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</script><link href="https://cdnjs.cloudflare.com/ajax/libs/normalize/4.2.0/normalize.min.css" rel="stylesheet" type="text/css"/><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/4.6.3/css/font-awesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/default.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.2.0/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link href="../assets/documenter.css" rel="stylesheet" type="text/css"/><link href="../../flux.css" rel="stylesheet" type="text/css"/></head><body><nav class="toc"><h1>Flux</h1><select id="version-selector" onChange="window.location.href=this.value" style="visibility: hidden"></select><form class="search" id="search-form" action="../search.html"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../index.html">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="basics.html">Basics</a></li><li><a class="toctext" href="recurrence.html">Recurrence</a></li><li><a class="toctext" href="regularisation.html">Regularisation</a></li><li class="current"><a class="toctext" href="layers.html">Model Reference</a><ul class="internal"><li><a class="toctext" href="#Basic-Layers-1">Basic Layers</a></li><li><a class="toctext" href="#Additional-Convolution-Layers-1">Additional Convolution Layers</a></li><li><a class="toctext" href="#Recurrent-Layers-1">Recurrent Layers</a></li><li><a class="toctext" href="#Activation-Functions-1">Activation Functions</a></li><li><a class="toctext" href="#Normalisation-and-Regularisation-1">Normalisation & Regularisation</a></li></ul></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../training/optimisers.html">Optimisers</a></li><li><a class="toctext" href="../training/training.html">Training</a></li></ul></li><li><a class="toctext" href="../data/onehot.html">One-Hot Encoding</a></li><li><a class="toctext" href="../gpu.html">GPU Support</a></li><li><a class="toctext" href="../saving.html">Saving & Loading</a></li><li><span class="toctext">Internals</span><ul><li><a class="toctext" href="../internals/tracker.html">Backpropagation</a></li></ul></li><li><a class="toctext" href="../community.html">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Building Models</li><li><a href="layers.html">Model Reference</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/layers.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Model Reference</span><a class="fa fa-bars" href="#"></a></div></header><h2><a class="nav-anchor" id="Basic-Layers-1" href="#Basic-Layers-1">Basic Layers</a></h2><p>These core layers form the foundation of almost all neural networks.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Chain" href="#Flux.Chain"><code>Flux.Chain</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Chain(layers...)</code></pre><p>Chain multiple layers / functions together, so that they are called in sequence on a given input.</p><pre><code class="language-julia">m = Chain(x -> x^2, x -> x+1)
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</script><link href="https://cdnjs.cloudflare.com/ajax/libs/normalize/4.2.0/normalize.min.css" rel="stylesheet" type="text/css"/><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/4.6.3/css/font-awesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/default.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.2.0/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link href="../assets/documenter.css" rel="stylesheet" type="text/css"/><link href="../../flux.css" rel="stylesheet" type="text/css"/></head><body><nav class="toc"><h1>Flux</h1><select id="version-selector" onChange="window.location.href=this.value" style="visibility: hidden"></select><form class="search" id="search-form" action="../search.html"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../index.html">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="basics.html">Basics</a></li><li><a class="toctext" href="recurrence.html">Recurrence</a></li><li><a class="toctext" href="regularisation.html">Regularisation</a></li><li class="current"><a class="toctext" href="layers.html">Model Reference</a><ul class="internal"><li><a class="toctext" href="#Basic-Layers-1">Basic Layers</a></li><li><a class="toctext" href="#Recurrent-Layers-1">Recurrent Layers</a></li><li><a class="toctext" href="#Activation-Functions-1">Activation Functions</a></li><li><a class="toctext" href="#Normalisation-and-Regularisation-1">Normalisation & Regularisation</a></li></ul></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../training/optimisers.html">Optimisers</a></li><li><a class="toctext" href="../training/training.html">Training</a></li></ul></li><li><a class="toctext" href="../data/onehot.html">One-Hot Encoding</a></li><li><a class="toctext" href="../gpu.html">GPU Support</a></li><li><a class="toctext" href="../saving.html">Saving & Loading</a></li><li><span class="toctext">Internals</span><ul><li><a class="toctext" href="../internals/tracker.html">Backpropagation</a></li></ul></li><li><a class="toctext" href="../community.html">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Building Models</li><li><a href="layers.html">Model Reference</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/layers.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Model Reference</span><a class="fa fa-bars" href="#"></a></div></header><h2><a class="nav-anchor" id="Basic-Layers-1" href="#Basic-Layers-1">Basic Layers</a></h2><p>These core layers form the foundation of almost all neural networks.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Chain" href="#Flux.Chain"><code>Flux.Chain</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Chain(layers...)</code></pre><p>Chain multiple layers / functions together, so that they are called in sequence on a given input.</p><pre><code class="language-julia">m = Chain(x -> x^2, x -> x+1)
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m(5) == 26
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m = Chain(Dense(10, 5), Dense(5, 2))
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x = rand(10)
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m(x) == m[2](m[1](x))</code></pre><p><code>Chain</code> also supports indexing and slicing, e.g. <code>m[2]</code> or <code>m[1:end-1]</code>. <code>m[1:3](x)</code> will calculate the output of the first three layers.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/basic.jl#L1-L18">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Dense" href="#Flux.Dense"><code>Flux.Dense</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Dense(in::Integer, out::Integer, σ = identity)</code></pre><p>Creates a traditional <code>Dense</code> layer with parameters <code>W</code> and <code>b</code>.</p><pre><code class="language-none">y = σ.(W * x .+ b)</code></pre><p>The input <code>x</code> must be a vector of length <code>in</code>, or a batch of vectors represented as an <code>in × N</code> matrix. The out <code>y</code> will be a vector or batch of length <code>out</code>.</p><pre><code class="language-julia">julia> d = Dense(5, 2)
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m(x) == m[2](m[1](x))</code></pre><p><code>Chain</code> also supports indexing and slicing, e.g. <code>m[2]</code> or <code>m[1:end-1]</code>. <code>m[1:3](x)</code> will calculate the output of the first three layers.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/basic.jl#L1-L18">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Dense" href="#Flux.Dense"><code>Flux.Dense</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Dense(in::Integer, out::Integer, σ = identity)</code></pre><p>Creates a traditional <code>Dense</code> layer with parameters <code>W</code> and <code>b</code>.</p><pre><code class="language-none">y = σ.(W * x .+ b)</code></pre><p>The input <code>x</code> must be a vector of length <code>in</code>, or a batch of vectors represented as an <code>in × N</code> matrix. The out <code>y</code> will be a vector or batch of length <code>out</code>.</p><pre><code class="language-julia">julia> d = Dense(5, 2)
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Dense(5, 2)
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julia> d(rand(5))
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Tracked 2-element Array{Float64,1}:
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0.00257447
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-0.00449443</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/basic.jl#L43-L62">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Conv" href="#Flux.Conv"><code>Flux.Conv</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Conv(size, in=>out)
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Conv(size, in=>out, relu)</code></pre><p>Standard convolutional layer. <code>size</code> should be a tuple like <code>(2, 2)</code>. <code>in</code> and <code>out</code> specify the number of input and output channels respectively.</p><p>Data should be stored in WHCN order. In other words, a 100×100 RGB image would be a <code>100×100×3</code> array, and a batch of 50 would be a <code>100×100×3×50</code> array.</p><p>Takes the keyword arguments <code>pad</code>, <code>stride</code> and <code>dilation</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/conv.jl#L8-L19">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.MaxPool" href="#Flux.MaxPool"><code>Flux.MaxPool</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">MaxPool(k)</code></pre><p>Max pooling layer. <code>k</code> stands for the size of the window for each dimension of the input.</p><p>Takes the keyword arguments <code>pad</code> and <code>stride</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/conv.jl#L111-L117">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.MeanPool" href="#Flux.MeanPool"><code>Flux.MeanPool</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">MeanPool(k)</code></pre><p>Mean pooling layer. <code>k</code> stands for the size of the window for each dimension of the input.</p><p>Takes the keyword arguments <code>pad</code> and <code>stride</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/conv.jl#L133-L139">source</a></section><h2><a class="nav-anchor" id="Additional-Convolution-Layers-1" href="#Additional-Convolution-Layers-1">Additional Convolution Layers</a></h2><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.DepthwiseConv" href="#Flux.DepthwiseConv"><code>Flux.DepthwiseConv</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">DepthwiseConv(size, in)
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DepthwiseConv(size, in=>mul)
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DepthwiseConv(size, in=>mul, relu)</code></pre><p>Depthwise convolutional layer. <code>size</code> should be a tuple like <code>(2, 2)</code>. <code>in</code> and <code>mul</code> specify the number of input channels and channel multiplier respectively. In case the <code>mul</code> is not specified it is taken as 1.</p><p>Data should be stored in WHCN order. In other words, a 100×100 RGB image would be a <code>100×100×3</code> array, and a batch of 50 would be a <code>100×100×3×50</code> array.</p><p>Takes the keyword arguments <code>pad</code> and <code>stride</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/conv.jl#L60-L73">source</a></section><h2><a class="nav-anchor" id="Recurrent-Layers-1" href="#Recurrent-Layers-1">Recurrent Layers</a></h2><p>Much like the core layers above, but can be used to process sequence data (as well as other kinds of structured data).</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.RNN" href="#Flux.RNN"><code>Flux.RNN</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">RNN(in::Integer, out::Integer, σ = tanh)</code></pre><p>The most basic recurrent layer; essentially acts as a <code>Dense</code> layer, but with the output fed back into the input each time step.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/recurrent.jl#L105-L110">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.LSTM" href="#Flux.LSTM"><code>Flux.LSTM</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">LSTM(in::Integer, out::Integer)</code></pre><p>Long Short Term Memory recurrent layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.</p><p>See <a href="http://colah.github.io/posts/2015-08-Understanding-LSTMs/">this article</a> for a good overview of the internals.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/recurrent.jl#L150-L158">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.GRU" href="#Flux.GRU"><code>Flux.GRU</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">GRU(in::Integer, out::Integer)</code></pre><p>Gated Recurrent Unit layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.</p><p>See <a href="http://colah.github.io/posts/2015-08-Understanding-LSTMs/">this article</a> for a good overview of the internals.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/recurrent.jl#L191-L199">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Recur" href="#Flux.Recur"><code>Flux.Recur</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Recur(cell)</code></pre><p><code>Recur</code> takes a recurrent cell and makes it stateful, managing the hidden state in the background. <code>cell</code> should be a model of the form:</p><pre><code class="language-none">h, y = cell(h, x...)</code></pre><p>For example, here's a recurrent network that keeps a running total of its inputs.</p><pre><code class="language-julia">accum(h, x) = (h+x, x)
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-0.00449443</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/basic.jl#L43-L62">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Conv" href="#Flux.Conv"><code>Flux.Conv</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Conv(size, in=>out)
