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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Community · Flux</title><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>One-Hot Encoding · Flux</title><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
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julia&gt; onehot(:b, [:a, :b, :c])
3-element Flux.OneHotVector:
false
true
false
julia&gt; onehot(:c, [:a, :b, :c])
3-element Flux.OneHotVector:
false
false
true</code></pre><p>The inverse is <code>onecold</code> (which can take a general probability distribution, as well as just booleans).</p><pre><code class="language-julia">julia&gt; onecold(ans, [:a, :b, :c])
:c
julia&gt; onecold([true, false, false], [:a, :b, :c])
:a
julia&gt; onecold([0.3, 0.2, 0.5], [:a, :b, :c])
:c</code></pre><h2><a class="nav-anchor" id="Batches-1" href="#Batches-1">Batches</a></h2><p><code>onehotbatch</code> creates a batch (matrix) of one-hot vectors, and <code>onecold</code> treats matrices as batches.</p><pre><code class="language-julia">julia&gt; using Flux: onehotbatch
julia&gt; onehotbatch([:b, :a, :b], [:a, :b, :c])
3×3 Flux.OneHotMatrix:
false true false
true false true
false false false
julia&gt; onecold(ans, [:a, :b, :c])
3-element Array{Symbol,1}:
:b
:a
:b</code></pre><p>Note that these operations returned <code>OneHotVector</code> and <code>OneHotMatrix</code> rather than <code>Array</code>s. <code>OneHotVector</code>s behave like normal vectors but avoid any unnecessary cost compared to using an integer index directly. For example, multiplying a matrix with a one-hot vector simply slices out the relevant row of the matrix under the hood.</p><footer><hr/><a class="previous" href="../../training/training/"><span class="direction">Previous</span><span class="title">Training</span></a><a class="next" href="../../gpu/"><span class="direction">Next</span><span class="title">GPU Support</span></a></footer></article></body></html>

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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>GPU Support · Flux</title><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
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W = cu(rand(2, 5)) # a 2×5 CuArray
b = cu(rand(2))
predict(x) = W*x .+ b
loss(x, y) = sum((predict(x) .- y).^2)
x, y = cu(rand(5)), cu(rand(2)) # Dummy data
loss(x, y) # ~ 3</code></pre><p>Note that we convert both the parameters (<code>W</code>, <code>b</code>) and the data set (<code>x</code>, <code>y</code>) to cuda arrays. Taking derivatives and training works exactly as before.</p><p>If you define a structured model, like a <code>Dense</code> layer or <code>Chain</code>, you just need to convert the internal parameters. Flux provides <code>mapleaves</code>, which allows you to alter all parameters of a model at once.</p><pre><code class="language-julia">d = Dense(10, 5, σ)
d = mapleaves(cu, d)
d.W # Tracked CuArray
d(cu(rand(10))) # CuArray output
m = Chain(Dense(10, 5, σ), Dense(5, 2), softmax)
m = mapleaves(cu, m)
d(cu(rand(10)))</code></pre><p>As a convenience, Flux provides the <code>gpu</code> function to convert models and data to the GPU if one is available. By default, it&#39;ll do nothing, but loading <code>CuArrays</code> will cause it to move data to the GPU instead.</p><pre><code class="language-julia">julia&gt; using Flux, CuArrays
julia&gt; m = Dense(10,5) |&gt; gpu
Dense(10, 5)
julia&gt; x = rand(10) |&gt; gpu
10-element CuArray{Float32,1}:
0.800225
⋮
0.511655
julia&gt; m(x)
Tracked 5-element CuArray{Float32,1}:
-0.30535
⋮
-0.618002</code></pre><p>The analogue <code>cpu</code> is also available for moving models and data back off of the GPU.</p><pre><code class="language-julia">julia&gt; x = rand(10) |&gt; gpu
10-element CuArray{Float32,1}:
0.235164
⋮
0.192538
julia&gt; x |&gt; cpu
10-element Array{Float32,1}:
0.235164
⋮
0.192538</code></pre><footer><hr/><a class="previous" href="../data/onehot/"><span class="direction">Previous</span><span class="title">One-Hot Encoding</span></a><a class="next" href="../saving/"><span class="direction">Next</span><span class="title">Saving &amp; Loading</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="../models/basics.html">Basics</a></li><li><a class="toctext" href="../models/recurrence.html">Recurrence</a></li><li><a class="toctext" href="../models/regularisation.html">Regularisation</a></li><li><a class="toctext" href="../models/layers.html">Model Reference</a></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 &amp; Loading</a></li><li><span class="toctext">Internals</span><ul><li class="current"><a class="toctext" href="tracker.html">Backpropagation</a><ul class="internal"><li><a class="toctext" href="#Taking-Gradients-1">Taking Gradients</a></li><li><a class="toctext" href="#Tracked-Arrays-1">Tracked Arrays</a></li><li><a class="toctext" href="#Custom-Gradients-1">Custom Gradients</a></li><li><a class="toctext" href="#Tracked-Internals-1">Tracked Internals</a></li></ul></li></ul></li><li><a class="toctext" href="../community.html">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Internals</li><li><a href="tracker.html">Backpropagation</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/internals/tracker.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Backpropagation</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Flux.Tracker-1" href="#Flux.Tracker-1">Flux.Tracker</a></h1><p>Backpropagation, or reverse-mode automatic differentiation, is handled by the <code>Flux.Tracker</code> module.</p><pre><code class="language-julia">julia&gt; using Flux.Tracker</code></pre><p>Here we discuss some more advanced uses of this module, as well as covering its internals.</p><h2><a class="nav-anchor" id="Taking-Gradients-1" href="#Taking-Gradients-1">Taking Gradients</a></h2><p>In the <a href="../models/basics.html">basics section</a> we covered basic usage of the <code>gradient</code> function.</p><pre><code class="language-julia">using Flux.Tracker
</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="../../assets/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/"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../../">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="../../models/basics/">Basics</a></li><li><a class="toctext" href="../../models/recurrence/">Recurrence</a></li><li><a class="toctext" href="../../models/regularisation/">Regularisation</a></li><li><a class="toctext" href="../../models/layers/">Model Reference</a></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../../training/optimisers/">Optimisers</a></li><li><a class="toctext" href="../../training/training/">Training</a></li></ul></li><li><a class="toctext" href="../../data/onehot/">One-Hot Encoding</a></li><li><a class="toctext" href="../../gpu/">GPU Support</a></li><li><a class="toctext" href="../../saving/">Saving &amp; Loading</a></li><li><span class="toctext">Internals</span><ul><li class="current"><a class="toctext" href>Backpropagation</a><ul class="internal"><li><a class="toctext" href="#Taking-Gradients-1">Taking Gradients</a></li><li><a class="toctext" href="#Tracked-Arrays-1">Tracked Arrays</a></li><li><a class="toctext" href="#Custom-Gradients-1">Custom Gradients</a></li><li><a class="toctext" href="#Tracked-Internals-1">Tracked Internals</a></li></ul></li></ul></li><li><a class="toctext" href="../../community/">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Internals</li><li><a href>Backpropagation</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/internals/tracker.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Backpropagation</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Flux.Tracker-1" href="#Flux.Tracker-1">Flux.Tracker</a></h1><p>Backpropagation, or reverse-mode automatic differentiation, is handled by the <code>Flux.Tracker</code> module.</p><pre><code class="language-julia">julia&gt; using Flux.Tracker</code></pre><p>Here we discuss some more advanced uses of this module, as well as covering its internals.</p><h2><a class="nav-anchor" id="Taking-Gradients-1" href="#Taking-Gradients-1">Taking Gradients</a></h2><p>In the <a href="../../models/basics/">basics section</a> we covered basic usage of the <code>gradient</code> function.</p><pre><code class="language-julia">using Flux.Tracker
