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3-element Flux.OneHotVector:
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3-element Array{Symbol,1}:
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:b
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:a
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:b</code></pre><p>Note that these operations returned <code>OneHotVector</code> and <code>OneHotMatrix</code> rather than <code>Array</code>s. <code>OneHotVector</code>s behave like normal vectors but avoid any unnecessary cost compared to using an integer index directly. For example, multiplying a matrix with a one-hot vector simply slices out the relevant row of the matrix under the hood.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../models/nnlib/">« NNlib</a><a class="docs-footer-nextpage" href="../dataloader/">DataLoader »</a></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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Wednesday 4 March 2020 00:24">Wednesday 4 March 2020</span>. Using Julia version 1.3.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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:b</code></pre><p>Note that these operations returned <code>OneHotVector</code> and <code>OneHotMatrix</code> rather than <code>Array</code>s. <code>OneHotVector</code>s behave like normal vectors but avoid any unnecessary cost compared to using an integer index directly. For example, multiplying a matrix with a one-hot vector simply slices out the relevant row of the matrix under the hood.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../models/nnlib/">« NNlib</a><a class="docs-footer-nextpage" href="../dataloader/">DataLoader »</a></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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Wednesday 4 March 2020 00:45">Wednesday 4 March 2020</span>. Using Julia version 1.3.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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m = Dense(10, 5)
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loss(x, y) = crossentropy(softmax(m(x)), y)</code></pre><p>We can regularise this by taking the (L2) norm of the parameters, <code>m.W</code> and <code>m.b</code>.</p><pre><code class="language-julia">using LinearAlgebra
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@ -36,4 +36,4 @@ julia> activations(c, rand(10))
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Float32[0.5192045, 0.48079553]
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julia> sum(norm, ans)
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2.1166067f0</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../recurrence/">« Recurrence</a><a class="docs-footer-nextpage" href="../layers/">Model Reference »</a></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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Wednesday 4 March 2020 00:24">Wednesday 4 March 2020</span>. Using Julia version 1.3.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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2.1166067f0</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../recurrence/">« Recurrence</a><a class="docs-footer-nextpage" href="../layers/">Model Reference »</a></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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Wednesday 4 March 2020 00:45">Wednesday 4 March 2020</span>. Using Julia version 1.3.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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julia> model = Chain(Dense(10,5,relu),Dense(5,2),softmax)
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Chain(Dense(10, 5, NNlib.relu), Dense(5, 2), NNlib.softmax)
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@ -47,4 +47,4 @@ evalcb = throttle(30) do
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# Show loss
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@save "model-checkpoint.bson" model
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end</code></pre><p>This will update the <code>"model-checkpoint.bson"</code> file every thirty seconds.</p><p>You can get more advanced by saving a series of models throughout training, for example</p><pre><code class="language-julia">@save "model-$(now()).bson" model</code></pre><p>will produce a series of models like <code>"model-2018-03-06T02:57:10.41.bson"</code>. You could also store the current test set loss, so that it's easy to (for example) revert to an older copy of the model if it starts to overfit.</p><pre><code class="language-julia">@save "model-$(now()).bson" model loss = testloss()</code></pre><p>You can even store optimiser state alongside the model, to resume training exactly where you left off.</p><pre><code class="language-julia">opt = ADAM()