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Conv(size, in=>out, relu)</code></pre><p>Standard convolutional layer. <code>size</code> should be a tuple like <code>(2, 2)</code>. <code>in</code> and <code>out</code> specify the number of input and output channels respectively.</p><p>Data should be stored in WHCN order. In other words, a 100×100 RGB image would be a <code>100×100×3</code> array, and a batch of 50 would be a <code>100×100×3×50</code> array.</p><p>Takes the keyword arguments <code>pad</code>, <code>stride</code> and <code>dilation</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/conv.jl#L8-L19">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.MaxPool" href="#Flux.MaxPool"><code>Flux.MaxPool</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">MaxPool(k)</code></pre><p>Max pooling layer. <code>k</code> stands for the size of the window for each dimension of the input.</p><p>Takes the keyword arguments <code>pad</code> and <code>stride</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/conv.jl#L55-L61">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.MeanPool" href="#Flux.MeanPool"><code>Flux.MeanPool</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">MeanPool(k)</code></pre><p>Mean pooling layer. <code>k</code> stands for the size of the window for each dimension of the input.</p><p>Takes the keyword arguments <code>pad</code> and <code>stride</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/conv.jl#L77-L83">source</a></section><h2><a class="nav-anchor" id="Recurrent-Layers-1" href="#Recurrent-Layers-1">Recurrent Layers</a></h2><p>Much like the core layers above, but can be used to process sequence data (as well as other kinds of structured data).</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.RNN" href="#Flux.RNN"><code>Flux.RNN</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">RNN(in::Integer, out::Integer, σ = tanh)</code></pre><p>The most basic recurrent layer; essentially acts as a <code>Dense</code> layer, but with the output fed back into the input each time step.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/recurrent.jl#L105-L110">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.LSTM" href="#Flux.LSTM"><code>Flux.LSTM</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">LSTM(in::Integer, out::Integer)</code></pre><p>Long Short Term Memory recurrent layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.</p><p>See <a href="http://colah.github.io/posts/2015-08-Understanding-LSTMs/">this article</a> for a good overview of the internals.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/recurrent.jl#L150-L158">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.GRU" href="#Flux.GRU"><code>Flux.GRU</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">GRU(in::Integer, out::Integer)</code></pre><p>Gated Recurrent Unit layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.</p><p>See <a href="http://colah.github.io/posts/2015-08-Understanding-LSTMs/">this article</a> for a good overview of the internals.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/recurrent.jl#L191-L199">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Recur" href="#Flux.Recur"><code>Flux.Recur</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Recur(cell)</code></pre><p><code>Recur</code> takes a recurrent cell and makes it stateful, managing the hidden state in the background. <code>cell</code> should be a model of the form:</p><pre><code class="language-none">h, y = cell(h, x...)</code></pre><p>For example, here's a recurrent network that keeps a running total of its inputs.</p><pre><code class="language-julia">accum(h, x) = (h+x, x)
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rnn = Flux.Recur(accum, 0)
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rnn(2) # 2
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rnn(3) # 3
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rnn.state # 5
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rnn.(1:10) # apply to a sequence
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rnn.state # 60</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/recurrent.jl#L7-L26">source</a></section><h2><a class="nav-anchor" id="Activation-Functions-1" href="#Activation-Functions-1">Activation Functions</a></h2><p>Non-linearities that go between layers of your model. Most of these functions are defined in <a href="https://github.com/FluxML/NNlib.jl">NNlib</a> but are available by default in Flux.</p><p>Note that, unless otherwise stated, activation functions operate on scalars. To apply them to an array you can call <code>σ.(xs)</code>, <code>relu.(xs)</code> and so on.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.σ" href="#NNlib.σ"><code>NNlib.σ</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">σ(x) = 1 / (1 + exp(-x))</code></pre><p>Classic <a href="https://en.wikipedia.org/wiki/Sigmoid_function">sigmoid</a> activation function.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.relu" href="#NNlib.relu"><code>NNlib.relu</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">relu(x) = max(0, x)</code></pre><p><a href="https://en.wikipedia.org/wiki/Rectifier_(neural_networks)">Rectified Linear Unit</a> activation function.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.leakyrelu" href="#NNlib.leakyrelu"><code>NNlib.leakyrelu</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">leakyrelu(x) = max(0.01x, x)</code></pre><p>Leaky <a href="https://en.wikipedia.org/wiki/Rectifier_(neural_networks)">Rectified Linear Unit</a> activation function. You can also specify the coefficient explicitly, e.g. <code>leakyrelu(x, 0.01)</code>.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.elu" href="#NNlib.elu"><code>NNlib.elu</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">elu(x, α = 1) =
|
||||
rnn.state # 60</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/recurrent.jl#L7-L26">source</a></section><h2><a class="nav-anchor" id="Activation-Functions-1" href="#Activation-Functions-1">Activation Functions</a></h2><p>Non-linearities that go between layers of your model. Most of these functions are defined in <a href="https://github.com/FluxML/NNlib.jl">NNlib</a> but are available by default in Flux.</p><p>Note that, unless otherwise stated, activation functions operate on scalars. To apply them to an array you can call <code>σ.(xs)</code>, <code>relu.(xs)</code> and so on.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.σ" href="#NNlib.σ"><code>NNlib.σ</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">σ(x) = 1 / (1 + exp(-x))</code></pre><p>Classic <a href="https://en.wikipedia.org/wiki/Sigmoid_function">sigmoid</a> activation function.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.relu" href="#NNlib.relu"><code>NNlib.relu</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">relu(x) = max(0, x)</code></pre><p><a href="https://en.wikipedia.org/wiki/Rectifier_(neural_networks)">Rectified Linear Unit</a> activation function.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.leakyrelu" href="#NNlib.leakyrelu"><code>NNlib.leakyrelu</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">leakyrelu(x) = max(0.01x, x)</code></pre><p>Leaky <a href="https://en.wikipedia.org/wiki/Rectifier_(neural_networks)">Rectified Linear Unit</a> activation function. You can also specify the coefficient explicitly, e.g. <code>leakyrelu(x, 0.01)</code>.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.elu" href="#NNlib.elu"><code>NNlib.elu</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">elu(x, α = 1) =
|
||||
x > 0 ? x : α * (exp(x) - 1)</code></pre><p>Exponential Linear Unit activation function. See <a href="https://arxiv.org/abs/1511.07289">Fast and Accurate Deep Network Learning by Exponential Linear Units</a>. You can also specify the coefficient explicitly, e.g. <code>elu(x, 1)</code>.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.swish" href="#NNlib.swish"><code>NNlib.swish</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">swish(x) = x * σ(x)</code></pre><p>Self-gated actvation function. See <a href="https://arxiv.org/pdf/1710.05941.pdf">Swish: a Self-Gated Activation Function</a>.</p></div></div></section><h2><a class="nav-anchor" id="Normalisation-and-Regularisation-1" href="#Normalisation-and-Regularisation-1">Normalisation & Regularisation</a></h2><p>These layers don't affect the structure of the network but may improve training times or reduce overfitting.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.testmode!" href="#Flux.testmode!"><code>Flux.testmode!</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">testmode!(m)
|
||||
testmode!(m, false)</code></pre><p>Put layers like <a href="layers.html#Flux.Dropout"><code>Dropout</code></a> and <a href="layers.html#Flux.BatchNorm"><code>BatchNorm</code></a> into testing mode (or back to training mode with <code>false</code>).</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/normalise.jl#L1-L7">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.BatchNorm" href="#Flux.BatchNorm"><code>Flux.BatchNorm</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">BatchNorm(channels::Integer, σ = identity;
|
||||
testmode!(m, false)</code></pre><p>Put layers like <a href="layers.html#Flux.Dropout"><code>Dropout</code></a> and <a href="layers.html#Flux.BatchNorm"><code>BatchNorm</code></a> into testing mode (or back to training mode with <code>false</code>).</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/normalise.jl#L1-L7">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.BatchNorm" href="#Flux.BatchNorm"><code>Flux.BatchNorm</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">BatchNorm(channels::Integer, σ = identity;
|
||||
initβ = zeros, initγ = ones,
|
||||
ϵ = 1e-8, momentum = .1)</code></pre><p>Batch Normalization layer. The <code>channels</code> input should be the size of the channel dimension in your data (see below).</p><p>Given an array with <code>N</code> dimensions, call the <code>N-1</code>th the channel dimension. (For a batch of feature vectors this is just the data dimension, for <code>WHCN</code> images it's the usual channel dimension.)</p><p><code>BatchNorm</code> computes the mean and variance for each each <code>W×H×1×N</code> slice and shifts them to have a new mean and variance (corresponding to the learnable, per-channel <code>bias</code> and <code>scale</code> parameters).</p><p>See <a href="https://arxiv.org/pdf/1502.03167.pdf">Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift</a>.</p><p>Example:</p><pre><code class="language-julia">m = Chain(
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Dense(28^2, 64),
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BatchNorm(64, relu),
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Dense(64, 10),
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BatchNorm(10),
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softmax)</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/normalise.jl#L69-L98">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Dropout" href="#Flux.Dropout"><code>Flux.Dropout</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Dropout(p)</code></pre><p>A Dropout layer. For each input, either sets that input to <code>0</code> (with probability <code>p</code>) or scales it by <code>1/(1-p)</code>. This is used as a regularisation, i.e. it reduces overfitting during training.</p><p>Does nothing to the input once in <a href="layers.html#Flux.testmode!"><code>testmode!</code></a>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/normalise.jl#L15-L23">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.LayerNorm" href="#Flux.LayerNorm"><code>Flux.LayerNorm</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">LayerNorm(h::Integer)</code></pre><p>A <a href="https://arxiv.org/pdf/1607.06450.pdf">normalisation layer</a> designed to be used with recurrent hidden states of size <code>h</code>. Normalises the mean/stddev of each input before applying a per-neuron gain/bias.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/normalise.jl#L46-L53">source</a></section><footer><hr/><a class="previous" href="regularisation.html"><span class="direction">Previous</span><span class="title">Regularisation</span></a><a class="next" href="../training/optimisers.html"><span class="direction">Next</span><span class="title">Optimisers</span></a></footer></article></body></html>
|
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softmax)</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/normalise.jl#L69-L98">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Dropout" href="#Flux.Dropout"><code>Flux.Dropout</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Dropout(p)</code></pre><p>A Dropout layer. For each input, either sets that input to <code>0</code> (with probability <code>p</code>) or scales it by <code>1/(1-p)</code>. This is used as a regularisation, i.e. it reduces overfitting during training.</p><p>Does nothing to the input once in <a href="layers.html#Flux.testmode!"><code>testmode!</code></a>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/normalise.jl#L15-L23">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.LayerNorm" href="#Flux.LayerNorm"><code>Flux.LayerNorm</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">LayerNorm(h::Integer)</code></pre><p>A <a href="https://arxiv.org/pdf/1607.06450.pdf">normalisation layer</a> designed to be used with recurrent hidden states of size <code>h</code>. Normalises the mean/stddev of each input before applying a per-neuron gain/bias.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/normalise.jl#L46-L53">source</a></section><footer><hr/><a class="previous" href="regularisation.html"><span class="direction">Previous</span><span class="title">Regularisation</span></a><a class="next" href="../training/optimisers.html"><span class="direction">Next</span><span class="title">Optimisers</span></a></footer></article></body></html>
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"text": "Consider a simple linear regression. We create some dummy data, calculate a loss, and backpropagate to calculate gradients for the parameters W and b.using Flux.Tracker\n\nW = param(rand(2, 5))\nb = param(rand(2))\n\npredict(x) = W*x .+ b\nloss(x, y) = sum((predict(x) .- y).^2)\n\nx, y = rand(5), rand(2) # Dummy data\nl = loss(x, y) # ~ 3\n\nparams = Params([W, b])\ngrads = Tracker.gradient(() -> loss(x, y), params)We want to update each parameter, using the gradient, in order to improve (reduce) the loss. Here\'s one way to do that:using Flux.Tracker: grad, update!\n\nfunction sgd()\n η = 0.1 # Learning Rate\n for p in (W, b)\n update!(p, -η * grads[p])\n end\nendIf we call sgd, the parameters W and b will change and our loss should go down.There are two pieces here: one is that we need a list of trainable parameters for the model ([W, b] in this case), and the other is the update step. In this case the update is simply gradient descent (x .-= η .* Δ), but we might choose to do something more advanced, like adding momentum.In this case, getting the variables is trivial, but you can imagine it\'d be more of a pain with some complex stack of layers.m = Chain(\n Dense(10, 5, σ),\n Dense(5, 2), softmax)Instead of having to write [m[1].W, m[1].b, ...], Flux provides a params function params(m) that returns a list of all parameters in the model for you.For the update step, there\'s nothing whatsoever wrong with writing the loop above – it\'ll work just fine – but Flux provides various optimisers that make it more convenient.opt = SGD([W, b], 0.1) # Gradient descent with learning rate 0.1\n\nopt() # Carry out the update, modifying `W` and `b`.An optimiser takes a parameter list and returns a function that does the same thing as update above. We can pass either opt or update to our training loop, which will then run the optimiser after every mini-batch of data."