Tracker.gradient((a, b) -&gt; a*b, 2, 3) # (3.0 (tracked), 2.0 (tracked))</code></pre><p><code>gradient</code> is actually just a thin wrapper around the backpropagator-based interface, <code>forward</code>.</p><pre><code class="language-julia">using Flux.Tracker: forward
@ -63,4 +63,4 @@ Flux.Tracker.Tracked{Array{Float64,1}}(0x00000000, Flux.Tracker.Call{Nothing,Tup
-2.0
-2.0</code></pre><p>The tracker also contains a <code>Call</code> object, which simply represents a function call that was made at some point during the forward pass. For example, the <code>+</code> call would look like this:</p><pre><code class="language-julia">julia&gt; Tracker.Call(+, 1, 2)
Flux.Tracker.Call{Base.#+,Tuple{Int64,Int64}}(+, (1, 2))</code></pre><p>In the case of the <code>y</code> we produced above, we can see that it stores the call that produced it – that is, <code>W*x</code>.</p><pre><code class="language-julia">julia&gt; y.tracker.f
Flux.Tracker.Call{...}(*, (param([1.0 2.0; 3.0 4.0]), param([5.0, 6.0])))</code></pre><p>Notice that because the arguments to the call may also be tracked arrays, storing their own calls, this means that <code>Tracker</code> ends up forming a data structure that records everything that happened during the forward pass (often known as a <em>tape</em>).</p><p>When we call <code>back!(y, [1, -1])</code>, the sensitivities <code>[1, -1]</code> simply get forwarded to <code>y</code>&#39;s call (<code>*</code>), effectively calling</p><pre><code class="language-julia">Tracker.back(*, [1, -1], W, x)</code></pre><p>which in turn calculates the sensitivities of the arguments (<code>W</code> and <code>x</code>) and back-propagates through their calls. This is recursive, so it will walk the entire program graph and propagate gradients to the original model parameters.</p><footer><hr/><a class="previous" href="../saving.html"><span class="direction">Previous</span><span class="title">Saving &amp; Loading</span></a><a class="next" href="../community.html"><span class="direction">Next</span><span class="title">Community</span></a></footer></article></body></html>
Flux.Tracker.Call{...}(*, (param([1.0 2.0; 3.0 4.0]), param([5.0, 6.0])))</code></pre><p>Notice that because the arguments to the call may also be tracked arrays, storing their own calls, this means that <code>Tracker</code> ends up forming a data structure that records everything that happened during the forward pass (often known as a <em>tape</em>).</p><p>When we call <code>back!(y, [1, -1])</code>, the sensitivities <code>[1, -1]</code> simply get forwarded to <code>y</code>&#39;s call (<code>*</code>), effectively calling</p><pre><code class="language-julia">Tracker.back(*, [1, -1], W, x)</code></pre><p>which in turn calculates the sensitivities of the arguments (<code>W</code> and <code>x</code>) and back-propagates through their calls. This is recursive, so it will walk the entire program graph and propagate gradients to the original model parameters.</p><footer><hr/><a class="previous" href="../../saving/"><span class="direction">Previous</span><span class="title">Saving &amp; Loading</span></a><a class="next" href="../../community/"><span class="direction">Next</span><span class="title">Community</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 class="current"><a class="toctext" href="basics.html">Basics</a><ul class="internal"><li><a class="toctext" href="#Taking-Gradients-1">Taking Gradients</a></li><li><a class="toctext" href="#Simple-Models-1">Simple Models</a></li><li><a class="toctext" href="#Building-Layers-1">Building Layers</a></li><li><a class="toctext" href="#Stacking-It-Up-1">Stacking It Up</a></li><li><a class="toctext" href="#Layer-helpers-1">Layer helpers</a></li></ul></li><li><a class="toctext" href="recurrence.html">Recurrence</a></li><li><a class="toctext" href="regularisation.html">Regularisation</a></li><li><a class="toctext" href="layers.html">Model Reference</a></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 &amp; 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="basics.html">Basics</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/basics.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Basics</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Model-Building-Basics-1" href="#Model-Building-Basics-1">Model-Building Basics</a></h1><h2><a class="nav-anchor" id="Taking-Gradients-1" href="#Taking-Gradients-1">Taking Gradients</a></h2><p>Flux&#39;s core feature is taking gradients of Julia code. The <code>gradient</code> function takes another Julia function <code>f</code> and a set of arguments, and returns the gradient with respect to each argument. (It&#39;s a good idea to try pasting these examples in the Julia terminal.)</p><pre><code class="language-julia">using Flux.Tracker
</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="../../assets/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/"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../../">Home</a></li><li><span class="toctext">Building Models</span><ul><li class="current"><a class="toctext" href>Basics</a><ul class="internal"><li><a class="toctext" href="#Taking-Gradients-1">Taking Gradients</a></li><li><a class="toctext" href="#Simple-Models-1">Simple Models</a></li><li><a class="toctext" href="#Building-Layers-1">Building Layers</a></li><li><a class="toctext" href="#Stacking-It-Up-1">Stacking It Up</a></li><li><a class="toctext" href="#Layer-helpers-1">Layer helpers</a></li></ul></li><li><a class="toctext" href="../recurrence/">Recurrence</a></li><li><a class="toctext" href="../regularisation/">Regularisation</a></li><li><a class="toctext" href="../layers/">Model Reference</a></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../../training/optimisers/">Optimisers</a></li><li><a class="toctext" href="../../training/training/">Training</a></li></ul></li><li><a class="toctext" href="../../data/onehot/">One-Hot Encoding</a></li><li><a class="toctext" href="../../gpu/">GPU Support</a></li><li><a class="toctext" href="../../saving/">Saving &amp; Loading</a></li><li><span class="toctext">Internals</span><ul><li><a class="toctext" href="../../internals/tracker/">Backpropagation</a></li></ul></li><li><a class="toctext" href="../../community/">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Building Models</li><li><a href>Basics</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/basics.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Basics</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Model-Building-Basics-1" href="#Model-Building-Basics-1">Model-Building Basics</a></h1><h2><a class="nav-anchor" id="Taking-Gradients-1" href="#Taking-Gradients-1">Taking Gradients</a></h2><p>Flux&#39;s core feature is taking gradients of Julia code. The <code>gradient</code> function takes another Julia function <code>f</code> and a set of arguments, and returns the gradient with respect to each argument. (It&#39;s a good idea to try pasting these examples in the Julia terminal.)</p><pre><code class="language-julia">using Flux.Tracker
