activation λ is applied.

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

Use testmode! during inference.

Examples

julia> using Statistics
@@ -605,7 +605,7 @@
 julia> Flux.trainmode!(m);
 
 julia> isapprox(std(m(xs)), 1, atol=0.1) && std(xs) != std(m(xs))
-true
source
Flux.Dropout — Type
Dropout(p; [dims, rng, active])

Layer implementing dropout with the given probability. This is used as a regularisation, i.e. to reduce overfitting.

While training, it sets each input to 0 (with probability p) or else scales it by 1 / (1 - p), using the NNlib.dropout function. While testing, it has no effect.

By default the mode will switch automatically, but it can also be controlled manually via Flux.testmode!, or by passing keyword active=true for training mode.

By default every input is treated independently. With the dims keyword, instead it takes a random choice only along that dimension. For example Dropout(p; dims = 3) will randomly zero out entire channels on WHCN input (also called 2D dropout).

Keyword rng lets you specify a custom random number generator. (Only supported on the CPU.)

Examples

julia> m = Chain(Dense(ones(3,2)), Dropout(0.4))
+true
source
Flux.Dropout — Type
Dropout(p; [dims, rng, active])

Layer implementing dropout with the given probability. This is used as a regularisation, i.e. to reduce overfitting.

While training, it sets each input to 0 (with probability p) or else scales it by 1 / (1 - p), using the NNlib.dropout function. While testing, it has no effect.

By default the mode will switch automatically, but it can also be controlled manually via Flux.testmode!, or by passing keyword active=true for training mode.

By default every input is treated independently. With the dims keyword, instead it takes a random choice only along that dimension. For example Dropout(p; dims = 3) will randomly zero out entire channels on WHCN input (also called 2D dropout).

Keyword rng lets you specify a custom random number generator. (Only supported on the CPU.)

Examples

julia> m = Chain(Dense(ones(3,2)), Dropout(0.4))
 Chain(
   Dense(2 => 3),                        # 9 parameters
   Dropout(0.4),
@@ -637,7 +637,7 @@
 1.9989999999999961
 
 julia> mean(iszero, y)  # is about 0.4
-0.4003
source
Flux.AlphaDropout — Type
AlphaDropout(p; [rng, active])

A dropout layer. Used in Self-Normalizing Neural Networks. The AlphaDropout layer ensures that mean and variance of activations remain the same as before.

Does nothing to the input once testmode! is true.

Examples

julia> using Statistics
+0.4003
source
Flux.AlphaDropout — Type
AlphaDropout(p; [rng, active])

A dropout layer. Used in Self-Normalizing Neural Networks. The AlphaDropout layer ensures that mean and variance of activations remain the same as before.

Does nothing to the input once testmode! is true.

Examples

julia> using Statistics
 
 julia> x = randn32(1000,1);
 
@@ -648,7 +648,7 @@
 julia> y = m(x);
 
 julia> isapprox(std(x), std(y), atol=0.2)
-true
source
Flux.LayerNorm — Type
LayerNorm(size..., λ=identity; affine=true, eps=1f-5)

A normalisation layer designed to be used with recurrent hidden states. The argument size should be an integer or a tuple of integers.

In the forward pass, the layer normalises the mean and standard deviation of the input, then applies the elementwise activation λ. The input is normalised along the first length(size) dimensions for tuple size, and along the first dimension for integer size. The input is expected to have first dimensions' size equal to size.

If affine=true, it also applies a learnable shift and rescaling using the Scale layer.

See also BatchNorm, InstanceNorm, GroupNorm, and normalise.

Examples

julia> using Statistics
+true
source
Flux.LayerNorm — Type
LayerNorm(size..., λ=identity; affine=true, eps=1f-5)

A normalisation layer designed to be used with recurrent hidden states. The argument size should be an integer or a tuple of integers.

In the forward pass, the layer normalises the mean and standard deviation of the input, then applies the elementwise activation λ. The input is normalised along the first length(size) dimensions for tuple size, and along the first dimension for integer size. The input is expected to have first dimensions' size equal to size.

If affine=true, it also applies a learnable shift and rescaling using the Scale layer.

See also BatchNorm, InstanceNorm, GroupNorm, and normalise.

Examples

julia> using Statistics
 
 julia> xs = rand(3, 3, 3, 2);  # a batch of 2 images, each having 3 channels
 
@@ -657,7 +657,7 @@
 julia> y = m(xs);
 
 julia> isapprox(std(y, dims=1:3), ones(1, 1, 1, 2), atol=0.1) && std(y, dims=1:3) != std(xs, dims=1:3)
-true
source
Flux.InstanceNorm — Type
InstanceNorm(channels::Integer, λ=identity;
+true
source
Flux.InstanceNorm — Type
InstanceNorm(channels::Integer, λ=identity;
              initβ=zeros32, initγ=ones32,
              affine=false, track_stats=false,
              eps=1f-5, momentum=0.1f0)

Instance Normalization layer. channels should be the size of the channel dimension in your data (see below).

Given an array with N > 2 dimensions, call the N-1th the channel dimension. For WHCN images it's the usual channel dimension.

InstanceNorm computes the mean and variance for each D_1×...×D_{N-2}×1×1 input slice and normalises the input accordingly.

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

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

Warning: the defaults for affine and track_stats used to be true in previous Flux versions (< v0.12).

Examples

julia> using Statistics
@@ -669,7 +669,7 @@
 julia> y = m(xs);
 
 julia> isapprox(std(y, dims=1:2), ones(1, 1, 3, 2), atol=0.2) && std(y, dims=1:2) != std(xs, dims=1:2)
-true
source
Flux.GroupNorm — Type
GroupNorm(channels::Int, G::Int, λ = identity;
+true
source
Flux.GroupNorm — Type
GroupNorm(channels::Int, G::Int, λ = identity;
           initβ = zeros32,
           initγ = ones32,
           affine = true,
@@ -686,7 +686,7 @@
 true
 
 julia> isapprox(std(y[:, :, 3:4, 2]), 1, atol=0.1) && std(xs[:, :, 3:4, 2]) != std(y[:, :, 3:4, 2])
-true
source
Flux.normalise — Function
normalise(x; dims=ndims(x), eps=1e-5)

Normalise x to mean 0 and standard deviation 1 across the dimension(s) given by dims. Per default, dims is the last dimension. eps is a small term added to the denominator for numerical stability.

Examples

julia> using Statistics
+true
source
Flux.normalise — Function
normalise(x; dims=ndims(x), eps=1e-5)

Normalise x to mean 0 and standard deviation 1 across the dimension(s) given by dims. Per default, dims is the last dimension. eps is a small term added to the denominator for numerical stability.

Examples

julia> using Statistics
 
 julia> x = [90, 100, 110, 130, 70];
 
@@ -709,7 +709,7 @@
 julia> y = Flux.normalise(x, dims=1);
 
 julia> isapprox(std(y; dims=1, corrected=false), ones(1, 10), atol=1e-5)
-true
source

Test vs. Train

Several normalisation layers behave differently under training and inference (testing). By default, Flux will automatically determine when a layer evaluation is part of training or inference.