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@ -29,7 +29,4 @@ end</code></pre><p>If we call <code>sgd</code>, the parameters <code>W</code> an
|
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Dense(10, 5, σ),
|
||||
Dense(5, 2), softmax)</code></pre><p>Instead of having to write <code>[m[1].W, m[1].b, ...]</code>, Flux provides a params function <code>params(m)</code> that returns a list of all parameters in the model for you.</p><p>For the update step, there's nothing whatsoever wrong with writing the loop above – it'll work just fine – but Flux provides various <em>optimisers</em> that make it more convenient.</p><pre><code class="language-julia">opt = SGD([W, b], 0.1) # Gradient descent with learning rate 0.1
|
||||
|
||||
opt() # Carry out the update, modifying `W` and `b`.</code></pre><p>An optimiser takes a parameter list and returns a function that does the same thing as <code>update</code> above. We can pass either <code>opt</code> or <code>update</code> to our <a href="training.html">training loop</a>, which will then run the optimiser after every mini-batch of data.</p><h2><a class="nav-anchor" id="Optimiser-Reference-1" href="#Optimiser-Reference-1">Optimiser Reference</a></h2><p>All optimisers return a function that, when called, will update the parameters passed to it.</p><pre><code class="language-none">SGD
|
||||
Momentum
|
||||
Nesterov
|
||||
ADAM</code></pre><footer><hr/><a class="previous" href="../models/layers.html"><span class="direction">Previous</span><span class="title">Model Reference</span></a><a class="next" href="training.html"><span class="direction">Next</span><span class="title">Training</span></a></footer></article></body></html>
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opt() # Carry out the update, modifying `W` and `b`.</code></pre><p>An optimiser takes a parameter list and returns a function that does the same thing as <code>update</code> above. We can pass either <code>opt</code> or <code>update</code> to our <a href="training.html">training loop</a>, which will then run the optimiser after every mini-batch of data.</p><h2><a class="nav-anchor" id="Optimiser-Reference-1" href="#Optimiser-Reference-1">Optimiser Reference</a></h2><p>All optimisers return a function that, when called, will update the parameters passed to it.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Optimise.SGD" href="#Flux.Optimise.SGD"><code>Flux.Optimise.SGD</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">SGD(params, η = 0.1; decay = 0)</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>Supports inverse decaying learning rate if the <code>decay</code> argument is provided.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/optimise/interface.jl#L14-L21">source</a></section><section class="docstring"><div 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">Function</span>.</div><div><div><pre><code class="language-none">Momentum(params, η = 0.01; ρ = 0.9, decay = 0)</code></pre><p>SGD with learning rate <code>η</code>, momentum <code>ρ</code> and optional learning rate inverse decay.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/optimise/interface.jl#L25-L29">source</a></section><section class="docstring"><div 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">Function</span>.</div><div><div><pre><code class="language-none">Nesterov(params, η = 0.01; ρ = 0.9, decay = 0)</code></pre><p>SGD with learning rate <code>η</code>, Nesterov momentum <code>ρ</code> and optional learning rate inverse decay.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/optimise/interface.jl#L33-L37">source</a></section><section class="docstring"><div 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">Function</span>.</div><div><div><pre><code class="language-none">ADAM(params, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)</code></pre><p><a href="https://arxiv.org/abs/1412.6980v8">ADAM</a> optimiser.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/optimise/interface.jl#L51-L55">source</a></section><footer><hr/><a class="previous" href="../models/layers.html"><span class="direction">Previous</span><span class="title">Model Reference</span></a><a class="next" href="training.html"><span class="direction">Next</span><span class="title">Training</span></a></footer></article></body></html>
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</script><link href="https://cdnjs.cloudflare.com/ajax/libs/normalize/4.2.0/normalize.min.css" rel="stylesheet" type="text/css"/><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/4.6.3/css/font-awesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/default.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.2.0/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link href="../assets/documenter.css" rel="stylesheet" type="text/css"/><link href="../../flux.css" rel="stylesheet" type="text/css"/></head><body><nav class="toc"><h1>Flux</h1><select id="version-selector" onChange="window.location.href=this.value" style="visibility: hidden"></select><form class="search" id="search-form" action="../search.html"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../index.html">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="basics.html">Basics</a></li><li><a class="toctext" href="recurrence.html">Recurrence</a></li><li><a class="toctext" href="regularisation.html">Regularisation</a></li><li class="current"><a class="toctext" href="layers.html">Model Reference</a><ul class="internal"><li><a class="toctext" href="#Basic-Layers-1">Basic Layers</a></li><li><a class="toctext" href="#Additional-Convolution-Layers-1">Additional Convolution Layers</a></li><li><a class="toctext" href="#Recurrent-Layers-1">Recurrent Layers</a></li><li><a class="toctext" href="#Activation-Functions-1">Activation Functions</a></li><li><a class="toctext" href="#Normalisation-and-Regularisation-1">Normalisation & Regularisation</a></li></ul></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../training/optimisers.html">Optimisers</a></li><li><a class="toctext" href="../training/training.html">Training</a></li></ul></li><li><a class="toctext" href="../data/onehot.html">One-Hot Encoding</a></li><li><a class="toctext" href="../gpu.html">GPU Support</a></li><li><a class="toctext" href="../saving.html">Saving & Loading</a></li><li><span class="toctext">Internals</span><ul><li><a class="toctext" href="../internals/tracker.html">Backpropagation</a></li></ul></li><li><a class="toctext" href="../community.html">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Building Models</li><li><a href="layers.html">Model Reference</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/layers.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Model Reference</span><a class="fa fa-bars" href="#"></a></div></header><h2><a class="nav-anchor" id="Basic-Layers-1" href="#Basic-Layers-1">Basic Layers</a></h2><p>These core layers form the foundation of almost all neural networks.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Chain" href="#Flux.Chain"><code>Flux.Chain</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Chain(layers...)</code></pre><p>Chain multiple layers / functions together, so that they are called in sequence on a given input.</p><pre><code class="language-julia">m = Chain(x -> x^2, x -> x+1)
|
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</script><link href="https://cdnjs.cloudflare.com/ajax/libs/normalize/4.2.0/normalize.min.css" rel="stylesheet" type="text/css"/><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/4.6.3/css/font-awesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/default.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.2.0/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link href="../assets/documenter.css" rel="stylesheet" type="text/css"/><link href="../../flux.css" rel="stylesheet" type="text/css"/></head><body><nav class="toc"><h1>Flux</h1><select id="version-selector" onChange="window.location.href=this.value" style="visibility: hidden"></select><form class="search" id="search-form" action="../search.html"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../index.html">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="basics.html">Basics</a></li><li><a class="toctext" href="recurrence.html">Recurrence</a></li><li><a class="toctext" href="regularisation.html">Regularisation</a></li><li class="current"><a class="toctext" href="layers.html">Model Reference</a><ul class="internal"><li><a class="toctext" href="#Basic-Layers-1">Basic Layers</a></li><li><a class="toctext" href="#Recurrent-Layers-1">Recurrent Layers</a></li><li><a class="toctext" href="#Activation-Functions-1">Activation Functions</a></li><li><a class="toctext" href="#Normalisation-and-Regularisation-1">Normalisation & Regularisation</a></li></ul></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../training/optimisers.html">Optimisers</a></li><li><a class="toctext" href="../training/training.html">Training</a></li></ul></li><li><a class="toctext" href="../data/onehot.html">One-Hot Encoding</a></li><li><a class="toctext" href="../gpu.html">GPU Support</a></li><li><a class="toctext" href="../saving.html">Saving & Loading</a></li><li><span class="toctext">Internals</span><ul><li><a class="toctext" href="../internals/tracker.html">Backpropagation</a></li></ul></li><li><a class="toctext" href="../community.html">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Building Models</li><li><a href="layers.html">Model Reference</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/layers.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Model Reference</span><a class="fa fa-bars" href="#"></a></div></header><h2><a class="nav-anchor" id="Basic-Layers-1" href="#Basic-Layers-1">Basic Layers</a></h2><p>These core layers form the foundation of almost all neural networks.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Chain" href="#Flux.Chain"><code>Flux.Chain</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Chain(layers...)</code></pre><p>Chain multiple layers / functions together, so that they are called in sequence on a given input.</p><pre><code class="language-julia">m = Chain(x -> x^2, x -> x+1)
|
||||
m(5) == 26
|
||||
|
||||
m = Chain(Dense(10, 5), Dense(5, 2))
|
||||
x = rand(10)
|
||||
m(x) == m[2](m[1](x))</code></pre><p><code>Chain</code> also supports indexing and slicing, e.g. <code>m[2]</code> or <code>m[1:end-1]</code>. <code>m[1:3](x)</code> will calculate the output of the first three layers.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/basic.jl#L1-L18">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Dense" href="#Flux.Dense"><code>Flux.Dense</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Dense(in::Integer, out::Integer, σ = identity)</code></pre><p>Creates a traditional <code>Dense</code> layer with parameters <code>W</code> and <code>b</code>.</p><pre><code class="language-none">y = σ.(W * x .+ b)</code></pre><p>The input <code>x</code> must be a vector of length <code>in</code>, or a batch of vectors represented as an <code>in × N</code> matrix. The out <code>y</code> will be a vector or batch of length <code>out</code>.</p><pre><code class="language-julia">julia> d = Dense(5, 2)