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@save "model-$(now()).bson" model opt</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../gpu/">« GPU Support</a><a class="docs-footer-nextpage" href="../ecosystem/">The Julia Ecosystem »</a></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Wednesday 4 March 2020 00:24">Wednesday 4 March 2020</span>. Using Julia version 1.3.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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@save "model-$(now()).bson" model opt</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../gpu/">« GPU Support</a><a class="docs-footer-nextpage" href="../ecosystem/">The Julia Ecosystem »</a></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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Wednesday 4 March 2020 00:45">Wednesday 4 March 2020</span>. Using Julia version 1.3.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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</script><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link href="../../assets/flux.css" rel="stylesheet" type="text/css"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit">Flux</span></div><form class="docs-search" action="../../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><span class="tocitem">Building Models</span><ul><li><a class="tocitem" href="../../models/basics/">Basics</a></li><li><a class="tocitem" href="../../models/recurrence/">Recurrence</a></li><li><a class="tocitem" href="../../models/regularisation/">Regularisation</a></li><li><a class="tocitem" href="../../models/layers/">Model Reference</a></li><li><a class="tocitem" href="../../models/advanced/">Advanced Model Building</a></li><li><a class="tocitem" href="../../models/nnlib/">NNlib</a></li></ul></li><li><span class="tocitem">Handling Data</span><ul><li><a class="tocitem" href="../../data/onehot/">One-Hot Encoding</a></li><li><a class="tocitem" href="../../data/dataloader/">DataLoader</a></li></ul></li><li><span class="tocitem">Training Models</span><ul><li class="is-active"><a class="tocitem" href>Optimisers</a><ul class="internal"><li><a class="tocitem" href="#Optimiser-Reference-1"><span>Optimiser Reference</span></a></li><li><a class="tocitem" href="#Optimiser-Interface-1"><span>Optimiser Interface</span></a></li><li><a class="tocitem" href="#Composing-Optimisers-1"><span>Composing Optimisers</span></a></li><li><a class="tocitem" href="#Decays-1"><span>Decays</span></a></li></ul></li><li><a class="tocitem" href="../training/">Training</a></li></ul></li><li><a class="tocitem" href="../../gpu/">GPU Support</a></li><li><a class="tocitem" href="../../saving/">Saving & Loading</a></li><li><a class="tocitem" href="../../ecosystem/">The Julia Ecosystem</a></li><li><a class="tocitem" href="../../performance/">Performance Tips</a></li><li><a class="tocitem" href="../../community/">Community</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Training Models</a></li><li class="is-active"><a href>Optimisers</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Optimisers</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/training/optimisers.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Optimisers-1"><a class="docs-heading-anchor" href="#Optimisers-1">Optimisers</a><a class="docs-heading-anchor-permalink" href="#Optimisers-1" title="Permalink"></a></h1><p>Consider a <a href="../../models/basics/">simple linear regression</a>. We create some dummy data, calculate a loss, and backpropagate to calculate gradients for the parameters <code>W</code> and <code>b</code>.</p><pre><code class="language-julia">using Flux
|
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|
||||
W = rand(2, 5)
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b = rand(2)
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@ -28,7 +28,7 @@ end</code></pre><p>Running this will alter the parameters <code>W</code> and <co
|
||||
for p in (W, b)
|
||||
update!(opt, p, grads[p])
|
||||
end</code></pre><p>An optimiser <code>update!</code> accepts a parameter and a gradient, and updates the parameter according to the chosen rule. We can also pass <code>opt</code> to our <a href="../training/">training loop</a>, which will update all parameters of the model in a loop. However, we can now easily replace <code>Descent</code> with a more advanced optimiser such as <code>ADAM</code>.</p><h2 id="Optimiser-Reference-1"><a class="docs-heading-anchor" href="#Optimiser-Reference-1">Optimiser Reference</a><a class="docs-heading-anchor-permalink" href="#Optimiser-Reference-1" title="Permalink"></a></h2><p>All optimisers return an object that, when passed to <code>train!</code>, will update the parameters passed to it.</p><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.update!" href="#Flux.Optimise.update!"><code>Flux.Optimise.update!</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">update!(opt, p, g)