Warning

This automatic train/test detection works best with Zygote, the default automatic differentiation package. It may not work with other packages such as Tracker, Yota, or ForwardDiff.

The functions Flux.trainmode! and Flux.testmode! let you manually specify which behaviour you want. When called on a model, they will place all layers within the model into the specified mode.

Flux.testmode! — Method
testmode!(model, [mode]) -> model

Set a layer, or all layers in a model, to test mode. This disables the effect of Dropout and some other regularisation layers.

If you manually set a model into test mode, you need to manually place it back into train mode during training phase, using trainmode!.

There is an optional second argument, which takes a symbol :auto to reset all layers back to the default automatic mode.

Example

julia> d = Dropout(0.3)
+true
source

Test vs. Train

Several normalisation layers behave differently under training and inference (testing). By default, Flux will automatically determine when a layer evaluation is part of training or inference.

Warning

This automatic train/test detection works best with Zygote, the default automatic differentiation package. It may not work with other packages such as Tracker, Yota, or ForwardDiff.

The functions Flux.trainmode! and Flux.testmode! let you manually specify which behaviour you want. When called on a model, they will place all layers within the model into the specified mode.

Flux.testmode! — Method
testmode!(model, [mode]) -> model

Set a layer, or all layers in a model, to test mode. This disables the effect of Dropout and some other regularisation layers.

If you manually set a model into test mode, you need to manually place it back into train mode during training phase, using trainmode!.

There is an optional second argument, which takes a symbol :auto to reset all layers back to the default automatic mode.

Example

julia> d = Dropout(0.3)
 Dropout(0.3)
 
 julia> testmode!(d)   # dropout is now always disabled
@@ -719,4 +719,4 @@
 Dropout(0.3, active=true)
 
 julia> testmode!(d, :auto)  # back to default
-Dropout(0.3)
source
Flux.testmode! — Method
testmode!(model, inactive)

This two-argument method is largely internal. It recurses into the model, and until a method like testmode!(d::Dropout, inactive) alters the activity of a layer. Custom layers can support manual testmode! / trainmode! switching by defining such a method.

Possible values of inactive are:

  • true for testing, i.e. active=false
  • false for training, same as trainmode!(m)
  • :auto or nothing for Flux to detect training automatically.
Compat

This method may be removed in a future breaking change, to separate the user-facing testmode! from the internal recursion.

source
Flux.trainmode! — Function
trainmode!(model) -> model

Set a layer, or all layers in a model, to training mode. Opposite to testmode!, see further details there.

source
+Dropout(0.3)source
Flux.testmode! — Method
testmode!(model, inactive)

This two-argument method is largely internal. It recurses into the model, and until a method like testmode!(d::Dropout, inactive) alters the activity of a layer. Custom layers can support manual testmode! / trainmode! switching by defining such a method.

Possible values of inactive are:

  • true for testing, i.e. active=false
  • false for training, same as trainmode!(m)
  • :auto or nothing for Flux to detect training automatically.
Compat

This method may be removed in a future breaking change, to separate the user-facing testmode! from the internal recursion.

source
Flux.trainmode! — Function
trainmode!(model) -> model

Set a layer, or all layers in a model, to training mode. Opposite to testmode!, see further details there.

source
diff --git a/dev/reference/models/losses/index.html b/dev/reference/models/losses/index.html index b830685b09..c4d868860d 100644 --- a/dev/reference/models/losses/index.html +++ b/dev/reference/models/losses/index.html @@ -10,16 +10,16 @@ loss(ŷ, y, agg=identity) # no aggregation.

Function listing

Flux.Losses.mae — Function
mae(ŷ, y; agg = mean)

Return the loss corresponding to mean absolute error:

agg(abs.(ŷ .- y))

Example

julia> y_model = [1.1, 1.9, 3.1];
 
 julia> Flux.mae(y_model, 1:3)
-0.10000000000000009
source
Flux.Losses.mse — Function
mse(ŷ, y; agg = mean)

Return the loss corresponding to mean square error:

agg((ŷ .- y) .^ 2)

See also: mae, msle, crossentropy.

Example

julia> y_model = [1.1, 1.9, 3.1];
+0.10000000000000009
source
Flux.Losses.mse — Function
mse(ŷ, y; agg = mean)

Return the loss corresponding to mean square error:

agg((ŷ .- y) .^ 2)

See also: mae, msle, crossentropy.

Example

julia> y_model = [1.1, 1.9, 3.1];
 
 julia> y_true = 1:3;
 
 julia> Flux.mse(y_model, y_true)
-0.010000000000000018
source
Flux.Losses.msle — Function
msle(ŷ, y; agg = mean, eps = eps(eltype(ŷ)))

The loss corresponding to mean squared logarithmic errors, calculated as

agg((log.(ŷ .+ ϵ) .- log.(y .+ ϵ)) .^ 2)

The ϵ == eps term provides numerical stability. Penalizes an under-estimation more than an over-estimatation.

Example

julia> Flux.msle(Float32[1.1, 2.2, 3.3], 1:3)
+0.010000000000000018
source
Flux.Losses.msle — Function
msle(ŷ, y; agg = mean, eps = eps(eltype(ŷ)))

The loss corresponding to mean squared logarithmic errors, calculated as

agg((log.(ŷ .+ ϵ) .- log.(y .+ ϵ)) .^ 2)

The ϵ == eps term provides numerical stability. Penalizes an under-estimation more than an over-estimatation.

Example

julia> Flux.msle(Float32[1.1, 2.2, 3.3], 1:3)
 0.009084041f0
 
 julia> Flux.msle(Float32[0.9, 1.8, 2.7], 1:3)
-0.011100831f0
source
Flux.Losses.huber_loss — Function
huber_loss(ŷ, y; delta = 1, agg = mean)

Return the mean of the Huber loss given the prediction ŷ and true values y.

             | 0.5 * |ŷ - y|^2,            for |ŷ - y| <= δ
+0.011100831f0
source
Flux.Losses.huber_loss — Function
huber_loss(ŷ, y; delta = 1, agg = mean)

Return the mean of the Huber loss given the prediction ŷ and true values y.

             | 0.5 * |ŷ - y|^2,            for |ŷ - y| <= δ
 Huber loss = |
              |  δ * (|ŷ - y| - 0.5 * δ), otherwise

Example

julia> ŷ = [1.1, 2.1, 3.1];
 
@@ -27,7 +27,7 @@
 0.005000000000000009
 
 julia> Flux.huber_loss(ŷ, 1:3, delta=0.05)  # changes behaviour as |ŷ - y| > δ
-0.003750000000000005
source
Flux.Losses.label_smoothing — Function
label_smoothing(y::Union{Number, AbstractArray}, α; dims::Int=1)

Returns smoothed labels, meaning the confidence on label values are relaxed.