|
||||
m(x) == m[2](m[1](x))</code></pre><p><code>Chain</code> also supports indexing and slicing, e.g. <code>m[2]</code> or <code>m[1:end-1]</code>. <code>m[1:3](x)</code> will calculate the output of the first three layers.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/basic.jl#L1-L18">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Dense" href="#Flux.Dense"><code>Flux.Dense</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Dense(in::Integer, out::Integer, σ = identity)</code></pre><p>Creates a traditional <code>Dense</code> layer with parameters <code>W</code> and <code>b</code>.</p><pre><code class="language-none">y = σ.(W * x .+ b)</code></pre><p>The input <code>x</code> must be a vector of length <code>in</code>, or a batch of vectors represented as an <code>in × N</code> matrix. The out <code>y</code> will be a vector or batch of length <code>out</code>.</p><pre><code class="language-julia">julia> d = Dense(5, 2)
|
||||
Dense(5, 2)
|
||||
|
||||
julia> d(rand(5))
|
||||
Tracked 2-element Array{Float64,1}:
|
||||
0.00257447
|
||||
-0.00449443</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/basic.jl#L43-L62">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Conv" href="#Flux.Conv"><code>Flux.Conv</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Conv(size, in=>out)
|
||||
Conv(size, in=>out, relu)</code></pre><p>Standard convolutional layer. <code>size</code> should be a tuple like <code>(2, 2)</code>. <code>in</code> and <code>out</code> specify the number of input and output channels respectively.</p><p>Data should be stored in WHCN order. In other words, a 100×100 RGB image would be a <code>100×100×3</code> array, and a batch of 50 would be a <code>100×100×3×50</code> array.</p><p>Takes the keyword arguments <code>pad</code>, <code>stride</code> and <code>dilation</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/conv.jl#L8-L19">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.MaxPool" href="#Flux.MaxPool"><code>Flux.MaxPool</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">MaxPool(k)</code></pre><p>Max pooling layer. <code>k</code> stands for the size of the window for each dimension of the input.</p><p>Takes the keyword arguments <code>pad</code> and <code>stride</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/conv.jl#L111-L117">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.MeanPool" href="#Flux.MeanPool"><code>Flux.MeanPool</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">MeanPool(k)</code></pre><p>Mean pooling layer. <code>k</code> stands for the size of the window for each dimension of the input.</p><p>Takes the keyword arguments <code>pad</code> and <code>stride</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/conv.jl#L133-L139">source</a></section><h2><a class="nav-anchor" id="Additional-Convolution-Layers-1" href="#Additional-Convolution-Layers-1">Additional Convolution Layers</a></h2><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.DepthwiseConv" href="#Flux.DepthwiseConv"><code>Flux.DepthwiseConv</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">DepthwiseConv(size, in)
|
||||
DepthwiseConv(size, in=>mul)
|
||||
DepthwiseConv(size, in=>mul, relu)</code></pre><p>Depthwise convolutional layer. <code>size</code> should be a tuple like <code>(2, 2)</code>. <code>in</code> and <code>mul</code> specify the number of input channels and channel multiplier respectively. In case the <code>mul</code> is not specified it is taken as 1.</p><p>Data should be stored in WHCN order. In other words, a 100×100 RGB image would be a <code>100×100×3</code> array, and a batch of 50 would be a <code>100×100×3×50</code> array.</p><p>Takes the keyword arguments <code>pad</code> and <code>stride</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/conv.jl#L60-L73">source</a></section><h2><a class="nav-anchor" id="Recurrent-Layers-1" href="#Recurrent-Layers-1">Recurrent Layers</a></h2><p>Much like the core layers above, but can be used to process sequence data (as well as other kinds of structured data).</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.RNN" href="#Flux.RNN"><code>Flux.RNN</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">RNN(in::Integer, out::Integer, σ = tanh)</code></pre><p>The most basic recurrent layer; essentially acts as a <code>Dense</code> layer, but with the output fed back into the input each time step.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/recurrent.jl#L105-L110">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.LSTM" href="#Flux.LSTM"><code>Flux.LSTM</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">LSTM(in::Integer, out::Integer)</code></pre><p>Long Short Term Memory recurrent layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.</p><p>See <a href="http://colah.github.io/posts/2015-08-Understanding-LSTMs/">this article</a> for a good overview of the internals.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/recurrent.jl#L150-L158">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.GRU" href="#Flux.GRU"><code>Flux.GRU</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">GRU(in::Integer, out::Integer)</code></pre><p>Gated Recurrent Unit layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.</p><p>See <a href="http://colah.github.io/posts/2015-08-Understanding-LSTMs/">this article</a> for a good overview of the internals.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/recurrent.jl#L191-L199">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Recur" href="#Flux.Recur"><code>Flux.Recur</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Recur(cell)</code></pre><p><code>Recur</code> takes a recurrent cell and makes it stateful, managing the hidden state in the background. <code>cell</code> should be a model of the form:</p><pre><code class="language-none">h, y = cell(h, x...)</code></pre><p>For example, here's a recurrent network that keeps a running total of its inputs.</p><pre><code class="language-julia">accum(h, x) = (h+x, x)
|
||||
-0.00449443</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/basic.jl#L43-L62">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Conv" href="#Flux.Conv"><code>Flux.Conv</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Conv(size, in=>out)
|
||||
Conv(size, in=>out, relu)</code></pre><p>Standard convolutional layer. <code>size</code> should be a tuple like <code>(2, 2)</code>. <code>in</code> and <code>out</code> specify the number of input and output channels respectively.</p><p>Data should be stored in WHCN order. In other words, a 100×100 RGB image would be a <code>100×100×3</code> array, and a batch of 50 would be a <code>100×100×3×50</code> array.</p><p>Takes the keyword arguments <code>pad</code>, <code>stride</code> and <code>dilation</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/conv.jl#L8-L19">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.MaxPool" href="#Flux.MaxPool"><code>Flux.MaxPool</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">MaxPool(k)</code></pre><p>Max pooling layer. <code>k</code> stands for the size of the window for each dimension of the input.</p><p>Takes the keyword arguments <code>pad</code> and <code>stride</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/conv.jl#L55-L61">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.MeanPool" href="#Flux.MeanPool"><code>Flux.MeanPool</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">MeanPool(k)</code></pre><p>Mean pooling layer. <code>k</code> stands for the size of the window for each dimension of the input.</p><p>Takes the keyword arguments <code>pad</code> and <code>stride</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/conv.jl#L77-L83">source</a></section><h2><a class="nav-anchor" id="Recurrent-Layers-1" href="#Recurrent-Layers-1">Recurrent Layers</a></h2><p>Much like the core layers above, but can be used to process sequence data (as well as other kinds of structured data).</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.RNN" href="#Flux.RNN"><code>Flux.RNN</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">RNN(in::Integer, out::Integer, σ = tanh)</code></pre><p>The most basic recurrent layer; essentially acts as a <code>Dense</code> layer, but with the output fed back into the input each time step.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/recurrent.jl#L105-L110">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.LSTM" href="#Flux.LSTM"><code>Flux.LSTM</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">LSTM(in::Integer, out::Integer)</code></pre><p>Long Short Term Memory recurrent layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.</p><p>See <a href="http://colah.github.io/posts/2015-08-Understanding-LSTMs/">this article</a> for a good overview of the internals.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/recurrent.jl#L150-L158">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.GRU" href="#Flux.GRU"><code>Flux.GRU</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">GRU(in::Integer, out::Integer)</code></pre><p>Gated Recurrent Unit layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.</p><p>See <a href="http://colah.github.io/posts/2015-08-Understanding-LSTMs/">this article</a> for a good overview of the internals.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/recurrent.jl#L191-L199">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Recur" href="#Flux.Recur"><code>Flux.Recur</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Recur(cell)</code></pre><p><code>Recur</code> takes a recurrent cell and makes it stateful, managing the hidden state in the background. <code>cell</code> should be a model of the form:</p><pre><code class="language-none">h, y = cell(h, x...)</code></pre><p>For example, here's a recurrent network that keeps a running total of its inputs.</p><pre><code class="language-julia">accum(h, x) = (h+x, x)
|
||||
rnn = Flux.Recur(accum, 0)
|
||||
rnn(2) # 2
|
||||
rnn(3) # 3
|
||||
rnn.state # 5
|
||||
rnn.(1:10) # apply to a sequence
|
||||