|
||||
update!(opt, ps::Params, gs)</code></pre><p>Perform an update step of the parameters <code>ps</code> (or the single parameter <code>p</code>) according to optimizer <code>opt</code> and the gradients <code>gs</code> (the gradient <code>g</code>).</p><p>As a result, the parameters are mutated and the optimizer's internal state may change. </p><p>update!(x, x̄)</p><p>Update the array <code>x</code> according to <code>x .-= x̄</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/af23a5756cf7d9a83b473b1edb0924b5a28b52d3/src/optimise/train.jl#L5-L17">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.Descent" href="#Flux.Optimise.Descent"><code>Flux.Optimise.Descent</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">Descent(η)</code></pre><p>Classic gradient descent optimiser with learning rate <code>η</code>. For each parameter <code>p</code> and its gradient <code>δp</code>, this runs <code>p -= η*δp</code></p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): The amount by which the gradients are discounted before updating the weights. Defaults to <code>0.1</code>.</li></ul><p><strong>Example</strong></p><pre><code class="language-julia-repl">opt = Descent() # uses default η (0.1)
|
||||
update!(opt, ps::Params, gs)</code></pre><p>Perform an update step of the parameters <code>ps</code> (or the single parameter <code>p</code>) according to optimizer <code>opt</code> and the gradients <code>gs</code> (the gradient <code>g</code>).</p><p>As a result, the parameters are mutated and the optimizer's internal state may change. </p><p>update!(x, x̄)</p><p>Update the array <code>x</code> according to <code>x .-= x̄</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/94ba1e8ede5d834eb92f7477e272b531ecdd9d16/src/optimise/train.jl#L5-L17">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.Descent" href="#Flux.Optimise.Descent"><code>Flux.Optimise.Descent</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">Descent(η)</code></pre><p>Classic gradient descent optimiser with learning rate <code>η</code>. For each parameter <code>p</code> and its gradient <code>δp</code>, this runs <code>p -= η*δp</code></p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): The amount by which the gradients are discounted before updating the weights. Defaults to <code>0.1</code>.</li></ul><p><strong>Example</strong></p><pre><code class="language-julia-repl">opt = Descent() # uses default η (0.1)
|
||||
|
||||
opt = Descent(0.3) # use provided η
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@ -38,23 +38,23 @@ gs = gradient(ps) do
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loss(x, y)
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||||
end
|
||||
|
||||
Flux.Optimise.update!(opt, ps, gs)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/af23a5756cf7d9a83b473b1edb0924b5a28b52d3/src/optimise/optimisers.jl#L8-L31">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.Momentum" href="#Flux.Optimise.Momentum"><code>Flux.Optimise.Momentum</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">Momentum(η, ρ)</code></pre><p>Gradient descent with learning rate <code>η</code> and momentum <code>ρ</code>.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (<code>η</code>): Amount by which gradients are discounted before updating the weights. Defaults to <code>0.01</code>.</li><li>Momentum (<code>ρ</code>): Parameter that accelerates descent in the relevant direction and dampens oscillations. Defaults to <code>0.9</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = Momentum() # uses defaults of η = 0.01 and ρ = 0.9
|
||||
Flux.Optimise.update!(opt, ps, gs)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/94ba1e8ede5d834eb92f7477e272b531ecdd9d16/src/optimise/optimisers.jl#L8-L31">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.Momentum" href="#Flux.Optimise.Momentum"><code>Flux.Optimise.Momentum</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">Momentum(η, ρ)</code></pre><p>Gradient descent with learning rate <code>η</code> and momentum <code>ρ</code>.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (<code>η</code>): Amount by which gradients are discounted before updating the weights. Defaults to <code>0.01</code>.</li><li>Momentum (<code>ρ</code>): Parameter that accelerates descent in the relevant direction and dampens oscillations. Defaults to <code>0.9</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = Momentum() # uses defaults of η = 0.01 and ρ = 0.9