When y is given as one-hot vector or batch of one-hot, its calculated as

y .* (1 - α) .+ α / size(y, dims)

when y is given as a number or batch of numbers for binary classification, its calculated as

y .* (1 - α) .+ α / 2

in which case the labels are squeezed towards 0.5.

α is a number in interval (0, 1) called the smoothing factor. Higher the value of α larger the smoothing of y.

dims denotes the one-hot dimension, unless dims=0 which denotes the application of label smoothing to binary distributions encoded in a single number.

Example

julia> y = Flux.onehotbatch([1, 1, 1, 0, 1, 0], 0:1)
+0.003750000000000005
source
Flux.Losses.label_smoothing — Function
label_smoothing(y::Union{Number, AbstractArray}, α; dims::Int=1)

Returns smoothed labels, meaning the confidence on label values are relaxed.

When y is given as one-hot vector or batch of one-hot, its calculated as

y .* (1 - α) .+ α / size(y, dims)

when y is given as a number or batch of numbers for binary classification, its calculated as

y .* (1 - α) .+ α / 2

in which case the labels are squeezed towards 0.5.

α is a number in interval (0, 1) called the smoothing factor. Higher the value of α larger the smoothing of y.

dims denotes the one-hot dimension, unless dims=0 which denotes the application of label smoothing to binary distributions encoded in a single number.

Example

julia> y = Flux.onehotbatch([1, 1, 1, 0, 1, 0], 0:1)
 2×6 OneHotMatrix(::Vector{UInt32}) with eltype Bool:
  ⋅  ⋅  ⋅  1  ⋅  1
  1  1  1  ⋅  1  ⋅
@@ -51,7 +51,7 @@
 true
 
 julia> Flux.crossentropy(y_dis, y) > Flux.crossentropy(y_dis, y_smoothed)
-true
source
Flux.Losses.crossentropy — Function
crossentropy(ŷ, y; dims = 1, eps = eps(eltype(ŷ)), agg = mean)

Return the cross entropy between the given probability distributions; calculated as

agg(-sum(y .* log.(ŷ .+ ϵ); dims))

Cross entropy is typically used as a loss in multi-class classification, in which case the labels y are given in a one-hot format. dims specifies the dimension (or the dimensions) containing the class probabilities. The prediction ŷ is supposed to sum to one across dims, as would be the case with the output of a softmax operation.

For numerical stability, it is recommended to use logitcrossentropy rather than softmax followed by crossentropy .

Use label_smoothing to smooth the true labels as preprocessing before computing the loss.

See also: logitcrossentropy, binarycrossentropy, logitbinarycrossentropy.

Example

julia> y_label = Flux.onehotbatch([0, 1, 2, 1, 0], 0:2)
+true
source
Flux.Losses.crossentropy — Function
crossentropy(ŷ, y; dims = 1, eps = eps(eltype(ŷ)), agg = mean)

Return the cross entropy between the given probability distributions; calculated as

agg(-sum(y .* log.(ŷ .+ ϵ); dims))

Cross entropy is typically used as a loss in multi-class classification, in which case the labels y are given in a one-hot format. dims specifies the dimension (or the dimensions) containing the class probabilities. The prediction ŷ is supposed to sum to one across dims, as would be the case with the output of a softmax operation.

For numerical stability, it is recommended to use logitcrossentropy rather than softmax followed by crossentropy .

Use label_smoothing to smooth the true labels as preprocessing before computing the loss.

See also: logitcrossentropy, binarycrossentropy, logitbinarycrossentropy.

Example

julia> y_label = Flux.onehotbatch([0, 1, 2, 1, 0], 0:2)
 3×5 OneHotMatrix(::Vector{UInt32}) with eltype Bool:
  1  ⋅  ⋅  ⋅  1
  ⋅  1  ⋅  1  ⋅
@@ -80,7 +80,7 @@
  0.05  0.05  0.9   0.05  0.05
 
 julia> Flux.crossentropy(y_model, y_smooth)
-1.5776052f0
source
Flux.Losses.logitcrossentropy — Function
logitcrossentropy(ŷ, y; dims = 1, agg = mean)

Return the cross entropy calculated by

agg(-sum(y .* logsoftmax(ŷ; dims); dims))

This is mathematically equivalent to crossentropy(softmax(ŷ), y), but is more numerically stable than using functions crossentropy and softmax separately.

See also: binarycrossentropy, logitbinarycrossentropy, label_smoothing.

Example

julia> y_label = Flux.onehotbatch(collect("abcabaa"), 'a':'c')
+1.5776052f0
source
Flux.Losses.logitcrossentropy — Function
logitcrossentropy(ŷ, y; dims = 1, agg = mean)

Return the cross entropy calculated by

agg(-sum(y .* logsoftmax(ŷ; dims); dims))

This is mathematically equivalent to crossentropy(softmax(ŷ), y), but is more numerically stable than using functions crossentropy and softmax separately.

See also: binarycrossentropy, logitbinarycrossentropy, label_smoothing.

Example

julia> y_label = Flux.onehotbatch(collect("abcabaa"), 'a':'c')
 3×7 OneHotMatrix(::Vector{UInt32}) with eltype Bool:
  1  ⋅  ⋅  1  ⋅  1  1
  ⋅  1  ⋅  ⋅  1  ⋅  ⋅
@@ -96,7 +96,7 @@
 1.5791205f0
 
 julia> Flux.crossentropy(softmax(y_model), y_label)
-1.5791197f0
source
Flux.Losses.binarycrossentropy — Function
binarycrossentropy(ŷ, y; agg = mean, eps = eps(eltype(ŷ)))

Return the binary cross-entropy loss, computed as

agg(@.(-y * log(ŷ + ϵ) - (1 - y) * log(1 - ŷ + ϵ)))

Where typically, the prediction ŷ is given by the output of a sigmoid activation. The ϵ == eps term is included to avoid infinity. Using logitbinarycrossentropy is recomended over binarycrossentropy for numerical stability.

Use label_smoothing to smooth the y value as preprocessing before computing the loss.

See also: crossentropy, logitcrossentropy.

Examples

julia> y_bin = Bool[1,0,1]
+1.5791197f0
source
Flux.Losses.binarycrossentropy — Function
binarycrossentropy(ŷ, y; agg = mean, eps = eps(eltype(ŷ)))

Return the binary cross-entropy loss, computed as

agg(@.(-y * log(ŷ + ϵ) - (1 - y) * log(1 - ŷ + ϵ)))

Where typically, the prediction ŷ is given by the output of a sigmoid activation. The ϵ == eps term is included to avoid infinity. Using logitbinarycrossentropy is recomended over binarycrossentropy for numerical stability.

Use label_smoothing to smooth the y value as preprocessing before computing the loss.

See also: crossentropy, logitcrossentropy.