rnn.state # 60</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/recurrent.jl#L7-L26">source</a></section><h2><a class="nav-anchor" id="Activation-Functions-1" href="#Activation-Functions-1">Activation Functions</a></h2><p>Non-linearities that go between layers of your model. Most of these functions are defined in <a href="https://github.com/FluxML/NNlib.jl">NNlib</a> but are available by default in Flux.</p><p>Note that, unless otherwise stated, activation functions operate on scalars. To apply them to an array you can call <code>σ.(xs)</code>, <code>relu.(xs)</code> and so on.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.σ" href="#NNlib.σ"><code>NNlib.σ</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">σ(x) = 1 / (1 + exp(-x))</code></pre><p>Classic <a href="https://en.wikipedia.org/wiki/Sigmoid_function">sigmoid</a> activation function.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.relu" href="#NNlib.relu"><code>NNlib.relu</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">relu(x) = max(0, x)</code></pre><p><a href="https://en.wikipedia.org/wiki/Rectifier_(neural_networks)">Rectified Linear Unit</a> activation function.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.leakyrelu" href="#NNlib.leakyrelu"><code>NNlib.leakyrelu</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">leakyrelu(x) = max(0.01x, x)</code></pre><p>Leaky <a href="https://en.wikipedia.org/wiki/Rectifier_(neural_networks)">Rectified Linear Unit</a> activation function. You can also specify the coefficient explicitly, e.g. <code>leakyrelu(x, 0.01)</code>.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.elu" href="#NNlib.elu"><code>NNlib.elu</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">elu(x, α = 1) =
|
||||
rnn.state # 60</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/recurrent.jl#L7-L26">source</a></section><h2><a class="nav-anchor" id="Activation-Functions-1" href="#Activation-Functions-1">Activation Functions</a></h2><p>Non-linearities that go between layers of your model. Most of these functions are defined in <a href="https://github.com/FluxML/NNlib.jl">NNlib</a> but are available by default in Flux.</p><p>Note that, unless otherwise stated, activation functions operate on scalars. To apply them to an array you can call <code>σ.(xs)</code>, <code>relu.(xs)</code> and so on.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.σ" href="#NNlib.σ"><code>NNlib.σ</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">σ(x) = 1 / (1 + exp(-x))</code></pre><p>Classic <a href="https://en.wikipedia.org/wiki/Sigmoid_function">sigmoid</a> activation function.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.relu" href="#NNlib.relu"><code>NNlib.relu</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">relu(x) = max(0, x)</code></pre><p><a href="https://en.wikipedia.org/wiki/Rectifier_(neural_networks)">Rectified Linear Unit</a> activation function.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.leakyrelu" href="#NNlib.leakyrelu"><code>NNlib.leakyrelu</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">leakyrelu(x) = max(0.01x, x)</code></pre><p>Leaky <a href="https://en.wikipedia.org/wiki/Rectifier_(neural_networks)">Rectified Linear Unit</a> activation function. You can also specify the coefficient explicitly, e.g. <code>leakyrelu(x, 0.01)</code>.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.elu" href="#NNlib.elu"><code>NNlib.elu</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">elu(x, α = 1) =
|
||||
x > 0 ? x : α * (exp(x) - 1)</code></pre><p>Exponential Linear Unit activation function. See <a href="https://arxiv.org/abs/1511.07289">Fast and Accurate Deep Network Learning by Exponential Linear Units</a>. You can also specify the coefficient explicitly, e.g. <code>elu(x, 1)</code>.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.swish" href="#NNlib.swish"><code>NNlib.swish</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">swish(x) = x * σ(x)</code></pre><p>Self-gated actvation function. See <a href="https://arxiv.org/pdf/1710.05941.pdf">Swish: a Self-Gated Activation Function</a>.</p></div></div></section><h2><a class="nav-anchor" id="Normalisation-and-Regularisation-1" href="#Normalisation-and-Regularisation-1">Normalisation & Regularisation</a></h2><p>These layers don't affect the structure of the network but may improve training times or reduce overfitting.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.testmode!" href="#Flux.testmode!"><code>Flux.testmode!</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">testmode!(m)
|
||||
testmode!(m, false)</code></pre><p>Put layers like <a href="layers.html#Flux.Dropout"><code>Dropout</code></a> and <a href="layers.html#Flux.BatchNorm"><code>BatchNorm</code></a> into testing mode (or back to training mode with <code>false</code>).</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/normalise.jl#L1-L7">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.BatchNorm" href="#Flux.BatchNorm"><code>Flux.BatchNorm</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">BatchNorm(channels::Integer, σ = identity;
|
||||
testmode!(m, false)</code></pre><p>Put layers like <a href="layers.html#Flux.Dropout"><code>Dropout</code></a> and <a href="layers.html#Flux.BatchNorm"><code>BatchNorm</code></a> into testing mode (or back to training mode with <code>false</code>).</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/normalise.jl#L1-L7">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.BatchNorm" href="#Flux.BatchNorm"><code>Flux.BatchNorm</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">BatchNorm(channels::Integer, σ = identity;
|
||||
initβ = zeros, initγ = ones,
|
||||
ϵ = 1e-8, momentum = .1)</code></pre><p>Batch Normalization layer. The <code>channels</code> input should be the size of the channel dimension in your data (see below).</p><p>Given an array with <code>N</code> dimensions, call the <code>N-1</code>th the channel dimension. (For a batch of feature vectors this is just the data dimension, for <code>WHCN</code> images it's the usual channel dimension.)</p><p><code>BatchNorm</code> computes the mean and variance for each each <code>W×H×1×N</code> slice and shifts them to have a new mean and variance (corresponding to the learnable, per-channel <code>bias</code> and <code>scale</code> parameters).</p><p>See <a href="https://arxiv.org/pdf/1502.03167.pdf">Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift</a>.</p><p>Example:</p><pre><code class="language-julia">m = Chain(
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Dense(28^2, 64),
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BatchNorm(64, relu),
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Dense(64, 10),
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BatchNorm(10),
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softmax)</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/normalise.jl#L69-L98">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Dropout" href="#Flux.Dropout"><code>Flux.Dropout</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Dropout(p)</code></pre><p>A Dropout layer. For each input, either sets that input to <code>0</code> (with probability <code>p</code>) or scales it by <code>1/(1-p)</code>. This is used as a regularisation, i.e. it reduces overfitting during training.</p><p>Does nothing to the input once in <a href="layers.html#Flux.testmode!"><code>testmode!</code></a>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/normalise.jl#L15-L23">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.LayerNorm" href="#Flux.LayerNorm"><code>Flux.LayerNorm</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">LayerNorm(h::Integer)</code></pre><p>A <a href="https://arxiv.org/pdf/1607.06450.pdf">normalisation layer</a> designed to be used with recurrent hidden states of size <code>h</code>. Normalises the mean/stddev of each input before applying a per-neuron gain/bias.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/normalise.jl#L46-L53">source</a></section><footer><hr/><a class="previous" href="regularisation.html"><span class="direction">Previous</span><span class="title">Regularisation</span></a><a class="next" href="../training/optimisers.html"><span class="direction">Next</span><span class="title">Optimisers</span></a></footer></article></body></html>
|
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softmax)</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/normalise.jl#L69-L98">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Dropout" href="#Flux.Dropout"><code>Flux.Dropout</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Dropout(p)</code></pre><p>A Dropout layer. For each input, either sets that input to <code>0</code> (with probability <code>p</code>) or scales it by <code>1/(1-p)</code>. This is used as a regularisation, i.e. it reduces overfitting during training.</p><p>Does nothing to the input once in <a href="layers.html#Flux.testmode!"><code>testmode!</code></a>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/normalise.jl#L15-L23">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.LayerNorm" href="#Flux.LayerNorm"><code>Flux.LayerNorm</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">LayerNorm(h::Integer)</code></pre><p>A <a href="https://arxiv.org/pdf/1607.06450.pdf">normalisation layer</a> designed to be used with recurrent hidden states of size <code>h</code>. Normalises the mean/stddev of each input before applying a per-neuron gain/bias.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/normalise.jl#L46-L53">source</a></section><footer><hr/><a class="previous" href="regularisation.html"><span class="direction">Previous</span><span class="title">Regularisation</span></a><a class="next" href="../training/optimisers.html"><span class="direction">Next</span><span class="title">Optimisers</span></a></footer></article></body></html>
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"text": "Consider a simple linear regression. We create some dummy data, calculate a loss, and backpropagate to calculate gradients for the parameters W and b.using Flux.Tracker\n\nW = param(rand(2, 5))\nb = param(rand(2))\n\npredict(x) = W*x .+ b\nloss(x, y) = sum((predict(x) .- y).^2)\n\nx, y = rand(5), rand(2) # Dummy data\nl = loss(x, y) # ~ 3\n\nparams = Params([W, b])\ngrads = Tracker.gradient(() -> loss(x, y), params)We want to update each parameter, using the gradient, in order to improve (reduce) the loss. Here\'s one way to do that:using Flux.Tracker: grad, update!\n\nfunction sgd()\n η = 0.1 # Learning Rate\n for p in (W, b)\n update!(p, -η * grads[p])\n end\nendIf we call sgd, the parameters W and b will change and our loss should go down.There are two pieces here: one is that we need a list of trainable parameters for the model ([W, b] in this case), and the other is the update step. In this case the update is simply gradient descent (x .-= η .* Δ), but we might choose to do something more advanced, like adding momentum.In this case, getting the variables is trivial, but you can imagine it\'d be more of a pain with some complex stack of layers.m = Chain(\n Dense(10, 5, σ),\n Dense(5, 2), softmax)Instead of having to write [m[1].W, m[1].b, ...], Flux provides a params function params(m) that returns a list of all parameters in the model for you.For the update step, there\'s nothing whatsoever wrong with writing the loop above – it\'ll work just fine – but Flux provides various optimisers that make it more convenient.opt = SGD([W, b], 0.1) # Gradient descent with learning rate 0.1\n\nopt() # Carry out the update, modifying `W` and `b`.An optimiser takes a parameter list and returns a function that does the same thing as update above. We can pass either opt or update to our training loop, which will then run the optimiser after every mini-batch of data."