|
||||
|
||||
opt = Momentum(0.01, 0.99)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/af23a5756cf7d9a83b473b1edb0924b5a28b52d3/src/optimise/optimisers.jl#L42-L57">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.Nesterov" href="#Flux.Optimise.Nesterov"><code>Flux.Optimise.Nesterov</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">Nesterov(η, ρ)</code></pre><p>Gradient descent with learning rate <code>η</code> and Nesterov momentum <code>ρ</code>.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Amount by which the gradients are dicsounted berfore updating the weights. Defaults to <code>0.001</code>.</li><li>Nesterov Momentum (ρ): Parameters controlling the amount of nesterov momentum to be applied. Defaults to <code>0.9</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = Nesterov() # uses defaults η = 0.001 and ρ = 0.9
|
||||
opt = Momentum(0.01, 0.99)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/94ba1e8ede5d834eb92f7477e272b531ecdd9d16/src/optimise/optimisers.jl#L42-L57">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.Nesterov" href="#Flux.Optimise.Nesterov"><code>Flux.Optimise.Nesterov</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">Nesterov(η, ρ)</code></pre><p>Gradient descent with learning rate <code>η</code> and Nesterov momentum <code>ρ</code>.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Amount by which the gradients are dicsounted berfore updating the weights. Defaults to <code>0.001</code>.</li><li>Nesterov Momentum (ρ): Parameters controlling the amount of nesterov momentum to be applied. Defaults to <code>0.9</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = Nesterov() # uses defaults η = 0.001 and ρ = 0.9
|
||||
|
||||
opt = Nesterov(0.003, 0.95)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/af23a5756cf7d9a83b473b1edb0924b5a28b52d3/src/optimise/optimisers.jl#L73-L88">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.RMSProp" href="#Flux.Optimise.RMSProp"><code>Flux.Optimise.RMSProp</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">RMSProp(η, ρ)</code></pre><p>Implements the RMSProp algortihm. Often a good choice for recurrent networks. Parameters other than learning rate generally don't need tuning.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Defaults to <code>0.001</code>.</li><li>Rho (ρ): Defaults to <code>0.9</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = RMSProp() # uses default η = 0.001 and ρ = 0.9
|
||||
opt = Nesterov(0.003, 0.95)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/94ba1e8ede5d834eb92f7477e272b531ecdd9d16/src/optimise/optimisers.jl#L73-L88">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.RMSProp" href="#Flux.Optimise.RMSProp"><code>Flux.Optimise.RMSProp</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">RMSProp(η, ρ)</code></pre><p>Implements the RMSProp algortihm. Often a good choice for recurrent networks. Parameters other than learning rate generally don't need tuning.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Defaults to <code>0.001</code>.</li><li>Rho (ρ): Defaults to <code>0.9</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = RMSProp() # uses default η = 0.001 and ρ = 0.9
|
||||
|
||||
opt = RMSProp(0.002, 0.95)</code></pre><p><strong>References</strong></p><p><a href="https://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf">RMSProp</a></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/af23a5756cf7d9a83b473b1edb0924b5a28b52d3/src/optimise/optimisers.jl#L105-L123">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.ADAM" href="#Flux.Optimise.ADAM"><code>Flux.Optimise.ADAM</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">ADAM(η, β::Tuple)</code></pre><p>Implements the ADAM optimiser.</p><p><strong>Paramters</strong></p><ul><li>Learning Rate (<code>η</code>): Defaults to <code>0.001</code>.</li><li>Beta (<code>β::Tuple</code>): The first element refers to β1 and the second to β2. Defaults to <code>(0.9, 0.999)</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = ADAM() # uses the default η = 0.001 and β = (0.9, 0.999)
|
||||
opt = RMSProp(0.002, 0.95)</code></pre><p><strong>References</strong></p><p><a href="https://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf">RMSProp</a></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/94ba1e8ede5d834eb92f7477e272b531ecdd9d16/src/optimise/optimisers.jl#L105-L123">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.ADAM" href="#Flux.Optimise.ADAM"><code>Flux.Optimise.ADAM</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">ADAM(η, β::Tuple)</code></pre><p>Implements the ADAM optimiser.</p><p><strong>Paramters</strong></p><ul><li>Learning Rate (<code>η</code>): Defaults to <code>0.001</code>.</li><li>Beta (<code>β::Tuple</code>): The first element refers to β1 and the second to β2. Defaults to <code>(0.9, 0.999)</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = ADAM() # uses the default η = 0.001 and β = (0.9, 0.999)