f(x) = 3x^2 + 2x + 1
@ -53,7 +53,7 @@ gs = Tracker.gradient(() -&gt; loss(x, y), Params([W, b]))</code></pre><p>Now th
# Update the parameter and reset the gradient
update!(W, -0.1Δ)
loss(x, y) # ~ 2.5</code></pre><p>The loss has decreased a little, meaning that our prediction <code>x</code> is closer to the target <code>y</code>. If we have some data we can already try <a href="../training/training.html">training the model</a>.</p><p>All deep learning in Flux, however complex, is a simple generalisation of this example. Of course, models can <em>look</em> very different – they might have millions of parameters or complex control flow. Let&#39;s see how Flux handles more complex models.</p><h2><a class="nav-anchor" id="Building-Layers-1" href="#Building-Layers-1">Building Layers</a></h2><p>It&#39;s common to create more complex models than the linear regression above. For example, we might want to have two linear layers with a nonlinearity like <a href="https://en.wikipedia.org/wiki/Sigmoid_function">sigmoid</a> (<code>σ</code>) in between them. In the above style we could write this as:</p><pre><code class="language-julia">W1 = param(rand(3, 5))
loss(x, y) # ~ 2.5</code></pre><p>The loss has decreased a little, meaning that our prediction <code>x</code> is closer to the target <code>y</code>. If we have some data we can already try <a href="../../training/training/">training the model</a>.</p><p>All deep learning in Flux, however complex, is a simple generalisation of this example. Of course, models can <em>look</em> very different – they might have millions of parameters or complex control flow. Let&#39;s see how Flux handles more complex models.</p><h2><a class="nav-anchor" id="Building-Layers-1" href="#Building-Layers-1">Building Layers</a></h2><p>It&#39;s common to create more complex models than the linear regression above. For example, we might want to have two linear layers with a nonlinearity like <a href="https://en.wikipedia.org/wiki/Sigmoid_function">sigmoid</a> (<code>σ</code>) in between them. In the above style we could write this as:</p><pre><code class="language-julia">W1 = param(rand(3, 5))
b1 = param(rand(3))
layer1(x) = W1 * x .+ b1
@ -104,4 +104,4 @@ model2(rand(10)) # =&gt; 2-element vector</code></pre><p>This quickly starts to
m(rand(10))</code></pre><p>Likewise, <code>Chain</code> will happily work with any Julia function.</p><pre><code class="language-julia">m = Chain(x -&gt; x^2, x -&gt; x+1)
m(5) # =&gt; 26</code></pre><h2><a class="nav-anchor" id="Layer-helpers-1" href="#Layer-helpers-1">Layer helpers</a></h2><p>Flux provides a set of helpers for custom layers, which you can enable by calling</p><pre><code class="language-julia">Flux.@treelike Affine</code></pre><p>This enables a useful extra set of functionality for our <code>Affine</code> layer, such as <a href="../training/optimisers.html">collecting its parameters</a> or <a href="../gpu.html">moving it to the GPU</a>.</p><footer><hr/><a class="previous" href="../index.html"><span class="direction">Previous</span><span class="title">Home</span></a><a class="next" href="recurrence.html"><span class="direction">Next</span><span class="title">Recurrence</span></a></footer></article></body></html>
m(5) # =&gt; 26</code></pre><h2><a class="nav-anchor" id="Layer-helpers-1" href="#Layer-helpers-1">Layer helpers</a></h2><p>Flux provides a set of helpers for custom layers, which you can enable by calling</p><pre><code class="language-julia">Flux.@treelike Affine</code></pre><p>This enables a useful extra set of functionality for our <code>Affine</code> layer, such as <a href="../../training/optimisers/">collecting its parameters</a> or <a href="../../gpu/">moving it to the GPU</a>.</p><footer><hr/><a class="previous" href="../../"><span class="direction">Previous</span><span class="title">Home</span></a><a class="next" href="../recurrence/"><span class="direction">Next</span><span class="title">Recurrence</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 &amp; 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 &amp; 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 -&gt; x^2, x -&gt; x+1)
</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="../../assets/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/"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../../">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="../basics/">Basics</a></li><li><a class="toctext" href="../recurrence/">Recurrence</a></li><li><a class="toctext" href="../regularisation/">Regularisation</a></li><li class="current"><a class="toctext" href>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 &amp; Regularisation</a></li></ul></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../../training/optimisers/">Optimisers</a></li><li><a class="toctext" href="../../training/training/">Training</a></li></ul></li><li><a class="toctext" href="../../data/onehot/">One-Hot Encoding</a></li><li><a class="toctext" href="../../gpu/">GPU Support</a></li><li><a class="toctext" href="../../saving/">Saving &amp; Loading</a></li><li><span class="toctext">Internals</span><ul><li><a class="toctext" href="../../internals/tracker/">Backpropagation</a></li></ul></li><li><a class="toctext" href="../../community/">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Building Models</li><li><a href>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 -&gt; x^2, x -&gt; 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/9d56807bcd32461547dc8c4c0b3e8ef90057c2b8/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&gt; 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/347678344e7ff9a1f4a99a7bd2e27118559f3a52/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&gt; d = Dense(5, 2)
Dense(5, 2)
julia&gt; 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/9d56807bcd32461547dc8c4c0b3e8ef90057c2b8/src/layers/basic.jl#L45-L64">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=&gt;out)
Conv(size, in=&gt;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/9d56807bcd32461547dc8c4c0b3e8ef90057c2b8/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/9d56807bcd32461547dc8c4c0b3e8ef90057c2b8/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/9d56807bcd32461547dc8c4c0b3e8ef90057c2b8/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)
-0.00449443</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/347678344e7ff9a1f4a99a7bd2e27118559f3a52/src/layers/basic.jl#L45-L64">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=&gt;out)