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@ -29,7 +29,4 @@ end</code></pre><p>If we call <code>sgd</code>, the parameters <code>W</code> an
|
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Dense(10, 5, σ),
|
||||
Dense(5, 2), softmax)</code></pre><p>Instead of having to write <code>[m[1].W, m[1].b, ...]</code>, Flux provides a params function <code>params(m)</code> that returns a list of all parameters in the model for you.</p><p>For the update step, there's nothing whatsoever wrong with writing the loop above – it'll work just fine – but Flux provides various <em>optimisers</em> that make it more convenient.</p><pre><code class="language-julia">opt = SGD([W, b], 0.1) # Gradient descent with learning rate 0.1
|
||||
|
||||
opt() # Carry out the update, modifying `W` and `b`.</code></pre><p>An optimiser takes a parameter list and returns a function that does the same thing as <code>update</code> above. We can pass either <code>opt</code> or <code>update</code> to our <a href="training.html">training loop</a>, which will then run the optimiser after every mini-batch of data.</p><h2><a class="nav-anchor" id="Optimiser-Reference-1" href="#Optimiser-Reference-1">Optimiser Reference</a></h2><p>All optimisers return a function that, when called, will update the parameters passed to it.</p><pre><code class="language-none">SGD
|
||||
Momentum
|
||||
Nesterov
|
||||
ADAM</code></pre><footer><hr/><a class="previous" href="../models/layers.html"><span class="direction">Previous</span><span class="title">Model Reference</span></a><a class="next" href="training.html"><span class="direction">Next</span><span class="title">Training</span></a></footer></article></body></html>
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opt() # Carry out the update, modifying `W` and `b`.</code></pre><p>An optimiser takes a parameter list and returns a function that does the same thing as <code>update</code> above. We can pass either <code>opt</code> or <code>update</code> to our <a href="training.html">training loop</a>, which will then run the optimiser after every mini-batch of data.</p><h2><a class="nav-anchor" id="Optimiser-Reference-1" href="#Optimiser-Reference-1">Optimiser Reference</a></h2><p>All optimisers return a function that, when called, will update the parameters passed to it.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Optimise.SGD" href="#Flux.Optimise.SGD"><code>Flux.Optimise.SGD</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">SGD(params, η = 0.1; decay = 0)</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>Supports inverse decaying learning rate if the <code>decay</code> argument is provided.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/optimise/interface.jl#L14-L21">source</a></section><section class="docstring"><div 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">Function</span>.</div><div><div><pre><code class="language-none">Momentum(params, η = 0.01; ρ = 0.9, decay = 0)</code></pre><p>SGD with learning rate <code>η</code>, momentum <code>ρ</code> and optional learning rate inverse decay.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/optimise/interface.jl#L25-L29">source</a></section><section class="docstring"><div 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">Function</span>.</div><div><div><pre><code class="language-none">Nesterov(params, η = 0.01; ρ = 0.9, decay = 0)</code></pre><p>SGD with learning rate <code>η</code>, Nesterov momentum <code>ρ</code> and optional learning rate inverse decay.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/optimise/interface.jl#L33-L37">source</a></section><section class="docstring"><div 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">Function</span>.</div><div><div><pre><code class="language-none">ADAM(params, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)</code></pre><p><a href="https://arxiv.org/abs/1412.6980v8">ADAM</a> optimiser.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/optimise/interface.jl#L51-L55">source</a></section><footer><hr/><a class="previous" href="../models/layers.html"><span class="direction">Previous</span><span class="title">Model Reference</span></a><a class="next" href="training.html"><span class="direction">Next</span><span class="title">Training</span></a></footer></article></body></html>
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</script><link href="https://cdnjs.cloudflare.com/ajax/libs/normalize/4.2.0/normalize.min.css" rel="stylesheet" type="text/css"/><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/4.6.3/css/font-awesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/default.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.2.0/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link href="../assets/documenter.css" rel="stylesheet" type="text/css"/><link href="../../flux.css" rel="stylesheet" type="text/css"/></head><body><nav class="toc"><h1>Flux</h1><select id="version-selector" onChange="window.location.href=this.value" style="visibility: hidden"></select><form class="search" id="search-form" action="../search.html"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../index.html">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="basics.html">Basics</a></li><li><a class="toctext" href="recurrence.html">Recurrence</a></li><li><a class="toctext" href="regularisation.html">Regularisation</a></li><li class="current"><a class="toctext" href="layers.html">Model Reference</a><ul class="internal"><li><a class="toctext" href="#Basic-Layers-1">Basic Layers</a></li><li><a class="toctext" href="#Additional-Convolution-Layers-1">Additional Convolution Layers</a></li><li><a class="toctext" href="#Recurrent-Layers-1">Recurrent Layers</a></li><li><a class="toctext" href="#Activation-Functions-1">Activation Functions</a></li><li><a class="toctext" href="#Normalisation-and-Regularisation-1">Normalisation & Regularisation</a></li></ul></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../training/optimisers.html">Optimisers</a></li><li><a class="toctext" href="../training/training.html">Training</a></li></ul></li><li><a class="toctext" href="../data/onehot.html">One-Hot Encoding</a></li><li><a class="toctext" href="../gpu.html">GPU Support</a></li><li><a class="toctext" href="../saving.html">Saving & Loading</a></li><li><span class="toctext">Internals</span><ul><li><a class="toctext" href="../internals/tracker.html">Backpropagation</a></li></ul></li><li><a class="toctext" href="../community.html">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Building Models</li><li><a href="layers.html">Model Reference</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/layers.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Model Reference</span><a class="fa fa-bars" href="#"></a></div></header><h2><a class="nav-anchor" id="Basic-Layers-1" href="#Basic-Layers-1">Basic Layers</a></h2><p>These core layers form the foundation of almost all neural networks.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Chain" href="#Flux.Chain"><code>Flux.Chain</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Chain(layers...)</code></pre><p>Chain multiple layers / functions together, so that they are called in sequence on a given input.</p><pre><code class="language-julia">m = Chain(x -> x^2, x -> x+1)
|
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</script><link href="https://cdnjs.cloudflare.com/ajax/libs/normalize/4.2.0/normalize.min.css" rel="stylesheet" type="text/css"/><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/4.6.3/css/font-awesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/default.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.2.0/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link href="../assets/documenter.css" rel="stylesheet" type="text/css"/><link href="../../flux.css" rel="stylesheet" type="text/css"/></head><body><nav class="toc"><h1>Flux</h1><select id="version-selector" onChange="window.location.href=this.value" style="visibility: hidden"></select><form class="search" id="search-form" action="../search.html"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../index.html">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="basics.html">Basics</a></li><li><a class="toctext" href="recurrence.html">Recurrence</a></li><li><a class="toctext" href="regularisation.html">Regularisation</a></li><li class="current"><a class="toctext" href="layers.html">Model Reference</a><ul class="internal"><li><a class="toctext" href="#Basic-Layers-1">Basic Layers</a></li><li><a class="toctext" href="#Recurrent-Layers-1">Recurrent Layers</a></li><li><a class="toctext" href="#Activation-Functions-1">Activation Functions</a></li><li><a class="toctext" href="#Normalisation-and-Regularisation-1">Normalisation & Regularisation</a></li></ul></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../training/optimisers.html">Optimisers</a></li><li><a class="toctext" href="../training/training.html">Training</a></li></ul></li><li><a class="toctext" href="../data/onehot.html">One-Hot Encoding</a></li><li><a class="toctext" href="../gpu.html">GPU Support</a></li><li><a class="toctext" href="../saving.html">Saving & Loading</a></li><li><span class="toctext">Internals</span><ul><li><a class="toctext" href="../internals/tracker.html">Backpropagation</a></li></ul></li><li><a class="toctext" href="../community.html">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Building Models</li><li><a href="layers.html">Model Reference</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/layers.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Model Reference</span><a class="fa fa-bars" href="#"></a></div></header><h2><a class="nav-anchor" id="Basic-Layers-1" href="#Basic-Layers-1">Basic Layers</a></h2><p>These core layers form the foundation of almost all neural networks.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Chain" href="#Flux.Chain"><code>Flux.Chain</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Chain(layers...)</code></pre><p>Chain multiple layers / functions together, so that they are called in sequence on a given input.</p><pre><code class="language-julia">m = Chain(x -> x^2, x -> x+1)
|
||||
m(5) == 26
|
||||
|
||||
m = Chain(Dense(10, 5), Dense(5, 2))
|
||||
x = rand(10)
|
||||
m(x) == m[2](m[1](x))</code></pre><p><code>Chain</code> also supports indexing and slicing, e.g. <code>m[2]</code> or <code>m[1:end-1]</code>. <code>m[1:3](x)</code> will calculate the output of the first three layers.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/basic.jl#L1-L18">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Dense" href="#Flux.Dense"><code>Flux.Dense</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Dense(in::Integer, out::Integer, σ = identity)</code></pre><p>Creates a traditional <code>Dense</code> layer with parameters <code>W</code> and <code>b</code>.</p><pre><code class="language-none">y = σ.(W * x .+ b)</code></pre><p>The input <code>x</code> must be a vector of length <code>in</code>, or a batch of vectors represented as an <code>in × N</code> matrix. The out <code>y</code> will be a vector or batch of length <code>out</code>.</p><pre><code class="language-julia">julia> d = Dense(5, 2)
|
||||
m(x) == m[2](m[1](x))</code></pre><p><code>Chain</code> also supports indexing and slicing, e.g. <code>m[2]</code> or <code>m[1:end-1]</code>. <code>m[1:3](x)</code> will calculate the output of the first three layers.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/basic.jl#L1-L18">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Dense" href="#Flux.Dense"><code>Flux.Dense</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Dense(in::Integer, out::Integer, σ = identity)</code></pre><p>Creates a traditional <code>Dense</code> layer with parameters <code>W</code> and <code>b</code>.</p><pre><code class="language-none">y = σ.(W * x .+ b)</code></pre><p>The input <code>x</code> must be a vector of length <code>in</code>, or a batch of vectors represented as an <code>in × N</code> matrix. The out <code>y</code> will be a vector or batch of length <code>out</code>.</p><pre><code class="language-julia">julia> d = Dense(5, 2)
|
||||
Dense(5, 2)
|
||||
|
||||
julia> d(rand(5))
|
||||
Tracked 2-element Array{Float64,1}:
|
||||
0.00257447
|
||||
-0.00449443</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/basic.jl#L43-L62">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Conv" href="#Flux.Conv"><code>Flux.Conv</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Conv(size, in=>out)
|
||||
Conv(size, in=>out, relu)</code></pre><p>Standard convolutional layer. <code>size</code> should be a tuple like <code>(2, 2)</code>. <code>in</code> and <code>out</code> specify the number of input and output channels respectively.</p><p>Data should be stored in WHCN order. In other words, a 100×100 RGB image would be a <code>100×100×3</code> array, and a batch of 50 would be a <code>100×100×3×50</code> array.</p><p>Takes the keyword arguments <code>pad</code>, <code>stride</code> and <code>dilation</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/conv.jl#L8-L19">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.MaxPool" href="#Flux.MaxPool"><code>Flux.MaxPool</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">MaxPool(k)</code></pre><p>Max pooling layer. <code>k</code> stands for the size of the window for each dimension of the input.</p><p>Takes the keyword arguments <code>pad</code> and <code>stride</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/conv.jl#L111-L117">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.MeanPool" href="#Flux.MeanPool"><code>Flux.MeanPool</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">MeanPool(k)</code></pre><p>Mean pooling layer. <code>k</code> stands for the size of the window for each dimension of the input.</p><p>Takes the keyword arguments <code>pad</code> and <code>stride</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/conv.jl#L133-L139">source</a></section><h2><a class="nav-anchor" id="Additional-Convolution-Layers-1" href="#Additional-Convolution-Layers-1">Additional Convolution Layers</a></h2><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.DepthwiseConv" href="#Flux.DepthwiseConv"><code>Flux.DepthwiseConv</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">DepthwiseConv(size, in)