Examples

julia> y_bin = Bool[1,0,1]
 3-element Vector{Bool}:
  1
  0
@@ -119,7 +119,7 @@
  1  ⋅  1
 
 julia> Flux.crossentropy(y_prob, y_hot)
-0.43989f0
source
Flux.Losses.logitbinarycrossentropy — Function
logitbinarycrossentropy(ŷ, y; agg = mean)

Mathematically equivalent to binarycrossentropy(σ(ŷ), y) but is more numerically stable.

See also: crossentropy, logitcrossentropy.

Examples

julia> y_bin = Bool[1,0,1];
+0.43989f0
source
Flux.Losses.logitbinarycrossentropy — Function
logitbinarycrossentropy(ŷ, y; agg = mean)

Mathematically equivalent to binarycrossentropy(σ(ŷ), y) but is more numerically stable.

See also: crossentropy, logitcrossentropy.

Examples

julia> y_bin = Bool[1,0,1];
 
 julia> y_model = Float32[2, -1, pi]
 3-element Vector{Float32}:
@@ -131,7 +131,7 @@
 0.160832f0
 
 julia> Flux.binarycrossentropy(sigmoid.(y_model), y_bin)
-0.16083185f0
source
Flux.Losses.kldivergence — Function
kldivergence(ŷ, y; agg = mean, eps = eps(eltype(ŷ)))

Return the Kullback-Leibler divergence between the given probability distributions.

The KL divergence is a measure of how much one probability distribution is different from the other. It is always non-negative, and zero only when both the distributions are equal.

Example

julia> p1 = [1 0; 0 1]
+0.16083185f0
source
Flux.Losses.kldivergence — Function
kldivergence(ŷ, y; agg = mean, eps = eps(eltype(ŷ)))

Return the Kullback-Leibler divergence between the given probability distributions.

The KL divergence is a measure of how much one probability distribution is different from the other. It is always non-negative, and zero only when both the distributions are equal.

Example

julia> p1 = [1 0; 0 1]
 2×2 Matrix{Int64}:
  1  0
  0  1
@@ -151,10 +151,10 @@
 0.0
 
 julia> Flux.kldivergence(p1, p2; eps = 0)  # about 17.3 with the regulator
-Inf
source
Flux.Losses.poisson_loss — Function
poisson_loss(ŷ, y; agg = mean)

Return how much the predicted distribution ŷ diverges from the expected Poisson distribution y; calculated as -

sum(ŷ .- y .* log.(ŷ)) / size(y, 2)

More information..

Example

julia> y_model = [1, 3, 3];  # data should only take integral values
+Inf
source
Flux.Losses.poisson_loss — Function
poisson_loss(ŷ, y; agg = mean)

Return how much the predicted distribution ŷ diverges from the expected Poisson distribution y; calculated as -

sum(ŷ .- y .* log.(ŷ)) / size(y, 2)

More information..

Example

julia> y_model = [1, 3, 3];  # data should only take integral values
 
 julia> Flux.poisson_loss(y_model, 1:3)
-0.5023128522198171
source
Flux.Losses.hinge_loss — Function
hinge_loss(ŷ, y; agg = mean)

Return the hinge_loss given the prediction ŷ and true labels y (containing 1 or -1); calculated as

sum(max.(0, 1 .- ŷ .* y)) / size(y, 2)

Usually used with classifiers like Support Vector Machines. See also: squared_hinge_loss

Example

julia> y_true = [1, -1, 1, 1];
+0.5023128522198171
source
Flux.Losses.hinge_loss — Function
hinge_loss(ŷ, y; agg = mean)

Return the hinge_loss given the prediction ŷ and true labels y (containing 1 or -1); calculated as

sum(max.(0, 1 .- ŷ .* y)) / size(y, 2)

Usually used with classifiers like Support Vector Machines. See also: squared_hinge_loss

Example

julia> y_true = [1, -1, 1, 1];
 
 julia> y_pred = [0.1, 0.3, 1, 1.5];
 
@@ -168,7 +168,7 @@
 true
 
 julia> Flux.hinge_loss(y_pred[2], y_true[2]) != 0 # opposite signs
-true
source
Flux.Losses.squared_hinge_loss — Function
squared_hinge_loss(ŷ, y)

Return the squared hinge_loss loss given the prediction ŷ and true labels y (containing 1 or -1); calculated as

sum((max.(0, 1 .- ŷ .* y)).^2) / size(y, 2)

Usually used with classifiers like Support Vector Machines. See also: hinge_loss

Example

julia> y_true = [1, -1, 1, 1];
+true
source
Flux.Losses.squared_hinge_loss — Function
squared_hinge_loss(ŷ, y)

Return the squared hinge_loss loss given the prediction ŷ and true labels y (containing 1 or -1); calculated as

sum((max.(0, 1 .- ŷ .* y)).^2) / size(y, 2)

Usually used with classifiers like Support Vector Machines. See also: hinge_loss

Example

julia> y_true = [1, -1, 1, 1];
 
 julia> y_pred = [0.1, 0.3, 1, 1.5];
 
@@ -182,13 +182,13 @@
 true
 
 julia> Flux.squared_hinge_loss(y_pred[2], y_true[2]) != 0
-true
source
Flux.Losses.dice_coeff_loss — Function
dice_coeff_loss(ŷ, y; smooth = 1)

Return a loss based on the dice coefficient. Used in the V-Net image segmentation architecture. The dice coefficient is similar to the F1_score. Loss calculated as:

1 - 2*sum(|ŷ .* y| + smooth) / (sum(ŷ.^2) + sum(y.^2) + smooth)

Example

julia> y_pred = [1.1, 2.1, 3.1];
+true
source
Flux.Losses.dice_coeff_loss — Function
dice_coeff_loss(ŷ, y; smooth = 1)

Return a loss based on the dice coefficient. Used in the V-Net image segmentation architecture. The dice coefficient is similar to the F1_score. Loss calculated as:

1 - 2*sum(|ŷ .* y| + smooth) / (sum(ŷ.^2) + sum(y.^2) + smooth)

Example

julia> y_pred = [1.1, 2.1, 3.1];
 
 julia> Flux.dice_coeff_loss(y_pred, 1:3)
 0.000992391663909964
 
 julia> 1 - Flux.dice_coeff_loss(y_pred, 1:3)  # ~ F1 score for image segmentation
-0.99900760833609
source
Flux.Losses.tversky_loss — Function
tversky_loss(ŷ, y; beta = 0.7)

Return the Tversky loss. Used with imbalanced data to give more weight to false negatives. Larger β == beta weigh recall more than precision (by placing more emphasis on false negatives). Calculated as:

1 - sum(|y .* ŷ| + 1) / (sum(y .* ŷ + (1 - β)*(1 .- y) .* ŷ + β*y .* (1 .- ŷ)) + 1)
source
Flux.Losses.binary_focal_loss — Function
binary_focal_loss(ŷ, y; agg=mean, gamma=2, eps=eps(eltype(ŷ)))

Return the binaryfocalloss The input, 'ŷ', is expected to be normalized (i.e. softmax output).

For gamma = 0, the loss is mathematically equivalent to Losses.binarycrossentropy.