|
||||
|
||||
opt = ADAM(0.001, (0.9, 0.8))</code></pre><p><strong>References</strong></p><p><a href="https://arxiv.org/abs/1412.6980v8">ADAM</a> optimiser.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/af23a5756cf7d9a83b473b1edb0924b5a28b52d3/src/optimise/optimisers.jl#L139-L157">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.AdaMax" href="#Flux.Optimise.AdaMax"><code>Flux.Optimise.AdaMax</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">AdaMax(η, β::Tuple)</code></pre><p>Variant of ADAM based on ∞-norm.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Defaults to <code>0.001</code></li><li>Beta (β::Tuple): The first element refers to β1 and the second to β2. Defaults to <code>(0.9, 0.999)</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = AdaMax() # uses default η and β
|
||||
opt = ADAM(0.001, (0.9, 0.8))</code></pre><p><strong>References</strong></p><p><a href="https://arxiv.org/abs/1412.6980v8">ADAM</a> optimiser.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/94ba1e8ede5d834eb92f7477e272b531ecdd9d16/src/optimise/optimisers.jl#L139-L157">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.AdaMax" href="#Flux.Optimise.AdaMax"><code>Flux.Optimise.AdaMax</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">AdaMax(η, β::Tuple)</code></pre><p>Variant of ADAM based on ∞-norm.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Defaults to <code>0.001</code></li><li>Beta (β::Tuple): The first element refers to β1 and the second to β2. Defaults to <code>(0.9, 0.999)</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = AdaMax() # uses default η and β
|
||||
|
||||
opt = AdaMax(0.001, (0.9, 0.995))</code></pre><p><strong>References</strong></p><p><a href="https://arxiv.org/abs/1412.6980v9">AdaMax</a> optimiser.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/af23a5756cf7d9a83b473b1edb0924b5a28b52d3/src/optimise/optimisers.jl#L221-L238">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.ADAGrad" href="#Flux.Optimise.ADAGrad"><code>Flux.Optimise.ADAGrad</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">ADAGrad(η)</code></pre><p>Implements AdaGrad. It has parameter specific learning rates based on how frequently it is updated.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Defaults to <code>0.1</code></li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = ADAGrad() # uses default η = 0.1
|
||||
opt = AdaMax(0.001, (0.9, 0.995))</code></pre><p><strong>References</strong></p><p><a href="https://arxiv.org/abs/1412.6980v9">AdaMax</a> optimiser.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/94ba1e8ede5d834eb92f7477e272b531ecdd9d16/src/optimise/optimisers.jl#L221-L238">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.ADAGrad" href="#Flux.Optimise.ADAGrad"><code>Flux.Optimise.ADAGrad</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">ADAGrad(η)</code></pre><p>Implements AdaGrad. It has parameter specific learning rates based on how frequently it is updated.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Defaults to <code>0.1</code></li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = ADAGrad() # uses default η = 0.1
|
||||
|
||||
opt = ADAGrad(0.001)</code></pre><p><strong>References</strong></p><p><a href="http://www.jmlr.org/papers/volume12/duchi11a/duchi11a.pdf">ADAGrad</a> optimiser. Parameters don't need tuning.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/af23a5756cf7d9a83b473b1edb0924b5a28b52d3/src/optimise/optimisers.jl#L257-L275">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.ADADelta" href="#Flux.Optimise.ADADelta"><code>Flux.Optimise.ADADelta</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">ADADelta(ρ)</code></pre><p>Version of ADAGrad that adapts learning rate based on a window of past gradient updates. Parameters don't need tuning.</p><p><strong>Parameters</strong></p><ul><li>Rho (ρ): Factor by which gradient is decayed at each time step. Defaults to <code>0.9</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = ADADelta() # uses default ρ = 0.9
|
||||