|
||||
DepthwiseConv(size, in=>mul)
|
||||
DepthwiseConv(size, in=>mul, relu)</code></pre><p>Depthwise convolutional layer. <code>size</code> should be a tuple like <code>(2, 2)</code>. <code>in</code> and <code>mul</code> specify the number of input channels and channel multiplier respectively. In case the <code>mul</code> is not specified it is taken as 1.</p><p>Data should be stored in WHCN order. In other words, a 100×100 RGB image would be a <code>100×100×3</code> array, and a batch of 50 would be a <code>100×100×3×50</code> array.</p><p>Takes the keyword arguments <code>pad</code> and <code>stride</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/conv.jl#L60-L73">source</a></section><h2><a class="nav-anchor" id="Recurrent-Layers-1" href="#Recurrent-Layers-1">Recurrent Layers</a></h2><p>Much like the core layers above, but can be used to process sequence data (as well as other kinds of structured data).</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.RNN" href="#Flux.RNN"><code>Flux.RNN</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">RNN(in::Integer, out::Integer, σ = tanh)</code></pre><p>The most basic recurrent layer; essentially acts as a <code>Dense</code> layer, but with the output fed back into the input each time step.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/recurrent.jl#L105-L110">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.LSTM" href="#Flux.LSTM"><code>Flux.LSTM</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">LSTM(in::Integer, out::Integer)</code></pre><p>Long Short Term Memory recurrent layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.</p><p>See <a href="http://colah.github.io/posts/2015-08-Understanding-LSTMs/">this article</a> for a good overview of the internals.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/recurrent.jl#L150-L158">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.GRU" href="#Flux.GRU"><code>Flux.GRU</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">GRU(in::Integer, out::Integer)</code></pre><p>Gated Recurrent Unit layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.</p><p>See <a href="http://colah.github.io/posts/2015-08-Understanding-LSTMs/">this article</a> for a good overview of the internals.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/recurrent.jl#L191-L199">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Recur" href="#Flux.Recur"><code>Flux.Recur</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Recur(cell)</code></pre><p><code>Recur</code> takes a recurrent cell and makes it stateful, managing the hidden state in the background. <code>cell</code> should be a model of the form:</p><pre><code class="language-none">h, y = cell(h, x...)</code></pre><p>For example, here's a recurrent network that keeps a running total of its inputs.</p><pre><code class="language-julia">accum(h, x) = (h+x, x)
|
||||
-0.00449443</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/basic.jl#L43-L62">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Conv" href="#Flux.Conv"><code>Flux.Conv</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Conv(size, in=>out)
|
||||
Conv(size, in=>out, relu)</code></pre><p>Standard convolutional layer. <code>size</code> should be a tuple like <code>(2, 2)</code>. <code>in</code> and <code>out</code> specify the number of input and output channels respectively.</p><p>Data should be stored in WHCN order. In other words, a 100×100 RGB image would be a <code>100×100×3</code> array, and a batch of 50 would be a <code>100×100×3×50</code> array.</p><p>Takes the keyword arguments <code>pad</code>, <code>stride</code> and <code>dilation</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/conv.jl#L8-L19">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.MaxPool" href="#Flux.MaxPool"><code>Flux.MaxPool</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">MaxPool(k)</code></pre><p>Max pooling layer. <code>k</code> stands for the size of the window for each dimension of the input.</p><p>Takes the keyword arguments <code>pad</code> and <code>stride</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/conv.jl#L55-L61">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.MeanPool" href="#Flux.MeanPool"><code>Flux.MeanPool</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">MeanPool(k)</code></pre><p>Mean pooling layer. <code>k</code> stands for the size of the window for each dimension of the input.</p><p>Takes the keyword arguments <code>pad</code> and <code>stride</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/conv.jl#L77-L83">source</a></section><h2><a class="nav-anchor" id="Recurrent-Layers-1" href="#Recurrent-Layers-1">Recurrent Layers</a></h2><p>Much like the core layers above, but can be used to process sequence data (as well as other kinds of structured data).</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.RNN" href="#Flux.RNN"><code>Flux.RNN</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">RNN(in::Integer, out::Integer, σ = tanh)</code></pre><p>The most basic recurrent layer; essentially acts as a <code>Dense</code> layer, but with the output fed back into the input each time step.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/recurrent.jl#L105-L110">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.LSTM" href="#Flux.LSTM"><code>Flux.LSTM</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">LSTM(in::Integer, out::Integer)</code></pre><p>Long Short Term Memory recurrent layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.</p><p>See <a href="http://colah.github.io/posts/2015-08-Understanding-LSTMs/">this article</a> for a good overview of the internals.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/recurrent.jl#L150-L158">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.GRU" href="#Flux.GRU"><code>Flux.GRU</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">GRU(in::Integer, out::Integer)</code></pre><p>Gated Recurrent Unit layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.</p><p>See <a href="http://colah.github.io/posts/2015-08-Understanding-LSTMs/">this article</a> for a good overview of the internals.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/recurrent.jl#L191-L199">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Recur" href="#Flux.Recur"><code>Flux.Recur</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Recur(cell)</code></pre><p><code>Recur</code> takes a recurrent cell and makes it stateful, managing the hidden state in the background. <code>cell</code> should be a model of the form:</p><pre><code class="language-none">h, y = cell(h, x...)</code></pre><p>For example, here's a recurrent network that keeps a running total of its inputs.</p><pre><code class="language-julia">accum(h, x) = (h+x, x)
|
||||
rnn = Flux.Recur(accum, 0)
|
||||
rnn(2) # 2
|
||||
rnn(3) # 3
|
||||
rnn.state # 5
|
||||
rnn.(1:10) # apply to a sequence
|
||||
rnn.state # 60</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/recurrent.jl#L7-L26">source</a></section><h2><a class="nav-anchor" id="Activation-Functions-1" href="#Activation-Functions-1">Activation Functions</a></h2><p>Non-linearities that go between layers of your model. Most of these functions are defined in <a href="https://github.com/FluxML/NNlib.jl">NNlib</a> but are available by default in Flux.</p><p>Note that, unless otherwise stated, activation functions operate on scalars. To apply them to an array you can call <code>σ.(xs)</code>, <code>relu.(xs)</code> and so on.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.σ" href="#NNlib.σ"><code>NNlib.σ</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">σ(x) = 1 / (1 + exp(-x))</code></pre><p>Classic <a href="https://en.wikipedia.org/wiki/Sigmoid_function">sigmoid</a> activation function.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.relu" href="#NNlib.relu"><code>NNlib.relu</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">relu(x) = max(0, x)</code></pre><p><a href="https://en.wikipedia.org/wiki/Rectifier_(neural_networks)">Rectified Linear Unit</a> activation function.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.leakyrelu" href="#NNlib.leakyrelu"><code>NNlib.leakyrelu</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">leakyrelu(x) = max(0.01x, x)</code></pre><p>Leaky <a href="https://en.wikipedia.org/wiki/Rectifier_(neural_networks)">Rectified Linear Unit</a> activation function. You can also specify the coefficient explicitly, e.g. <code>leakyrelu(x, 0.01)</code>.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.elu" href="#NNlib.elu"><code>NNlib.elu</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">elu(x, α = 1) =
|
||||
rnn.state # 60</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/recurrent.jl#L7-L26">source</a></section><h2><a class="nav-anchor" id="Activation-Functions-1" href="#Activation-Functions-1">Activation Functions</a></h2><p>Non-linearities that go between layers of your model. Most of these functions are defined in <a href="https://github.com/FluxML/NNlib.jl">NNlib</a> but are available by default in Flux.</p><p>Note that, unless otherwise stated, activation functions operate on scalars. To apply them to an array you can call <code>σ.(xs)</code>, <code>relu.(xs)</code> and so on.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.σ" href="#NNlib.σ"><code>NNlib.σ</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">σ(x) = 1 / (1 + exp(-x))</code></pre><p>Classic <a href="https://en.wikipedia.org/wiki/Sigmoid_function">sigmoid</a> activation function.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.relu" href="#NNlib.relu"><code>NNlib.relu</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">relu(x) = max(0, x)</code></pre><p><a href="https://en.wikipedia.org/wiki/Rectifier_(neural_networks)">Rectified Linear Unit</a> activation function.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.leakyrelu" href="#NNlib.leakyrelu"><code>NNlib.leakyrelu</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">leakyrelu(x) = max(0.01x, x)</code></pre><p>Leaky <a href="https://en.wikipedia.org/wiki/Rectifier_(neural_networks)">Rectified Linear Unit</a> activation function. You can also specify the coefficient explicitly, e.g. <code>leakyrelu(x, 0.01)</code>.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.elu" href="#NNlib.elu"><code>NNlib.elu</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">elu(x, α = 1) =
|
||||
x > 0 ? x : α * (exp(x) - 1)</code></pre><p>Exponential Linear Unit activation function. See <a href="https://arxiv.org/abs/1511.07289">Fast and Accurate Deep Network Learning by Exponential Linear Units</a>. You can also specify the coefficient explicitly, e.g. <code>elu(x, 1)</code>.</p></div></div></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="NNlib.swish" href="#NNlib.swish"><code>NNlib.swish</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">swish(x) = x * σ(x)</code></pre><p>Self-gated actvation function. See <a href="https://arxiv.org/pdf/1710.05941.pdf">Swish: a Self-Gated Activation Function</a>.</p></div></div></section><h2><a class="nav-anchor" id="Normalisation-and-Regularisation-1" href="#Normalisation-and-Regularisation-1">Normalisation & Regularisation</a></h2><p>These layers don't affect the structure of the network but may improve training times or reduce overfitting.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.testmode!" href="#Flux.testmode!"><code>Flux.testmode!</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">testmode!(m)
|
||||
testmode!(m, false)</code></pre><p>Put layers like <a href="layers.html#Flux.Dropout"><code>Dropout</code></a> and <a href="layers.html#Flux.BatchNorm"><code>BatchNorm</code></a> into testing mode (or back to training mode with <code>false</code>).</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/normalise.jl#L1-L7">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.BatchNorm" href="#Flux.BatchNorm"><code>Flux.BatchNorm</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">BatchNorm(channels::Integer, σ = identity;
|
||||
testmode!(m, false)</code></pre><p>Put layers like <a href="layers.html#Flux.Dropout"><code>Dropout</code></a> and <a href="layers.html#Flux.BatchNorm"><code>BatchNorm</code></a> into testing mode (or back to training mode with <code>false</code>).</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/normalise.jl#L1-L7">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.BatchNorm" href="#Flux.BatchNorm"><code>Flux.BatchNorm</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">BatchNorm(channels::Integer, σ = identity;
|
||||
initβ = zeros, initγ = ones,
|
||||
ϵ = 1e-8, momentum = .1)</code></pre><p>Batch Normalization layer. The <code>channels</code> input should be the size of the channel dimension in your data (see below).</p><p>Given an array with <code>N</code> dimensions, call the <code>N-1</code>th the channel dimension. (For a batch of feature vectors this is just the data dimension, for <code>WHCN</code> images it's the usual channel dimension.)</p><p><code>BatchNorm</code> computes the mean and variance for each each <code>W×H×1×N</code> slice and shifts them to have a new mean and variance (corresponding to the learnable, per-channel <code>bias</code> and <code>scale</code> parameters).</p><p>See <a href="https://arxiv.org/pdf/1502.03167.pdf">Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift</a>.</p><p>Example:</p><pre><code class="language-julia">m = Chain(