See also: Losses.focal_loss for multi-class setting

Example

julia> y = [0  1  0
+0.99900760833609
source
Flux.Losses.tversky_loss — Function
tversky_loss(ŷ, y; beta = 0.7)

Return the Tversky loss. Used with imbalanced data to give more weight to false negatives. Larger β == beta weigh recall more than precision (by placing more emphasis on false negatives). Calculated as:

1 - sum(|y .* ŷ| + 1) / (sum(y .* ŷ + (1 - β)*(1 .- y) .* ŷ + β*y .* (1 .- ŷ)) + 1)
source
Flux.Losses.binary_focal_loss — Function
binary_focal_loss(ŷ, y; agg=mean, gamma=2, eps=eps(eltype(ŷ)))

Return the binaryfocalloss The input, 'ŷ', is expected to be normalized (i.e. softmax output).

For gamma = 0, the loss is mathematically equivalent to Losses.binarycrossentropy.

See also: Losses.focal_loss for multi-class setting

Example

julia> y = [0  1  0
             1  0  1]
 2×3 Matrix{Int64}:
  0  1  0
@@ -201,7 +201,7 @@
  0.731059  0.5  0.731059
 
 julia> Flux.binary_focal_loss(ŷ, y) ≈ 0.0728675615927385
-true
source
Flux.Losses.focal_loss — Function
focal_loss(ŷ, y; dims=1, agg=mean, gamma=2, eps=eps(eltype(ŷ)))

Return the focal_loss which can be used in classification tasks with highly imbalanced classes. It down-weights well-classified examples and focuses on hard examples. The input, 'ŷ', is expected to be normalized (i.e. softmax output).

The modulating factor, γ == gamma, controls the down-weighting strength. For γ == 0, the loss is mathematically equivalent to Losses.crossentropy.

Example

julia> y = [1  0  0  0  1
+true
source
Flux.Losses.focal_loss — Function
focal_loss(ŷ, y; dims=1, agg=mean, gamma=2, eps=eps(eltype(ŷ)))

Return the focal_loss which can be used in classification tasks with highly imbalanced classes. It down-weights well-classified examples and focuses on hard examples. The input, 'ŷ', is expected to be normalized (i.e. softmax output).

The modulating factor, γ == gamma, controls the down-weighting strength. For γ == 0, the loss is mathematically equivalent to Losses.crossentropy.

Example

julia> y = [1  0  0  0  1
             0  1  0  1  0
             0  0  1  0  0]
 3×5 Matrix{Int64}:
@@ -216,10 +216,10 @@
  0.665241   0.665241   0.665241   0.665241   0.665241
 
 julia> Flux.focal_loss(ŷ, y) ≈ 1.1277571935622628
-true

See also: Losses.binary_focal_loss for binary (not one-hot) labels

source
Flux.Losses.siamese_contrastive_loss — Function
siamese_contrastive_loss(ŷ, y; margin = 1, agg = mean)

Return the contrastive loss which can be useful for training Siamese Networks. It is given by

agg(@. (1 - y) * ŷ^2 + y * max(0, margin - ŷ)^2)

Specify margin to set the baseline for distance at which pairs are dissimilar.

Example

julia> ŷ = [0.5, 1.5, 2.5];
+true

See also: Losses.binary_focal_loss for binary (not one-hot) labels

source
Flux.Losses.siamese_contrastive_loss — Function
siamese_contrastive_loss(ŷ, y; margin = 1, agg = mean)

Return the contrastive loss which can be useful for training Siamese Networks. It is given by

agg(@. (1 - y) * ŷ^2 + y * max(0, margin - ŷ)^2)

Specify margin to set the baseline for distance at which pairs are dissimilar.

Example

julia> ŷ = [0.5, 1.5, 2.5];
 
 julia> Flux.siamese_contrastive_loss(ŷ, 1:3)
 -4.833333333333333
 
 julia> Flux.siamese_contrastive_loss(ŷ, 1:3, margin = 2)
--4.0
source
+-4.0source diff --git a/dev/reference/outputsize/index.html b/dev/reference/outputsize/index.html index a81a6f7bd1..baa0fc5a1c 100644 --- a/dev/reference/outputsize/index.html +++ b/dev/reference/outputsize/index.html @@ -68,7 +68,7 @@ # plus 2 non-trainable, 10 parameters, summarysize 10.469 KiB. julia> outputsize(ans, (28, 28, 1, 32)) -(10, 32)

Limitations:

source
Flux.outputsize — Function
outputsize(m, x_size, y_size, ...; padbatch=false)

For model or layer m accepting multiple arrays as input, this returns size(m((x, y, ...))) given size_x = size(x), etc.

Examples

julia> x, y = rand(Float32, 5, 64), rand(Float32, 7, 64);
+(10, 32)

Limitations:

  • While @autosize (5, 32) Flux.Bilinear(_ => 7) is OK, something like Bilinear((_, _) => 7) will fail.
  • While Scale(_) and LayerNorm(_) are fine (and use the first dimension), Scale(_,_) and LayerNorm(_,_) will fail if size(x,1) != size(x,2).
source
Flux.outputsize — Function
outputsize(m, x_size, y_size, ...; padbatch=false)

For model or layer m accepting multiple arrays as input, this returns size(m((x, y, ...))) given size_x = size(x), etc.

Examples

julia> x, y = rand(Float32, 5, 64), rand(Float32, 7, 64);
 
 julia> par = Parallel(vcat, Dense(5 => 9), Dense(7 => 11));
 
@@ -81,4 +81,4 @@
 (13, 1)
 
 julia> par(x, y) == par((x, y)) == Chain(par, identity)((x, y))
-true

Notice that Chain only accepts multiple arrays as a tuple, while Parallel also accepts them as multiple arguments; outputsize always supplies the tuple.

source
+true

Notice that Chain only accepts multiple arrays as a tuple, while Parallel also accepts them as multiple arguments; outputsize always supplies the tuple.

source diff --git a/dev/reference/training/callbacks/index.html b/dev/reference/training/callbacks/index.html index d6f4160900..72bf18865f 100644 --- a/dev/reference/training/callbacks/index.html +++ b/dev/reference/training/callbacks/index.html @@ -10,7 +10,7 @@ sleep(1) end Flux -Fluxsource

Patience Helpers

Flux provides utilities for controlling your training procedure according to some monitored condition and a maximum patience. For example, you can use early_stopping to stop training when the model is converging or deteriorating, or you can use plateau to check if the model is stagnating.

For example, below we create a pseudo-loss function that decreases, bottoms out, and then increases. The early stopping trigger will break the loop before the loss increases too much.

# create a pseudo-loss that decreases for 4 calls, then starts increasing
+Flux
source

Patience Helpers

Flux provides utilities for controlling your training procedure according to some monitored condition and a maximum patience. For example, you can use early_stopping to stop training when the model is converging or deteriorating, or you can use plateau to check if the model is stagnating.