Conv(size, in=&gt;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/347678344e7ff9a1f4a99a7bd2e27118559f3a52/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/347678344e7ff9a1f4a99a7bd2e27118559f3a52/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/347678344e7ff9a1f4a99a7bd2e27118559f3a52/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=&gt;mul)
DepthwiseConv(size, in=&gt;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/9d56807bcd32461547dc8c4c0b3e8ef90057c2b8/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/9d56807bcd32461547dc8c4c0b3e8ef90057c2b8/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/9d56807bcd32461547dc8c4c0b3e8ef90057c2b8/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/9d56807bcd32461547dc8c4c0b3e8ef90057c2b8/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&#39;s a recurrent network that keeps a running total of its inputs.</p><pre><code class="language-julia">accum(h, x) = (h+x, x)
DepthwiseConv(size, in=&gt;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/347678344e7ff9a1f4a99a7bd2e27118559f3a52/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/347678344e7ff9a1f4a99a7bd2e27118559f3a52/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/347678344e7ff9a1f4a99a7bd2e27118559f3a52/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/347678344e7ff9a1f4a99a7bd2e27118559f3a52/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&#39;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/9d56807bcd32461547dc8c4c0b3e8ef90057c2b8/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/347678344e7ff9a1f4a99a7bd2e27118559f3a52/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 &gt; 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 &amp; Regularisation</a></h2><p>These layers don&#39;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/9d56807bcd32461547dc8c4c0b3e8ef90057c2b8/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="#Flux.Dropout"><code>Dropout</code></a> and <a href="#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/347678344e7ff9a1f4a99a7bd2e27118559f3a52/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&#39;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/9d56807bcd32461547dc8c4c0b3e8ef90057c2b8/src/layers/normalise.jl#L68-L96">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/9d56807bcd32461547dc8c4c0b3e8ef90057c2b8/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/9d56807bcd32461547dc8c4c0b3e8ef90057c2b8/src/layers/normalise.jl#L46-L52">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>
softmax)</code></pre></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/347678344e7ff9a1f4a99a7bd2e27118559f3a52/src/layers/normalise.jl#L68-L96">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="#Flux.testmode!"><code>testmode!</code></a>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/347678344e7ff9a1f4a99a7bd2e27118559f3a52/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/347678344e7ff9a1f4a99a7bd2e27118559f3a52/src/layers/normalise.jl#L46-L52">source</a></section><footer><hr/><a class="previous" href="../regularisation/"><span class="direction">Previous</span><span class="title">Regularisation</span></a><a class="next" href="../../training/optimisers/"><span class="direction">Next</span><span class="title">Optimisers</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 class="current"><a class="toctext" href="recurrence.html">Recurrence</a><ul class="internal"><li><a class="toctext" href="#Recurrent-Cells-1">Recurrent Cells</a></li><li><a class="toctext" href="#Stateful-Models-1">Stateful Models</a></li><li><a class="toctext" href="#Sequences-1">Sequences</a></li><li><a class="toctext" href="#Truncating-Gradients-1">Truncating Gradients</a></li></ul></li><li><a class="toctext" href="regularisation.html">Regularisation</a></li><li><a class="toctext" href="layers.html">Model Reference</a></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 &amp; 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="recurrence.html">Recurrence</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/recurrence.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Recurrence</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Recurrent-Models-1" href="#Recurrent-Models-1">Recurrent Models</a></h1><h2><a class="nav-anchor" id="Recurrent-Cells-1" href="#Recurrent-Cells-1">Recurrent Cells</a></h2><p>In the simple feedforward case, our model <code>m</code> is a simple function from various inputs <code>xᵢ</code> to predictions <code>yᵢ</code>. (For example, each <code>x</code> might be an MNIST digit and each <code>y</code> a digit label.) Each prediction is completely independent of any others, and using the same <code>x</code> will always produce the same <code>y</code>.</p><pre><code class="language-julia">y₁ = f(x₁)
</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="../../assets/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/"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../../">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="../basics/">Basics</a></li><li class="current"><a class="toctext" href>Recurrence</a><ul class="internal"><li><a class="toctext" href="#Recurrent-Cells-1">Recurrent Cells</a></li><li><a class="toctext" href="#Stateful-Models-1">Stateful Models</a></li><li><a class="toctext" href="#Sequences-1">Sequences</a></li><li><a class="toctext" href="#Truncating-Gradients-1">Truncating Gradients</a></li></ul></li><li><a class="toctext" href="../regularisation/">Regularisation</a></li><li><a class="toctext" href="../layers/">Model Reference</a></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../../training/optimisers/">Optimisers</a></li><li><a class="toctext" href="../../training/training/">Training</a></li></ul></li><li><a class="toctext" href="../../data/onehot/">One-Hot Encoding</a></li><li><a class="toctext" href="../../gpu/">GPU Support</a></li><li><a class="toctext" href="../../saving/">Saving &amp; Loading</a></li><li><span class="toctext">Internals</span><ul><li><a class="toctext" href="../../internals/tracker/">Backpropagation</a></li></ul></li><li><a class="toctext" href="../../community/">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Building Models</li><li><a href>Recurrence</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/recurrence.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Recurrence</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Recurrent-Models-1" href="#Recurrent-Models-1">Recurrent Models</a></h1><h2><a class="nav-anchor" id="Recurrent-Cells-1" href="#Recurrent-Cells-1">Recurrent Cells</a></h2><p>In the simple feedforward case, our model <code>m</code> is a simple function from various inputs <code>xᵢ</code> to predictions <code>yᵢ</code>. (For example, each <code>x</code> might be an MNIST digit and each <code>y</code> a digit label.) Each prediction is completely independent of any others, and using the same <code>x</code> will always produce the same <code>y</code>.</p><pre><code class="language-julia">y₁ = f(x₁)
y₂ = f(x₂)
y₃ = f(x₃)
# ...</code></pre><p>Recurrent networks introduce a <em>hidden state</em> that gets carried over each time we run the model. The model now takes the old <code>h</code> as an input, and produces a new <code>h</code> as output, each time we run it.</p><pre><code class="language-julia">h = # ... initial state ...