opt = ADADelta(0.89)</code></pre><p><strong>References</strong></p><p><a href="https://arxiv.org/abs/1212.5701">ADADelta</a> optimiser.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/af23a5756cf7d9a83b473b1edb0924b5a28b52d3/src/optimise/optimisers.jl#L290-L306">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.AMSGrad" href="#Flux.Optimise.AMSGrad"><code>Flux.Optimise.AMSGrad</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">AMSGrad(η, β::Tuple)</code></pre><p>Implements AMSGrad version of the ADAM optimiser. Parameters don't need tuning.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Defaults to <code>0.001</code>.</li><li>Beta (β::Tuple): The first element refers to β1 and the second to β2. Defaults to <code>(0.9, 0.999)</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = AMSGrad() # uses default η and β
|
||||
opt = AMSGrad(0.001, (0.89, 0.995))</code></pre><p><strong>References</strong></p><p><a href="https://openreview.net/forum?id=ryQu7f-RZ">AMSGrad</a> optimiser.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/af23a5756cf7d9a83b473b1edb0924b5a28b52d3/src/optimise/optimisers.jl#L323-L340">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.NADAM" href="#Flux.Optimise.NADAM"><code>Flux.Optimise.NADAM</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">NADAM(η, β::Tuple)</code></pre><p>Nesterov variant of ADAM. Parameters don't need tuning.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Defaults to <code>0.001</code>.</li><li>Beta (β::Tuple): The first element refers to β1 and the second to β2. Defaults to <code>(0.9, 0.999)</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = NADAM() # uses default η and β
|
||||
opt = NADAM(0.002, (0.89, 0.995))</code></pre><p><strong>References</strong></p><p><a href="http://cs229.stanford.edu/proj2015/054_report.pdf">NADAM</a> optimiser.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/af23a5756cf7d9a83b473b1edb0924b5a28b52d3/src/optimise/optimisers.jl#L358-L375">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.ADAMW" href="#Flux.Optimise.ADAMW"><code>Flux.Optimise.ADAMW</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">ADAMW(η, β::Tuple, decay)</code></pre><p>Variant of ADAM defined by fixing weight decay regularization.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Defaults to <code>0.001</code>.</li><li>Beta (β::Tuple): The first element refers to β1 and the second to β2. Defaults to (0.9, 0.999).</li><li>decay: Decay applied to weights during optimisation. Defaults to 0.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = ADAMW() # uses default η, β and decay
|
||||
opt = ADAMW(0.001, (0.89, 0.995), 0.1)</code></pre><p><strong>References</strong></p><p><a href="https://arxiv.org/abs/1711.05101">ADAMW</a></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/af23a5756cf7d9a83b473b1edb0924b5a28b52d3/src/optimise/optimisers.jl#L394-L412">source</a></section></article><h2 id="Optimiser-Interface-1"><a class="docs-heading-anchor" href="#Optimiser-Interface-1">Optimiser Interface</a><a class="docs-heading-anchor-permalink" href="#Optimiser-Interface-1" title="Permalink"></a></h2><p>Flux's optimisers are built around a <code>struct</code> that holds all the optimiser parameters along with a definition of how to apply the update rule associated with it. We do this via the <code>apply!</code> function which takes the optimiser as the first argument followed by the parameter and its corresponding gradient.</p><p>In this manner Flux also allows one to create custom optimisers to be used seamlessly. Let's work this with a simple example.</p><pre><code class="language-julia">mutable struct Momentum
|
||||
opt = ADAGrad(0.001)</code></pre><p><strong>References</strong></p><p><a href="http://www.jmlr.org/papers/volume12/duchi11a/duchi11a.pdf">ADAGrad</a> optimiser. Parameters don't need tuning.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/94ba1e8ede5d834eb92f7477e272b531ecdd9d16/src/optimise/optimisers.jl#L257-L275">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.ADADelta" href="#Flux.Optimise.ADADelta"><code>Flux.Optimise.ADADelta</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">ADADelta(ρ)</code></pre><p>Version of ADAGrad that adapts learning rate based on a window of past gradient updates. Parameters don't need tuning.</p><p><strong>Parameters</strong></p><ul><li>Rho (ρ): Factor by which gradient is decayed at each time step. Defaults to <code>0.9</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = ADADelta() # uses default ρ = 0.9
|
||||
opt = ADADelta(0.89)</code></pre><p><strong>References</strong></p><p><a href="https://arxiv.org/abs/1212.5701">ADADelta</a> optimiser.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/94ba1e8ede5d834eb92f7477e272b531ecdd9d16/src/optimise/optimisers.jl#L290-L306">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.AMSGrad" href="#Flux.Optimise.AMSGrad"><code>Flux.Optimise.AMSGrad</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">AMSGrad(η, β::Tuple)</code></pre><p>Implements AMSGrad version of the ADAM optimiser. Parameters don't need tuning.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Defaults to <code>0.001</code>.</li><li>Beta (β::Tuple): The first element refers to β1 and the second to β2. Defaults to <code>(0.9, 0.999)</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = AMSGrad() # uses default η and β