For example, below we create a pseudo-loss function that decreases, bottoms out, and then increases. The early stopping trigger will break the loop before the loss increases too much.

# create a pseudo-loss that decreases for 4 calls, then starts increasing
 # we call this like loss()
 loss = let t = 0
   () -> begin
@@ -61,7 +61,7 @@
        end
 [ Info: Epoch 1
 [ Info: Epoch 2
-[ Info: Epoch 3
source
Flux.early_stopping — Function
early_stopping(f, delay; distance = -, init_score = 0, min_dist = 0)

Return a function that internally counts by one when distance(best_score, f(...)) <= min_dist, where best_score is the last seen best value of f(...). If the count is greater than or equal to delay, the function returns true, otherwise it returns false. The count is reset when distance(best_score, f(...)) > min_dist.

Examples

julia> loss = let l = 0
+[ Info: Epoch 3
source
Flux.early_stopping — Function
early_stopping(f, delay; distance = -, init_score = 0, min_dist = 0)

Return a function that internally counts by one when distance(best_score, f(...)) <= min_dist, where best_score is the last seen best value of f(...). If the count is greater than or equal to delay, the function returns true, otherwise it returns false. The count is reset when distance(best_score, f(...)) > min_dist.

Examples

julia> loss = let l = 0
          () -> l += 1
        end; # pseudo loss function that returns increasing values
 
@@ -74,7 +74,7 @@
        end
 [ Info: Epoch 1
 [ Info: Epoch 2
-[ Info: Epoch 3
source
Flux.plateau — Function
plateau(f, width; distance = -, init_score = 0, min_dist = 1f-6)

Return a function that internally counts by one when abs(distance(last_score, f(...))) <= min_dist, where last_score holds the last value of f(...). If the count is greater than or equal to width, the function returns true, otherwise it returns false. The count is reset when abs(distance(last_score, f(...))) > min_dist.

Examples

julia> f = let v = 10
+[ Info: Epoch 3
source
Flux.plateau — Function
plateau(f, width; distance = -, init_score = 0, min_dist = 1f-6)

Return a function that internally counts by one when abs(distance(last_score, f(...))) <= min_dist, where last_score holds the last value of f(...). If the count is greater than or equal to width, the function returns true, otherwise it returns false. The count is reset when abs(distance(last_score, f(...))) > min_dist.

Examples

julia> f = let v = 10
          () -> v = v / abs(v) - v
        end; # -9, 8, -7, 6, ...
 
@@ -88,4 +88,4 @@
 [ Info: Epoch 1
 [ Info: Epoch 2
 [ Info: Epoch 3
-[ Info: Epoch 4
source
+[ Info: Epoch 4source diff --git a/dev/reference/training/reference/index.html b/dev/reference/training/reference/index.html index 43dd7c83ec..d57c243544 100644 --- a/dev/reference/training/reference/index.html +++ b/dev/reference/training/reference/index.html @@ -19,14 +19,14 @@ 10.19 julia> opt_state # mutated by Flux.train! -(weight = Leaf(Momentum(0.1, 0.9), [-2.018 3.027]), bias = Leaf(Momentum(0.1, 0.9), [-10.09]), σ = ())source
Flux.Optimise.train! — Method
train!(loss, model, data, opt_state)

Uses a loss function and training data to improve the model's parameters according to a particular optimisation rule encoded in opt_state. Iterates through data once, evaluating for each d in data either loss(model, d...) if d isa Tuple, or else loss(model, d) for other d.

If model is an Enzyme.Duplicated and Enzyme.jl is loaded, gradients will be computed with Enzyme, otherwise they will be computed with Zygote.

For example, with these definitions...

data = [(x1, y1), (x2, y2), (x3, y3)]
+(weight = Leaf(Momentum(0.1, 0.9), [-2.018 3.027]), bias = Leaf(Momentum(0.1, 0.9), [-10.09]), σ = ())
source
Flux.Optimise.train! — Method
train!(loss, model, data, opt_state)

Uses a loss function and training data to improve the model's parameters according to a particular optimisation rule encoded in opt_state. Iterates through data once, evaluating for each d in data either loss(model, d...) if d isa Tuple, or else loss(model, d) for other d.

If model is an Enzyme.Duplicated and Enzyme.jl is loaded, gradients will be computed with Enzyme, otherwise they will be computed with Zygote.

For example, with these definitions...

data = [(x1, y1), (x2, y2), (x3, y3)]
 
 loss3(m, x, y) = norm(m(x) .- y)        # the model is the first argument
 
 opt_state = Flux.setup(Adam(), model)   # explicit setup of optimiser momenta

...calling Flux.train!(loss3, model, data, opt_state) runs a loop much like this:

for d in data
     ∂L∂m = gradient(loss3, model, d...)[1]
     update!(opt_state, model, ∂L∂m)
-end

You can also write this loop yourself, if you need more flexibility. For this reason train! is not highly extensible. It adds only a few features to the loop above:

  • Stop with a DomainError if the loss is infinite or NaN at any point.

  • Show a progress bar using @withprogress.

New

This method was added in Flux 0.13.9. It has significant changes from the one used by Flux ≤ 0.13:

  • It now takes the model itself, not the result of Flux.params. (This is to move away from Zygote's "implicit" parameter handling, with Grads.)
  • Instead of loss being a function which accepts only the data, now it must also accept the model itself, as the first argument.
  • opt_state should be the result of Flux.setup. Using an optimiser such as Adam() without this step should give you a warning.
  • Callback functions are not supported. (But any code can be included in the above for loop.)
source
Optimisers.update — Function
Optimisers.update(tree, model, gradient) -> (tree, model)

Uses the optimiser and the gradient to change the trainable parameters in the model. Returns the improved model, and the optimiser states needed for the next update. The initial tree of states comes from setup.

See also update!, which will be faster for models of ordinary Arrays or CuArrays.

Example

julia> m = (x = Float32[1,2,3], y = tanh);
+end

You can also write this loop yourself, if you need more flexibility. For this reason train! is not highly extensible. It adds only a few features to the loop above:

  • Stop with a DomainError if the loss is infinite or NaN at any point.

  • Show a progress bar using @withprogress.

New

This method was added in Flux 0.13.9. It has significant changes from the one used by Flux ≤ 0.13:

  • It now takes the model itself, not the result of Flux.params. (This is to move away from Zygote's "implicit" parameter handling, with Grads.)
  • Instead of loss being a function which accepts only the data, now it must also accept the model itself, as the first argument.
  • opt_state should be the result of Flux.setup. Using an optimiser such as Adam() without this step should give you a warning.
  • Callback functions are not supported. (But any code can be included in the above for loop.)
source
Optimisers.update — Function
Optimisers.update(tree, model, gradient) -> (tree, model)

Uses the optimiser and the gradient to change the trainable parameters in the model. Returns the improved model, and the optimiser states needed for the next update. The initial tree of states comes from setup.

See also update!, which will be faster for models of ordinary Arrays or CuArrays.