@ -25,7 +25,7 @@ end
x = rand(10) # dummy data
h = rand(5) # initial hidden state
h, y = rnn(h, x)</code></pre><p>If you run the last line a few times, you&#39;ll notice the output <code>y</code> changing slightly even though the input <code>x</code> is the same.</p><p>We sometimes refer to functions like <code>rnn</code> above, which explicitly manage state, as recurrent <em>cells</em>. There are various recurrent cells available, which are documented in the <a href="layers.html">layer reference</a>. The hand-written example above can be replaced with:</p><pre><code class="language-julia">using Flux
h, y = rnn(h, x)</code></pre><p>If you run the last line a few times, you&#39;ll notice the output <code>y</code> changing slightly even though the input <code>x</code> is the same.</p><p>We sometimes refer to functions like <code>rnn</code> above, which explicitly manage state, as recurrent <em>cells</em>. There are various recurrent cells available, which are documented in the <a href="../layers/">layer reference</a>. The hand-written example above can be replaced with:</p><pre><code class="language-julia">using Flux
rnn2 = Flux.RNNCell(10, 5)
@ -39,4 +39,4 @@ m = Flux.Recur(rnn, h)
y = m(x)</code></pre><p>The <code>Recur</code> wrapper stores the state between runs in the <code>m.state</code> field.</p><p>If you use the <code>RNN(10, 5)</code> constructor – as opposed to <code>RNNCell</code> – you&#39;ll see that it&#39;s simply a wrapped cell.</p><pre><code class="language-julia">julia&gt; RNN(10, 5)
Recur(RNNCell(Dense(15, 5)))</code></pre><h2><a class="nav-anchor" id="Sequences-1" href="#Sequences-1">Sequences</a></h2><p>Often we want to work with sequences of inputs, rather than individual <code>x</code>s.</p><pre><code class="language-julia">seq = [rand(10) for i = 1:10]</code></pre><p>With <code>Recur</code>, applying our model to each element of a sequence is trivial:</p><pre><code class="language-julia">m.(seq) # returns a list of 5-element vectors</code></pre><p>This works even when we&#39;ve chain recurrent layers into a larger model.</p><pre><code class="language-julia">m = Chain(LSTM(10, 15), Dense(15, 5))
m.(seq)</code></pre><h2><a class="nav-anchor" id="Truncating-Gradients-1" href="#Truncating-Gradients-1">Truncating Gradients</a></h2><p>By default, calculating the gradients in a recurrent layer involves its entire history. For example, if we call the model on 100 inputs, we&#39;ll have to calculate the gradient for those 100 calls. If we then calculate another 10 inputs we have to calculate 110 gradients – this accumulates and quickly becomes expensive.</p><p>To avoid this we can <em>truncate</em> the gradient calculation, forgetting the history.</p><pre><code class="language-julia">truncate!(m)</code></pre><p>Calling <code>truncate!</code> wipes the slate clean, so we can call the model with more inputs without building up an expensive gradient computation.</p><p><code>truncate!</code> makes sense when you are working with multiple chunks of a large sequence, but we may also want to work with a set of independent sequences. In this case the hidden state should be completely reset to its original value, throwing away any accumulated information. <code>reset!</code> does this for you.</p><footer><hr/><a class="previous" href="basics.html"><span class="direction">Previous</span><span class="title">Basics</span></a><a class="next" href="regularisation.html"><span class="direction">Next</span><span class="title">Regularisation</span></a></footer></article></body></html>
m.(seq)</code></pre><h2><a class="nav-anchor" id="Truncating-Gradients-1" href="#Truncating-Gradients-1">Truncating Gradients</a></h2><p>By default, calculating the gradients in a recurrent layer involves its entire history. For example, if we call the model on 100 inputs, we&#39;ll have to calculate the gradient for those 100 calls. If we then calculate another 10 inputs we have to calculate 110 gradients – this accumulates and quickly becomes expensive.</p><p>To avoid this we can <em>truncate</em> the gradient calculation, forgetting the history.</p><pre><code class="language-julia">truncate!(m)</code></pre><p>Calling <code>truncate!</code> wipes the slate clean, so we can call the model with more inputs without building up an expensive gradient computation.</p><p><code>truncate!</code> makes sense when you are working with multiple chunks of a large sequence, but we may also want to work with a set of independent sequences. In this case the hidden state should be completely reset to its original value, throwing away any accumulated information. <code>reset!</code> does this for you.</p><footer><hr/><a class="previous" href="../basics/"><span class="direction">Previous</span><span class="title">Basics</span></a><a class="next" href="../regularisation/"><span class="direction">Next</span><span class="title">Regularisation</span></a></footer></article></body></html>

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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Regularisation · Flux</title><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
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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="../../assets/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/"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../../">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="../basics/">Basics</a></li><li><a class="toctext" href="../recurrence/">Recurrence</a></li><li class="current"><a class="toctext" href>Regularisation</a><ul class="internal"></ul></li><li><a class="toctext" href="../layers/">Model Reference</a></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../../training/optimisers/">Optimisers</a></li><li><a class="toctext" href="../../training/training/">Training</a></li></ul></li><li><a class="toctext" href="../../data/onehot/">One-Hot Encoding</a></li><li><a class="toctext" href="../../gpu/">GPU Support</a></li><li><a class="toctext" href="../../saving/">Saving &amp; Loading</a></li><li><span class="toctext">Internals</span><ul><li><a class="toctext" href="../../internals/tracker/">Backpropagation</a></li></ul></li><li><a class="toctext" href="../../community/">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Building Models</li><li><a href>Regularisation</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/regularisation.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Regularisation</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Regularisation-1" href="#Regularisation-1">Regularisation</a></h1><p>Applying regularisation to model parameters is straightforward. We just need to apply an appropriate regulariser, such as <code>norm</code>, to each model parameter and add the result to the overall loss.</p><p>For example, say we have a simple regression.</p><pre><code class="language-julia">using Flux: crossentropy
m = Dense(10, 5)
loss(x, y) = crossentropy(softmax(m(x)), y)</code></pre><p>We can regularise this by taking the (L2) norm of the parameters, <code>m.W</code> and <code>m.b</code>.</p><pre><code class="language-julia">penalty() = norm(m.W) + norm(m.b)