|
||||
opt = AMSGrad(0.001, (0.89, 0.995))</code></pre><p><strong>References</strong></p><p><a href="https://openreview.net/forum?id=ryQu7f-RZ">AMSGrad</a> optimiser.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/94ba1e8ede5d834eb92f7477e272b531ecdd9d16/src/optimise/optimisers.jl#L323-L340">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.NADAM" href="#Flux.Optimise.NADAM"><code>Flux.Optimise.NADAM</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">NADAM(η, β::Tuple)</code></pre><p>Nesterov variant of ADAM. Parameters don't need tuning.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Defaults to <code>0.001</code>.</li><li>Beta (β::Tuple): The first element refers to β1 and the second to β2. Defaults to <code>(0.9, 0.999)</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = NADAM() # uses default η and β
|
||||
opt = NADAM(0.002, (0.89, 0.995))</code></pre><p><strong>References</strong></p><p><a href="http://cs229.stanford.edu/proj2015/054_report.pdf">NADAM</a> optimiser.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/94ba1e8ede5d834eb92f7477e272b531ecdd9d16/src/optimise/optimisers.jl#L358-L375">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.ADAMW" href="#Flux.Optimise.ADAMW"><code>Flux.Optimise.ADAMW</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">ADAMW(η, β::Tuple, decay)</code></pre><p>Variant of ADAM defined by fixing weight decay regularization.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Defaults to <code>0.001</code>.</li><li>Beta (β::Tuple): The first element refers to β1 and the second to β2. Defaults to (0.9, 0.999).</li><li>decay: Decay applied to weights during optimisation. Defaults to 0.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = ADAMW() # uses default η, β and decay
|
||||
opt = ADAMW(0.001, (0.89, 0.995), 0.1)</code></pre><p><strong>References</strong></p><p><a href="https://arxiv.org/abs/1711.05101">ADAMW</a></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/94ba1e8ede5d834eb92f7477e272b531ecdd9d16/src/optimise/optimisers.jl#L394-L412">source</a></section></article><h2 id="Optimiser-Interface-1"><a class="docs-heading-anchor" href="#Optimiser-Interface-1">Optimiser Interface</a><a class="docs-heading-anchor-permalink" href="#Optimiser-Interface-1" title="Permalink"></a></h2><p>Flux's optimisers are built around a <code>struct</code> that holds all the optimiser parameters along with a definition of how to apply the update rule associated with it. We do this via the <code>apply!</code> function which takes the optimiser as the first argument followed by the parameter and its corresponding gradient.</p><p>In this manner Flux also allows one to create custom optimisers to be used seamlessly. Let's work this with a simple example.</p><pre><code class="language-julia">mutable struct Momentum
|
||||
eta
|
||||
rho
|
||||
velocity
|
||||
@ -81,4 +81,4 @@ for t = 1:10^5
|
||||
end
|
||||
|
||||
loss(rand(10)) # around 0.9</code></pre><p>In this manner it is possible to compose optimisers for some added flexibility.</p><h2 id="Decays-1"><a class="docs-heading-anchor" href="#Decays-1">Decays</a><a class="docs-heading-anchor-permalink" href="#Decays-1" title="Permalink"></a></h2><p>Similar to optimisers, Flux also defines some simple decays that can be used in conjunction with other optimisers, or standalone.</p><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.ExpDecay" href="#Flux.Optimise.ExpDecay"><code>Flux.Optimise.ExpDecay</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">ExpDecay(eta, decay, decay_step, clip)</code></pre><p>Discount the learning rate <code>eta</code> by a multiplicative factor <code>decay</code> every <code>decay_step</code> till a minimum of <code>clip</code>.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (eta): Defaults to <code>0.001</code>.</li><li>decay: Factor by which the learning rate is discounted. Defaults to <code>0.1</code>.</li><li>decay_step: Schedules decay operations by setting number of steps between two decay operations. Defaults to <code>1000</code>.</li><li>clip: Minimum value of learning rate. Defaults to <code>1e-4</code>.</li></ul><p><strong>Example</strong></p><p>To apply exponential decay to an optimiser:</p><pre><code class="language-julia">Optimiser(ExpDecay(..), Opt(..))