Example

julia> m = (x = Float32[1,2,3], y = tanh);
 
 julia> t = Optimisers.setup(Descent(0.1), m)
 (x = Leaf(Descent(0.1), nothing), y = ())
diff --git a/dev/reference/utilities/index.html b/dev/reference/utilities/index.html
index 19eefc80df..908c911c5a 100644
--- a/dev/reference/utilities/index.html
+++ b/dev/reference/utilities/index.html
@@ -32,7 +32,7 @@
 julia> ans.bias
 2-element Vector{Float32}:
  0.0
- 0.0

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
Flux.glorot_normal — Function
glorot_normal([rng], size...; gain = 1) -> Array
+ 0.0

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
Flux.glorot_normal — Function
glorot_normal([rng], size...; gain = 1) -> Array
 glorot_normal([rng]; kw...) -> Function

Return an Array{Float32} of the given size containing random numbers drawn from a normal distribution with standard deviation gain * sqrt(2 / (fan_in + fan_out)), using nfan.

This method is described in [1] and also known as Xavier initialization.

Examples

julia> using Statistics
 
 julia> round(std(Flux.glorot_normal(10, 1000)), digits=3)
@@ -48,7 +48,7 @@
 Dense(10 => 1000, tanh)  # 11_000 parameters
 
 julia> round(std(ans.weight), sigdigits=3)
-4.45f0

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
Flux.kaiming_uniform — Function
kaiming_uniform([rng], size...; gain = √2) -> Array
+4.45f0

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
Flux.kaiming_uniform — Function
kaiming_uniform([rng], size...; gain = √2) -> Array
 kaiming_uniform([rng]; kw...) -> Function

Return an Array{Float32} of the given size containing random numbers drawn from a uniform distribution on the interval [-x, x], where x = gain * sqrt(3/fan_in) using nfan.

This method is described in [1] and also known as He initialization.

Examples

julia> round.(extrema(Flux.kaiming_uniform(100, 10)), digits=3)
 (-0.774f0, 0.773f0)
 
@@ -56,7 +56,7 @@
 (-0.243f0, 0.245f0)
 
 julia> round.(extrema(Flux.kaiming_uniform(100, 100)), digits=3)
-(-0.245f0, 0.245f0)

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
Flux.kaiming_normal — Function
kaiming_normal([rng], size...; gain = √2) -> Array
+(-0.245f0, 0.245f0)

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
Flux.kaiming_normal — Function
kaiming_normal([rng], size...; gain = √2) -> Array
 kaiming_normal([rng]; kw...) -> Function

Return an Array{Float32} of the given size containing random numbers taken from a normal distribution standard deviation gain / sqrt(fan_in), using nfan.

This method is described in [1] and also known as He initialization.

Examples

julia> using Statistics
 
 julia> round(std(Flux.kaiming_normal(10, 1000)), digits=3)
@@ -66,7 +66,7 @@
 0.45f0
 
 julia> round(std(Flux.kaiming_normal(1000, 1000)), digits=3)
-0.045f0

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
Flux.truncated_normal — Function
truncated_normal([rng], size...; mean = 0, std = 1, lo = -2, hi = 2) -> Array
+0.045f0

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
Flux.truncated_normal — Function
truncated_normal([rng], size...; mean = 0, std = 1, lo = -2, hi = 2) -> Array
 truncated_normal([rng]; kw...) -> Function

Return an Array{Float32} 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)).

The values are generated by sampling a Uniform(0, 1) (rand()) and then applying the inverse CDF of the truncated normal distribution. This method works best when lo ≤ mean ≤ hi.

Examples

julia> using Statistics
 
 julia> Flux.truncated_normal(3, 4) |> summary
@@ -76,7 +76,7 @@
 (-2.0f0, 2.0f0)
 
 julia> round(std(Flux.truncated_normal(10^6; lo = -100, hi = 100)))
-1.0f0
source
Flux.lecun_normal — Function
lecun_normal([rng], size...) -> Array
+1.0f0
source
Flux.lecun_normal — Function
lecun_normal([rng], size...) -> Array
 lecun_normal([rng]; kw...) -> Function

Return an Array{Float32} of the given size containing random numbers drawn from a truncated normal distribution centered on 0 with stddev sqrt(1 / fan_in), where fan_in is the number of input units in the weight tensor.

Examples

julia> using Statistics
 
 julia> round(std(Flux.lecun_normal(10, 1000)), digits=3)
@@ -92,7 +92,7 @@
 Dense(10 => 1000, selu)  # 11_000 parameters
 
 julia> round(std(ans.weight), digits=3)
-0.313f0

References

[1] Lecun, Yann, et al. "Efficient backprop." Neural networks: Tricks of the trade. Springer, Berlin, Heidelberg, 2012. 9-48.

source
Flux.orthogonal — Function
orthogonal([rng], size...; gain = 1) -> Array
+0.313f0

References

[1] Lecun, Yann, et al. "Efficient backprop." Neural networks: Tricks of the trade. Springer, Berlin, Heidelberg, 2012. 9-48.

source
Flux.orthogonal — Function
orthogonal([rng], size...; gain = 1) -> Array
 orthogonal([rng]; kw...) -> Function

Return an Array{Float32} of the given size which is a (semi) orthogonal matrix, as described in [1].

Cannot construct a vector, i.e. length(size) == 1 is forbidden. For length(size) > 2, a prod(size[1:(end - 1)]) by size[end] orthogonal matrix is computed before reshaping it to the original dimensions.

Examples

julia> W = Flux.orthogonal(5, 7);
 
 julia> summary(W)
@@ -112,7 +112,7 @@
 julia> W3 = Flux.orthogonal(3, 3, 2, 4);
 
 julia> transpose(reshape(W3, :, 4)) * reshape(W3, :, 4) ≈ I(4)
-true

References

[1] 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
Flux.sparse_init — Function
sparse_init([rng], rows, cols; sparsity, std = 0.01) -> Array
+true

References

[1] 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
Flux.sparse_init — Function
sparse_init([rng], rows, cols; sparsity, std = 0.01) -> Array
 sparse_init([rng]; kw...) -> Function

Return a Matrix{Float32} of size rows, cols where each column contains a fixed fraction of zero elements given by sparsity. Non-zero elements are normally distributed with a mean of zero and standard deviation std.

This method is described in [1].

Examples

julia> count(iszero, Flux.sparse_init(10, 10, sparsity=1/5))
 20
 
@@ -125,7 +125,7 @@
 
 julia> count(iszero, ans.weight, dims=1)
 1×3 Matrix{Int64}:
- 5  5  5

References

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

source
Flux.identity_init — Function
identity_init(size...; gain=1, shift=0) -> Array
+ 5  5  5

References

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

source
Flux.identity_init — Function
identity_init(size...; gain=1, shift=0) -> Array
 identity_init(; kw...) -> Function

Return an Array{Float32} of the given size which yields an identity mapping when used as parameters in most Flux layers. Use gain to scale the identity by a constant.