loss(x, y) = crossentropy(softmax(m(x)), y) + penalty()</code></pre><p>When working with layers, Flux provides the <code>params</code> function to grab all parameters at once. We can easily penalise everything with <code>sum(norm, params)</code>.</p><pre><code class="language-julia">julia&gt; params(m)
2-element Array{Any,1}:
param([0.355408 0.533092; … 0.430459 0.171498])
param([0.0, 0.0, 0.0, 0.0, 0.0])
julia&gt; sum(norm, params(m))
26.01749952921026 (tracked)</code></pre><p>Here&#39;s a larger example with a multi-layer perceptron.</p><pre><code class="language-julia">m = Chain(
Dense(28^2, 128, relu),
Dense(128, 32, relu),
Dense(32, 10), softmax)
loss(x, y) = crossentropy(m(x), y) + sum(norm, params(m))
loss(rand(28^2), rand(10))</code></pre><p>One can also easily add per-layer regularisation via the <code>activations</code> function:</p><pre><code class="language-julia">julia&gt; c = Chain(Dense(10,5,σ),Dense(5,2),softmax)
Chain(Dense(10, 5, NNlib.σ), Dense(5, 2), NNlib.softmax)
julia&gt; activations(c, rand(10))
3-element Array{Any,1}:
param([0.71068, 0.831145, 0.751219, 0.227116, 0.553074])
param([0.0330606, -0.456104])
param([0.61991, 0.38009])
julia&gt; sum(norm, ans)
2.639678767773633 (tracked)</code></pre><footer><hr/><a class="previous" href="../recurrence/"><span class="direction">Previous</span><span class="title">Recurrence</span></a><a class="next" href="../layers/"><span class="direction">Next</span><span class="title">Model Reference</span></a></footer></article></body></html>

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@ -6,7 +6,7 @@ m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
ga('create', 'UA-36890222-9', 'auto');
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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="models/basics.html">Basics</a></li><li><a class="toctext" href="models/recurrence.html">Recurrence</a></li><li><a class="toctext" href="models/regularisation.html">Regularisation</a></li><li><a class="toctext" href="models/layers.html">Model Reference</a></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 class="current"><a class="toctext" href="saving.html">Saving &amp; Loading</a><ul class="internal"><li><a class="toctext" href="#Saving-Model-Weights-1">Saving Model Weights</a></li><li><a class="toctext" href="#Checkpointing-1">Checkpointing</a></li></ul></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><a href="saving.html">Saving &amp; Loading</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/saving.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Saving &amp; Loading</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Saving-and-Loading-Models-1" href="#Saving-and-Loading-Models-1">Saving and Loading Models</a></h1><p>You may wish to save models so that they can be loaded and run in a later session. The easiest way to do this is via <a href="https://github.com/MikeInnes/BSON.jl">BSON.jl</a>.</p><p>Save a model:</p><pre><code class="language-julia">julia&gt; using Flux
</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="../assets/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/"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="../models/basics/">Basics</a></li><li><a class="toctext" href="../models/recurrence/">Recurrence</a></li><li><a class="toctext" href="../models/regularisation/">Regularisation</a></li><li><a class="toctext" href="../models/layers/">Model Reference</a></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../training/optimisers/">Optimisers</a></li><li><a class="toctext" href="../training/training/">Training</a></li></ul></li><li><a class="toctext" href="../data/onehot/">One-Hot Encoding</a></li><li><a class="toctext" href="../gpu/">GPU Support</a></li><li class="current"><a class="toctext" href>Saving &amp; Loading</a><ul class="internal"><li><a class="toctext" href="#Saving-Model-Weights-1">Saving Model Weights</a></li><li><a class="toctext" href="#Checkpointing-1">Checkpointing</a></li></ul></li><li><span class="toctext">Internals</span><ul><li><a class="toctext" href="../internals/tracker/">Backpropagation</a></li></ul></li><li><a class="toctext" href="../community/">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li><a href>Saving &amp; Loading</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/saving.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Saving &amp; Loading</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Saving-and-Loading-Models-1" href="#Saving-and-Loading-Models-1">Saving and Loading Models</a></h1><p>You may wish to save models so that they can be loaded and run in a later session. The easiest way to do this is via <a href="https://github.com/MikeInnes/BSON.jl">BSON.jl</a>.</p><p>Save a model:</p><pre><code class="language-julia">julia&gt; using Flux
julia&gt; model = Chain(Dense(10,5,relu),Dense(5,2),softmax)
Chain(Dense(10, 5, NNlib.relu), Dense(5, 2), NNlib.softmax)
@ -20,7 +20,7 @@ julia&gt; using BSON: @load
julia&gt; @load &quot;mymodel.bson&quot; model
julia&gt; model
Chain(Dense(10, 5, NNlib.relu), Dense(5, 2), NNlib.softmax)</code></pre><p>Models are just normal Julia structs, so it&#39;s fine to use any Julia storage format for this purpose. BSON.jl is particularly well supported and most likely to be forwards compatible (that is, models saved now will load in future versions of Flux).</p><div class="admonition note"><div class="admonition-title">Note</div><div class="admonition-text"><p>If a saved model&#39;s weights are stored on the GPU, the model will not load later on if there is no GPU support available. It&#39;s best to <a href="gpu.html">move your model to the CPU</a> with <code>cpu(model)</code> before saving it.</p></div></div><h2><a class="nav-anchor" id="Saving-Model-Weights-1" href="#Saving-Model-Weights-1">Saving Model Weights</a></h2><p>In some cases it may be useful to save only the model parameters themselves, and rebuild the model architecture in your code. You can use <code>params(model)</code> to get model parameters. You can also use <code>data.(params)</code> to remove tracking.</p><pre><code class="language-Julia">julia&gt; using Flux
Chain(Dense(10, 5, NNlib.relu), Dense(5, 2), NNlib.softmax)</code></pre><p>Models are just normal Julia structs, so it&#39;s fine to use any Julia storage format for this purpose. BSON.jl is particularly well supported and most likely to be forwards compatible (that is, models saved now will load in future versions of Flux).</p><div class="admonition note"><div class="admonition-title">Note</div><div class="admonition-text"><p>If a saved model&#39;s weights are stored on the GPU, the model will not load later on if there is no GPU support available. It&#39;s best to <a href="../gpu/">move your model to the CPU</a> with <code>cpu(model)</code> before saving it.</p></div></div><h2><a class="nav-anchor" id="Saving-Model-Weights-1" href="#Saving-Model-Weights-1">Saving Model Weights</a></h2><p>In some cases it may be useful to save only the model parameters themselves, and rebuild the model architecture in your code. You can use <code>params(model)</code> to get model parameters. You can also use <code>data.(params)</code> to remove tracking.</p><pre><code class="language-Julia">julia&gt; using Flux
