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{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2024-12-03T09:00:05","documenter_version":"1.8.0"}}
{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2024-12-03T15:31:34","documenter_version":"1.8.0"}}
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return Affine(W, b)
end

Affine(3 =&gt; 1, bias=false) |&gt; gpu</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../overview/">« Fitting a Line</a><a class="docs-footer-nextpage" href="../custom_layers/">Custom Layers »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Tuesday 3 December 2024 09:00">Tuesday 3 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
Affine(3 =&gt; 1, bias=false) |&gt; gpu</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../overview/">« Fitting a Line</a><a class="docs-footer-nextpage" href="../custom_layers/">Custom Layers »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Tuesday 3 December 2024 15:31">Tuesday 3 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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# rms over all the mse
ŷs = model(x)
return sqrt(mean(Flux.mse(y, ŷ) for (y, ŷ) in zip(ys, ŷs)))
end</code></pre><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>This <code>Split</code> layer is available from the <a href="https://github.com/FluxML/Fluxperimental.jl">Fluxperimental.jl</a> package.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../basics/">« Gradients and Layers</a><a class="docs-footer-nextpage" href="../../training/training/">Training »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Tuesday 3 December 2024 09:00">Tuesday 3 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
end</code></pre><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>This <code>Split</code> layer is available from the <a href="https://github.com/FluxML/Fluxperimental.jl">Fluxperimental.jl</a> package.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../basics/">« Gradients and Layers</a><a class="docs-footer-nextpage" href="../../training/training/">Training »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Tuesday 3 December 2024 15:31">Tuesday 3 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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julia&gt; y_test
1×5 Matrix{Int64}:
26 30 34 38 42</code></pre><p>The predictions are good. Here&#39;s how we got there. </p><p>First, we gathered real-world data into the variables <code>x_train</code>, <code>y_train</code>, <code>x_test</code>, and <code>y_test</code>. The <code>x_*</code> data defines inputs, and the <code>y_*</code> data defines outputs. The <code>*_train</code> data is for training the model, and the <code>*_test</code> data is for verifying the model. Our data was based on the function <code>4x + 2</code>.</p><p>Then, we built a single input, single output predictive model, <code>predict = Dense(1 =&gt; 1)</code>. The initial predictions weren&#39;t accurate, because we had not trained the model yet.</p><p>After building the model, we trained it with <code>train!(loss, predict, data, opt)</code>. The loss function is first, followed by the model itself, the training data, and the <code>Descent</code> optimiser provided by Flux. We ran the training step once, and observed that the parameters changed and the loss went down. Then, we ran the <code>train!</code> many times to finish the training process.</p><p>After we trained the model, we verified it with the test data to verify the results. </p><p>This overall flow represents how Flux works. Let&#39;s drill down a bit to understand what&#39;s going on inside the individual layers of Flux.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../quickstart/">« Quick Start</a><a class="docs-footer-nextpage" href="../basics/">Gradients and Layers »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Tuesday 3 December 2024 09:00">Tuesday 3 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
26 30 34 38 42</code></pre><p>The predictions are good. Here&#39;s how we got there. </p><p>First, we gathered real-world data into the variables <code>x_train</code>, <code>y_train</code>, <code>x_test</code>, and <code>y_test</code>. The <code>x_*</code> data defines inputs, and the <code>y_*</code> data defines outputs. The <code>*_train</code> data is for training the model, and the <code>*_test</code> data is for verifying the model. Our data was based on the function <code>4x + 2</code>.</p><p>Then, we built a single input, single output predictive model, <code>predict = Dense(1 =&gt; 1)</code>. The initial predictions weren&#39;t accurate, because we had not trained the model yet.</p><p>After building the model, we trained it with <code>train!(loss, predict, data, opt)</code>. The loss function is first, followed by the model itself, the training data, and the <code>Descent</code> optimiser provided by Flux. We ran the training step once, and observed that the parameters changed and the loss went down. Then, we ran the <code>train!</code> many times to finish the training process.</p><p>After we trained the model, we verified it with the test data to verify the results. </p><p>This overall flow represents how Flux works. Let&#39;s drill down a bit to understand what&#39;s going on inside the individual layers of Flux.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../quickstart/">« Quick Start</a><a class="docs-footer-nextpage" href="../basics/">Gradients and Layers »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Tuesday 3 December 2024 15:31">Tuesday 3 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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y_hat = m(x)
Flux.logitcrossentropy(y_hat, y)
end
end</code></pre><ul><li>In our simple example, we conveniently created the model has a <a href="../../../reference/models/layers/#Flux.Chain"><code>Chain</code></a> of layers. </li></ul><p>For more complex models, you can define a custom struct <code>MyModel</code> containing layers and arrays and implement the call operator <code>(::MyModel)(x) = ...</code> to define the forward pass. This is all it is needed for Flux to work. Marking the struct with <a href="../../../reference/models/functors/#Flux.@layer"><code>Flux.@layer</code></a> will add some more functionality, like pretty printing and the ability to mark some internal fields as trainable or not (also see <a href="../../../reference/destructure/#Optimisers.trainable"><code>trainable</code></a>).</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../../">« Welcome</a><a class="docs-footer-nextpage" href="../overview/">Fitting a Line »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Tuesday 3 December 2024 09:00">Tuesday 3 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
end</code></pre><ul><li>In our simple example, we conveniently created the model has a <a href="../../../reference/models/layers/#Flux.Chain"><code>Chain</code></a> of layers. </li></ul><p>For more complex models, you can define a custom struct <code>MyModel</code> containing layers and arrays and implement the call operator <code>(::MyModel)(x) = ...</code> to define the forward pass. This is all it is needed for Flux to work. Marking the struct with <a href="../../../reference/models/functors/#Flux.@layer"><code>Flux.@layer</code></a> will add some more functionality, like pretty printing and the ability to mark some internal fields as trainable or not (also see <a href="../../../reference/destructure/#Optimisers.trainable"><code>trainable</code></a>).</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../../">« Welcome</a><a class="docs-footer-nextpage" href="../overview/">Fitting a Line »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Tuesday 3 December 2024 15:31">Tuesday 3 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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