|
||||
opt = Optimiser(ExpDecay(), ADAM())</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/af23a5756cf7d9a83b473b1edb0924b5a28b52d3/src/optimise/optimisers.jl#L471-L488">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.InvDecay" href="#Flux.Optimise.InvDecay"><code>Flux.Optimise.InvDecay</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">InvDecay(γ)</code></pre><p>Applies inverse time decay to an optimiser, i.e., the effective step size at iteration <code>n</code> is <code>eta / (1 + γ * n)</code> where <code>eta</code> is the initial step size. The wrapped optimiser's step size is not modified.</p><p><strong>Parameters</strong></p><ul><li>gamma (γ): Defaults to <code>0.001</code></li></ul><p><strong>Example</strong></p><pre><code class="language-julia">Optimiser(InvDecay(..), Opt(..))</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/af23a5756cf7d9a83b473b1edb0924b5a28b52d3/src/optimise/optimisers.jl#L443-L455">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.WeightDecay" href="#Flux.Optimise.WeightDecay"><code>Flux.Optimise.WeightDecay</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">WeightDecay(wd)</code></pre><p>Decays the weight by <code>wd</code></p><p><strong>Parameters</strong></p><ul><li>weight decay (wd): 0</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/af23a5756cf7d9a83b473b1edb0924b5a28b52d3/src/optimise/optimisers.jl#L509-L516">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../data/dataloader/">« DataLoader</a><a class="docs-footer-nextpage" href="../training/">Training »</a></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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Wednesday 4 March 2020 00:24">Wednesday 4 March 2020</span>. Using Julia version 1.3.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
|
||||
opt = Optimiser(ExpDecay(), ADAM())</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/94ba1e8ede5d834eb92f7477e272b531ecdd9d16/src/optimise/optimisers.jl#L471-L488">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.InvDecay" href="#Flux.Optimise.InvDecay"><code>Flux.Optimise.InvDecay</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">InvDecay(γ)</code></pre><p>Applies inverse time decay to an optimiser, i.e., the effective step size at iteration <code>n</code> is <code>eta / (1 + γ * n)</code> where <code>eta</code> is the initial step size. The wrapped optimiser's step size is not modified.</p><p><strong>Parameters</strong></p><ul><li>gamma (γ): Defaults to <code>0.001</code></li></ul><p><strong>Example</strong></p><pre><code class="language-julia">Optimiser(InvDecay(..), Opt(..))</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/94ba1e8ede5d834eb92f7477e272b531ecdd9d16/src/optimise/optimisers.jl#L443-L455">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.WeightDecay" href="#Flux.Optimise.WeightDecay"><code>Flux.Optimise.WeightDecay</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">WeightDecay(wd)</code></pre><p>Decays the weight by <code>wd</code></p><p><strong>Parameters</strong></p><ul><li>weight decay (wd): 0</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/94ba1e8ede5d834eb92f7477e272b531ecdd9d16/src/optimise/optimisers.jl#L509-L516">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../data/dataloader/">« DataLoader</a><a class="docs-footer-nextpage" href="../training/">Training »</a></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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Wednesday 4 March 2020 00:45">Wednesday 4 March 2020</span>. Using Julia version 1.3.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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