julia&gt; model = Chain(Dense(10,5,relu),Dense(5,2),softmax)
Chain(Dense(10, 5, NNlib.relu), Dense(5, 2), NNlib.softmax)
@ -38,7 +38,7 @@ julia&gt; using BSON: @load
julia&gt; @load &quot;mymodel.bson&quot; weights
julia&gt; Flux.loadparams!(model, weights)</code></pre><p>The new <code>model</code> we created will now be identical to the one we saved parameters for.</p><h2><a class="nav-anchor" id="Checkpointing-1" href="#Checkpointing-1">Checkpointing</a></h2><p>In longer training runs it&#39;s a good idea to periodically save your model, so that you can resume if training is interrupted (for example, if there&#39;s a power cut). You can do this by saving the model in the <a href="training/training.html">callback provided to <code>train!</code></a>.</p><pre><code class="language-julia">using Flux: throttle
julia&gt; Flux.loadparams!(model, weights)</code></pre><p>The new <code>model</code> we created will now be identical to the one we saved parameters for.</p><h2><a class="nav-anchor" id="Checkpointing-1" href="#Checkpointing-1">Checkpointing</a></h2><p>In longer training runs it&#39;s a good idea to periodically save your model, so that you can resume if training is interrupted (for example, if there&#39;s a power cut). You can do this by saving the model in the <a href="../training/training/">callback provided to <code>train!</code></a>.</p><pre><code class="language-julia">using Flux: throttle
using BSON: @save
m = Chain(Dense(10,5,relu),Dense(5,2),softmax)
@ -47,4 +47,4 @@ evalcb = throttle(30) do
# Show loss
@save &quot;model-checkpoint.bson&quot; model
end</code></pre><p>This will update the <code>&quot;model-checkpoint.bson&quot;</code> file every thirty seconds.</p><p>You can get more advanced by saving a series of models throughout training, for example</p><pre><code class="language-julia">@save &quot;model-$(now()).bson&quot; model</code></pre><p>will produce a series of models like <code>&quot;model-2018-03-06T02:57:10.41.bson&quot;</code>. You could also store the current test set loss, so that it&#39;s easy to (for example) revert to an older copy of the model if it starts to overfit.</p><pre><code class="language-julia">@save &quot;model-$(now()).bson&quot; model loss = testloss()</code></pre><p>You can even store optimiser state alongside the model, to resume training exactly where you left off.</p><pre><code class="language-julia">opt = ADAM(params(model))
@save &quot;model-$(now()).bson&quot; model opt</code></pre><footer><hr/><a class="previous" href="gpu.html"><span class="direction">Previous</span><span class="title">GPU Support</span></a><a class="next" href="internals/tracker.html"><span class="direction">Next</span><span class="title">Backpropagation</span></a></footer></article></body></html>
@save &quot;model-$(now()).bson&quot; model opt</code></pre><footer><hr/><a class="previous" href="../gpu/"><span class="direction">Previous</span><span class="title">GPU Support</span></a><a class="next" href="../internals/tracker/"><span class="direction">Next</span><span class="title">Backpropagation</span></a></footer></article></body></html>

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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Search · Flux</title><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
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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="../assets/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><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="../models/basics/">Basics</a></li><li><a class="toctext" href="../models/recurrence/">Recurrence</a></li><li><a class="toctext" href="../models/regularisation/">Regularisation</a></li><li><a class="toctext" href="../models/layers/">Model Reference</a></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../training/optimisers/">Optimisers</a></li><li><a class="toctext" href="../training/training/">Training</a></li></ul></li><li><a class="toctext" href="../data/onehot/">One-Hot Encoding</a></li><li><a class="toctext" href="../gpu/">GPU Support</a></li><li><a class="toctext" href="../saving/">Saving &amp; Loading</a></li><li><span class="toctext">Internals</span><ul><li><a class="toctext" href="../internals/tracker/">Backpropagation</a></li></ul></li><li><a class="toctext" href="../community/">Community</a></li></ul></nav><article><header><nav><ul><li>Search</li></ul></nav><hr/><div id="topbar"><span>Search</span><a class="fa fa-bars" href="#"></a></div></header><h1>Search</h1><p id="search-info">Number of results: <span id="search-results-number">loading...</span></p><ul id="search-results"></ul></article></body><script src="../search_index.js"></script><script src="../assets/search.js"></script></html>

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@ -1,7 +1,7 @@
var documenterSearchIndex = {"docs": [
{
"location": "index.html#",
"location": "#",
"page": "Home",
"title": "Home",
"category": "page",
@ -9,7 +9,7 @@ var documenterSearchIndex = {"docs": [
},
{
"location": "index.html#Flux:-The-Julia-Machine-Learning-Library-1",
"location": "#Flux:-The-Julia-Machine-Learning-Library-1",
"page": "Home",
"title": "Flux: The Julia Machine Learning Library",
"category": "section",
@ -17,7 +17,7 @@ var documenterSearchIndex = {"docs": [
},
{
"location": "index.html#Installation-1",
"location": "#Installation-1",
"page": "Home",
"title": "Installation",
"category": "section",
@ -25,7 +25,7 @@ var documenterSearchIndex = {"docs": [
},
{
"location": "index.html#Learning-Flux-1",
"location": "#Learning-Flux-1",
"page": "Home",
"title": "Learning Flux",
"category": "section",
@ -33,7 +33,7 @@ var documenterSearchIndex = {"docs": [
},
{
"location": "models/basics.html#",
"location": "models/basics/#",
"page": "Basics",
"title": "Basics",
"category": "page",
@ -41,7 +41,7 @@ var documenterSearchIndex = {"docs": [
},
{
"location": "models/basics.html#Model-Building-Basics-1",
"location": "models/basics/#Model-Building-Basics-1",
"page": "Basics",
"title": "Model-Building Basics",
"category": "section",
@ -49,7 +49,7 @@ var documenterSearchIndex = {"docs": [
},
{
"location": "models/basics.html#Taking-Gradients-1",
"location": "models/basics/#Taking-Gradients-1",
"page": "Basics",
"title": "Taking Gradients",
"category": "section",
@ -57,7 +57,7 @@ var documenterSearchIndex = {"docs": [
},
{
"location": "models/basics.html#Simple-Models-1",
"location": "models/basics/#Simple-Models-1",
"page": "Basics",
"title": "Simple Models",
"category": "section",
@ -65,7 +65,7 @@ var documenterSearchIndex = {"docs": [
},
{
"location": "models/basics.html#Building-Layers-1",
"location": "models/basics/#Building-Layers-1",
"page": "Basics",
"title": "Building Layers",
"category": "section",
@ -73,7 +73,7 @@ var documenterSearchIndex = {"docs": [
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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Optimisers · Flux</title><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