Often useful in the context of transfer learning, i.e when one wants to add more capacity to a model but start from the same mapping.

Has the following behaviour

  • 1D: A Vector of zeros (useful for an identity bias)
  • 2D: An identity matrix (useful for an identity matrix multiplication)
  • More than 2D: A dense block array of center tap spatial filters (useful for an identity convolution)

Some caveats:

  • Not all layers will be identity mapping when used with this init. Exceptions include recurrent layers and normalization layers.

  • Layers must have input_size == output_size for identity mapping to be possible. When this is not the case, extra dimensions of the array are padded with zeros.

  • For convolutional layers, in addition to the above, the kernel sizes must also be odd and padding must be applied so that output feature maps have the same size as input feature maps, e.g by using SamePad.

Use keyword shift (integer or tuple) to apply circular shift to the output, equivalent to Base.circshift(identity_init(size...), shift).

For consistency with other initialisers, it accepts rng::AbstractRNG as an optional first argument. But this is ignored, since the result is not random.

Examples

julia> Flux.identity_init(3,5)
 3×5 Matrix{Float32}:
  1.0  0.0  0.0  0.0  0.0
@@ -157,7 +157,7 @@
 [:, :, 1, 1] =
  10.0  20.0  30.0
  40.0  50.0  60.0
- 70.0  80.0  90.0
source
Flux.ones32 — Function
ones32(size...) = ones(Float32, size...)

Return an Array{Float32} of the given size filled with 1s.

source
Flux.zeros32 — Function
zeros32(size...) = zeros(Float32, size...)

Return an Array{Float32} of the given size filled with 0s.

source
Flux.rand32 — Function
rand32([rng], size...)

Return an Array{Float32} of the given size, filled like rand. When the size is not provided, rand32(rng::AbstractRNG) returns a function.

source
Flux.randn32 — Function
randn32([rng], size...)

Return an Array{Float32} of the given size, filled like randn. When the size is not provided, randn32(rng::AbstractRNG) returns a function.

source
Flux.create_bias — Function
create_bias(weights, bias, size...)

Return a bias parameter for a layer, based on the value given to the constructor's keyword bias=bias.

  • bias == true creates a trainable array of the given size, of the same type as weights, initialised to zero.
  • bias == false returns false, which is understood by AD to be non-differentiable.
  • bias::AbstractArray uses the array provided, provided it has the correct size. It will also correct the eltype to match that of weights.
source

These functions call:

Flux.rng_from_array — Function
rng_from_array(x)

Create an instance of the RNG most appropriate for x. As an example, if x is aCuArray, it will return a CUDA.default_rng(). If x is an Array instead, it will return a Random.default_rng().

source
Flux.nfan — Function
nfan(n_out, n_in=1) -> Tuple
+ 70.0  80.0  90.0
source
Flux.ones32 — Function
ones32(size...) = ones(Float32, size...)

Return an Array{Float32} of the given size filled with 1s.

source
Flux.zeros32 — Function
zeros32(size...) = zeros(Float32, size...)

Return an Array{Float32} of the given size filled with 0s.

source
Flux.rand32 — Function
rand32([rng], size...)

Return an Array{Float32} of the given size, filled like rand. When the size is not provided, rand32(rng::AbstractRNG) returns a function.

source
Flux.randn32 — Function
randn32([rng], size...)

Return an Array{Float32} of the given size, filled like randn. When the size is not provided, randn32(rng::AbstractRNG) returns a function.

source
Flux.create_bias — Function
create_bias(weights, bias, size...)

Return a bias parameter for a layer, based on the value given to the constructor's keyword bias=bias.

  • bias == true creates a trainable array of the given size, of the same type as weights, initialised to zero.
  • bias == false returns false, which is understood by AD to be non-differentiable.
  • bias::AbstractArray uses the array provided, provided it has the correct size. It will also correct the eltype to match that of weights.
source

These functions call:

Flux.rng_from_array — Function
rng_from_array(x)

Create an instance of the RNG most appropriate for x. As an example, if x is aCuArray, it will return a CUDA.default_rng(). If x is an Array instead, it will return a Random.default_rng().

source
Flux.nfan — Function
nfan(n_out, n_in=1) -> Tuple
 nfan(dims...)
 nfan(dims::Tuple)

For a layer characterized by dimensions dims, return a tuple (fan_in, fan_out), where fan_in is the number of input neurons connected to an output one, and fan_out is the number of output neurons connected to an input one.

This function is mainly used by weight initializers, e.g., kaiming_normal.

Examples

julia> layer = Dense(10, 20);
 
@@ -167,7 +167,7 @@
 julia> layer = Conv((3, 3), 2=>10);
 
 julia> Flux.nfan(size(layer.weight))
-(18, 90)
source

Changing the type of all parameters

The default eltype for models is Float32 since models are often trained/run on GPUs. The eltype of model m can be changed to Float64 by f64(m):

Flux.f64 — Function
f64(m)

Converts the eltype of model's floating point parameters to Float64. Recurses into structs marked with @layer.

See also f32 and f16.

source
Flux.f32 — Function
f32(m)

Converts the eltype of model's floating point parameters to Float32 (which is Flux's default). Recurses into structs marked with @layer.

See also f64 and f16.

source
Flux.f16 — Function
f16(m)

Converts the eltype of model's floating point parameters to Float16. Recurses into structs marked with @layer.

Support for Float16 is limited on many CPUs. Julia may convert to Float32 for each operation, which is slow.

See also f32 and f64.

Example

julia> m = Chain(Dense(784, 2048, relu), Dense(2048, 10))  # all Float32
+(18, 90)
source

Changing the type of all parameters

The default eltype for models is Float32 since models are often trained/run on GPUs. The eltype of model m can be changed to Float64 by f64(m):

Flux.f64 — Function
f64(m)

Converts the eltype of model's floating point parameters to Float64. Recurses into structs marked with @layer.

See also f32 and f16.

source
Flux.f32 — Function
f32(m)

Converts the eltype of model's floating point parameters to Float32 (which is Flux's default). Recurses into structs marked with @layer.

See also f64 and f16.

source
Flux.f16 — Function
f16(m)

Converts the eltype of model's floating point parameters to Float16. Recurses into structs marked with @layer.

Support for Float16 is limited on many CPUs. Julia may convert to Float32 for each operation, which is slow.

See also f32 and f64.

Example

julia> m = Chain(Dense(784, 2048, relu), Dense(2048, 10))  # all Float32
 Chain(
   Dense(784 => 2048, relu),             # 1_607_680 parameters
   Dense(2048 => 10),                    # 20_490 parameters
@@ -177,4 +177,4 @@
 Chain(
   Dense(784 => 2048, relu),             # 1_607_680 parameters
   Dense(2048 => 10),                    # 20_490 parameters
-)                   # Total: 4 arrays, 1_628_170 parameters, 3.106 MiB.
source
+) # Total: 4 arrays, 1_628_170 parameters, 3.106 MiB.source