|
||||
Dense(28^2, 64),
|
||||
BatchNorm(64, relu),
|
||||
Dense(64, 10),
|
||||
BatchNorm(10),
|
||||
softmax)</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/normalise.jl#L69-L98">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Dropout" href="#Flux.Dropout"><code>Flux.Dropout</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Dropout(p)</code></pre><p>A Dropout layer. For each input, either sets that input to <code>0</code> (with probability <code>p</code>) or scales it by <code>1/(1-p)</code>. This is used as a regularisation, i.e. it reduces overfitting during training.</p><p>Does nothing to the input once in <a href="layers.html#Flux.testmode!"><code>testmode!</code></a>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/normalise.jl#L15-L23">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.LayerNorm" href="#Flux.LayerNorm"><code>Flux.LayerNorm</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">LayerNorm(h::Integer)</code></pre><p>A <a href="https://arxiv.org/pdf/1607.06450.pdf">normalisation layer</a> designed to be used with recurrent hidden states of size <code>h</code>. Normalises the mean/stddev of each input before applying a per-neuron gain/bias.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/fc9f1e101f7f7a64bbef3ea23d59a0429f867e56/src/layers/normalise.jl#L46-L53">source</a></section><footer><hr/><a class="previous" href="regularisation.html"><span class="direction">Previous</span><span class="title">Regularisation</span></a><a class="next" href="../training/optimisers.html"><span class="direction">Next</span><span class="title">Optimisers</span></a></footer></article></body></html>
|
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softmax)</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/normalise.jl#L69-L98">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Dropout" href="#Flux.Dropout"><code>Flux.Dropout</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Dropout(p)</code></pre><p>A Dropout layer. For each input, either sets that input to <code>0</code> (with probability <code>p</code>) or scales it by <code>1/(1-p)</code>. This is used as a regularisation, i.e. it reduces overfitting during training.</p><p>Does nothing to the input once in <a href="layers.html#Flux.testmode!"><code>testmode!</code></a>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/normalise.jl#L15-L23">source</a></section><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.LayerNorm" href="#Flux.LayerNorm"><code>Flux.LayerNorm</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">LayerNorm(h::Integer)</code></pre><p>A <a href="https://arxiv.org/pdf/1607.06450.pdf">normalisation layer</a> designed to be used with recurrent hidden states of size <code>h</code>. Normalises the mean/stddev of each input before applying a per-neuron gain/bias.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/layers/normalise.jl#L46-L53">source</a></section><footer><hr/><a class="previous" href="regularisation.html"><span class="direction">Previous</span><span class="title">Regularisation</span></a><a class="next" href="../training/optimisers.html"><span class="direction">Next</span><span class="title">Optimisers</span></a></footer></article></body></html>
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@ -208,22 +208,6 @@ var documenterSearchIndex = {"docs": [
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"text": "These core layers form the foundation of almost all neural networks.Chain\nDense\nConv\nMaxPool\nMeanPool"
|
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|
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|
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{
|
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"location": "models/layers.html#Flux.DepthwiseConv",
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|
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|
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"category": "type",
|
||||
"text": "DepthwiseConv(size, in)\nDepthwiseConv(size, in=>mul)\nDepthwiseConv(size, in=>mul, relu)\n\nDepthwise convolutional layer. size should be a tuple like (2, 2). in and mul specify the number of input channels and channel multiplier respectively. In case the mul is not specified it is taken as 1.\n\nData should be stored in WHCN order. In other words, a 100×100 RGB image would be a 100×100×3 array, and a batch of 50 would be a 100×100×3×50 array.\n\nTakes the keyword arguments pad and stride.\n\n\n\n\n\n"
|
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|
||||
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||||
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|
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"page": "Model Reference",
|
||||
"title": "Additional Convolution Layers",
|
||||
"category": "section",
|
||||
"text": "DepthwiseConv"
|
||||
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|
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|
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{
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"location": "models/layers.html#Flux.RNN",
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"text": "Consider a simple linear regression. We create some dummy data, calculate a loss, and backpropagate to calculate gradients for the parameters W and b.using Flux.Tracker\n\nW = param(rand(2, 5))\nb = param(rand(2))\n\npredict(x) = W*x .+ b\nloss(x, y) = sum((predict(x) .- y).^2)\n\nx, y = rand(5), rand(2) # Dummy data\nl = loss(x, y) # ~ 3\n\nparams = Params([W, b])\ngrads = Tracker.gradient(() -> loss(x, y), params)We want to update each parameter, using the gradient, in order to improve (reduce) the loss. Here\'s one way to do that:using Flux.Tracker: grad, update!\n\nfunction sgd()\n η = 0.1 # Learning Rate\n for p in (W, b)\n update!(p, -η * grads[p])\n end\nendIf we call sgd, the parameters W and b will change and our loss should go down.There are two pieces here: one is that we need a list of trainable parameters for the model ([W, b] in this case), and the other is the update step. In this case the update is simply gradient descent (x .-= η .* Δ), but we might choose to do something more advanced, like adding momentum.In this case, getting the variables is trivial, but you can imagine it\'d be more of a pain with some complex stack of layers.m = Chain(\n Dense(10, 5, σ),\n Dense(5, 2), softmax)Instead of having to write [m[1].W, m[1].b, ...], Flux provides a params function params(m) that returns a list of all parameters in the model for you.For the update step, there\'s nothing whatsoever wrong with writing the loop above – it\'ll work just fine – but Flux provides various optimisers that make it more convenient.opt = SGD([W, b], 0.1) # Gradient descent with learning rate 0.1\n\nopt() # Carry out the update, modifying `W` and `b`.An optimiser takes a parameter list and returns a function that does the same thing as update above. We can pass either opt or update to our training loop, which will then run the optimiser after every mini-batch of data."
|
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},
|
||||
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{
|
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"page": "Optimisers",
|
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"title": "Flux.Optimise.SGD",
|
||||
"category": "function",
|
||||
"text": "SGD(params, η = 0.1; decay = 0)\n\nClassic gradient descent optimiser with learning rate η. For each parameter p and its gradient δp, this runs p -= η*δp.\n\nSupports inverse decaying learning rate if the decay argument is provided.\n\n\n\n\n\n"
|
||||
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|
||||
|
||||
{
|
||||
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|
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|
||||
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|
||||
"text": "Momentum(params, η = 0.01; ρ = 0.9, decay = 0)\n\nSGD with learning rate η, momentum ρ and optional learning rate inverse decay.\n\n\n\n\n\n"
|
||||
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|
||||
|
||||
{
|
||||
"location": "training/optimisers.html#Flux.Optimise.Nesterov",
|
||||
"page": "Optimisers",
|
||||
"title": "Flux.Optimise.Nesterov",
|
||||
"category": "function",
|
||||
"text": "Nesterov(params, η = 0.01; ρ = 0.9, decay = 0)\n\nSGD with learning rate η, Nesterov momentum ρ and optional learning rate inverse decay.\n\n\n\n\n\n"
|
||||
},
|
||||
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{
|
||||
"location": "training/optimisers.html#Flux.Optimise.ADAM",
|
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"page": "Optimisers",
|
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"title": "Flux.Optimise.ADAM",
|
||||
"category": "function",
|
||||
"text": "ADAM(params, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)\n\nADAM optimiser.\n\n\n\n\n\n"
|
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@ -29,7 +29,4 @@ end</code></pre><p>If we call <code>sgd</code>, the parameters <code>W</code> an
|
|||
Dense(10, 5, σ),
|
||||
Dense(5, 2), softmax)</code></pre><p>Instead of having to write <code>[m[1].W, m[1].b, ...]</code>, Flux provides a params function <code>params(m)</code> that returns a list of all parameters in the model for you.</p><p>For the update step, there's nothing whatsoever wrong with writing the loop above – it'll work just fine – but Flux provides various <em>optimisers</em> that make it more convenient.</p><pre><code class="language-julia">opt = SGD([W, b], 0.1) # Gradient descent with learning rate 0.1
|
||||
|
||||
opt() # Carry out the update, modifying `W` and `b`.</code></pre><p>An optimiser takes a parameter list and returns a function that does the same thing as <code>update</code> above. We can pass either <code>opt</code> or <code>update</code> to our <a href="training.html">training loop</a>, which will then run the optimiser after every mini-batch of data.</p><h2><a class="nav-anchor" id="Optimiser-Reference-1" href="#Optimiser-Reference-1">Optimiser Reference</a></h2><p>All optimisers return a function that, when called, will update the parameters passed to it.</p><pre><code class="language-none">SGD
|
||||
Momentum
|
||||
Nesterov
|
||||
ADAM</code></pre><footer><hr/><a class="previous" href="../models/layers.html"><span class="direction">Previous</span><span class="title">Model Reference</span></a><a class="next" href="training.html"><span class="direction">Next</span><span class="title">Training</span></a></footer></article></body></html>
|
||||
opt() # Carry out the update, modifying `W` and `b`.</code></pre><p>An optimiser takes a parameter list and returns a function that does the same thing as <code>update</code> above. We can pass either <code>opt</code> or <code>update</code> to our <a href="training.html">training loop</a>, which will then run the optimiser after every mini-batch of data.</p><h2><a class="nav-anchor" id="Optimiser-Reference-1" href="#Optimiser-Reference-1">Optimiser Reference</a></h2><p>All optimisers return a function that, when called, will update the parameters passed to it.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Optimise.SGD" href="#Flux.Optimise.SGD"><code>Flux.Optimise.SGD</code></a> — <span class="docstring-category">Function</span>.</div><div><div><pre><code class="language-none">SGD(params, η = 0.1; decay = 0)</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>Supports inverse decaying learning rate if the <code>decay</code> argument is provided.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/optimise/interface.jl#L14-L21">source</a></section><section class="docstring"><div 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">Function</span>.</div><div><div><pre><code class="language-none">Momentum(params, η = 0.01; ρ = 0.9, decay = 0)</code></pre><p>SGD with learning rate <code>η</code>, momentum <code>ρ</code> and optional learning rate inverse decay.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/optimise/interface.jl#L25-L29">source</a></section><section class="docstring"><div 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">Function</span>.</div><div><div><pre><code class="language-none">Nesterov(params, η = 0.01; ρ = 0.9, decay = 0)</code></pre><p>SGD with learning rate <code>η</code>, Nesterov momentum <code>ρ</code> and optional learning rate inverse decay.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/optimise/interface.jl#L33-L37">source</a></section><section class="docstring"><div 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">Function</span>.</div><div><div><pre><code class="language-none">ADAM(params, η = 0.001; β1 = 0.9, β2 = 0.999, ϵ = 1e-08, decay = 0)</code></pre><p><a href="https://arxiv.org/abs/1412.6980v8">ADAM</a> optimiser.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/63a3acbf5e82286ff66a26037b2ecc16d374dc85/src/optimise/interface.jl#L51-L55">source</a></section><footer><hr/><a class="previous" href="../models/layers.html"><span class="direction">Previous</span><span class="title">Model Reference</span></a><a class="next" href="training.html"><span class="direction">Next</span><span class="title">Training</span></a></footer></article></body></html>
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Reference in New Issue