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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="../../assets/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/"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../../">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="../../models/basics/">Basics</a></li><li><a class="toctext" href="../../models/recurrence/">Recurrence</a></li><li><a class="toctext" href="../../models/regularisation/">Regularisation</a></li><li><a class="toctext" href="../../models/layers/">Model Reference</a></li></ul></li><li><span class="toctext">Training Models</span><ul><li class="current"><a class="toctext" href>Optimisers</a><ul class="internal"><li><a class="toctext" href="#Optimiser-Reference-1">Optimiser Reference</a></li></ul></li><li><a class="toctext" href="../training/">Training</a></li></ul></li><li><a class="toctext" href="../../data/onehot/">One-Hot Encoding</a></li><li><a class="toctext" href="../../gpu/">GPU Support</a></li><li><a class="toctext" href="../../saving/">Saving &amp; Loading</a></li><li><span class="toctext">Internals</span><ul><li><a class="toctext" href="../../internals/tracker/">Backpropagation</a></li></ul></li><li><a class="toctext" href="../../community/">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Training Models</li><li><a href>Optimisers</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/training/optimisers.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Optimisers</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Optimisers-1" href="#Optimisers-1">Optimisers</a></h1><p>Consider a <a href="../../models/basics/">simple linear regression</a>. We create some dummy data, calculate a loss, and backpropagate to calculate gradients for the parameters <code>W</code> and <code>b</code>.</p><pre><code class="language-julia">using Flux.Tracker
W = param(rand(2, 5))
b = param(rand(2))
predict(x) = W*x .+ b
loss(x, y) = sum((predict(x) .- y).^2)
x, y = rand(5), rand(2) # Dummy data
l = loss(x, y) # ~ 3
params = Params([W, b])
grads = Tracker.gradient(() -&gt; loss(x, y), params)</code></pre><p>We want to update each parameter, using the gradient, in order to improve (reduce) the loss. Here&#39;s one way to do that:</p><pre><code class="language-julia">using Flux.Tracker: grad, update!
η = 0.1 # Learning Rate
for p in (W, b)
update!(p, -η * grads[p])
end</code></pre><p>Running this will alter the parameters <code>W</code> and <code>b</code> and our loss should go down. Flux provides a more general way to do optimiser updates like this.</p><pre><code class="language-julia">opt = Descent(0.1) # Gradient descent with learning rate 0.1
for p in (W, b)
update!(opt, p, -η * grads[p])
end</code></pre><p>An optimiser <code>update!</code> accepts a parameter and a gradient, and updates the parameter according to the chosen rule. We can also pass <code>opt</code> to our <a href="../training/">training loop</a>, which will update all parameters of the model in a loop. However, we can now easily replace <code>Descent</code> with a more advanced optimiser such as <code>ADAM</code>.</p><h2><a class="nav-anchor" id="Optimiser-Reference-1" href="#Optimiser-Reference-1">Optimiser Reference</a></h2><p>All optimisers return an object that, when passed to <code>train!</code>, will update the parameters passed to it.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Optimise.Descent" href="#Flux.Optimise.Descent"><code>Flux.Optimise.Descent</code></a> — <span class="docstring-category">Type</span>.</div><div><div><pre><code class="language-none">Descent(η)</code></pre><p>Classic gradient descent optimiser with learning rate <code>η</code>. For each parameter <code>p</code> and its gradient <code>δp</code>, this runs <code>p -= η*δp</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/347678344e7ff9a1f4a99a7bd2e27118559f3a52/src/optimise/optimisers.jl#L9-L14">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">Type</span>.</div><div><div><pre><code class="language-none">Momentum(params, η = 0.01; ρ = 0.9)</code></pre><p>Gradient descent with learning rate <code>η</code> and momentum <code>ρ</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/347678344e7ff9a1f4a99a7bd2e27118559f3a52/src/optimise/optimisers.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">Type</span>.</div><div><div><pre><code class="language-none">Nesterov(eta, ρ = 0.9)</code></pre><p>Gradient descent with learning rate <code>η</code> and Nesterov momentum <code>ρ</code>.</p></div></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/347678344e7ff9a1f4a99a7bd2e27118559f3a52/src/optimise/optimisers.jl#L45-L49">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">Type</span>.</div><div><div><pre><code class="language-none">ADAM(η = 0.001, β = (0.9, 0.999))</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/347678344e7ff9a1f4a99a7bd2e27118559f3a52/src/optimise/optimisers.jl#L88-L92">source</a></section><footer><hr/><a class="previous" href="../../models/layers/"><span class="direction">Previous</span><span class="title">Model Reference</span></a><a class="next" href="../training/"><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="../../assets/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/"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../../">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="../../models/basics/">Basics</a></li><li><a class="toctext" href="../../models/recurrence/">Recurrence</a></li><li><a class="toctext" href="../../models/regularisation/">Regularisation</a></li><li><a class="toctext" href="../../models/layers/">Model Reference</a></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../optimisers/">Optimisers</a></li><li class="current"><a class="toctext" href>Training</a><ul class="internal"><li><a class="toctext" href="#Loss-Functions-1">Loss Functions</a></li><li><a class="toctext" href="#Datasets-1">Datasets</a></li><li><a class="toctext" href="#Callbacks-1">Callbacks</a></li></ul></li></ul></li><li><a class="toctext" href="../../data/onehot/">One-Hot Encoding</a></li><li><a class="toctext" href="../../gpu/">GPU Support</a></li><li><a class="toctext" href="../../saving/">Saving &amp; Loading</a></li><li><span class="toctext">Internals</span><ul><li><a class="toctext" href="../../internals/tracker/">Backpropagation</a></li></ul></li><li><a class="toctext" href="../../community/">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Training Models</li><li><a href>Training</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/training/training.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Training</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Training-1" href="#Training-1">Training</a></h1><p>To actually train a model we need three things:</p><ul><li>A <em>objective function</em>, that evaluates how well a model is doing given some input data.</li><li>A collection of data points that will be provided to the objective function.</li><li>An <a href="../optimisers/">optimiser</a> that will update the model parameters appropriately.</li></ul><p>With these we can call <code>Flux.train!</code>:</p><pre><code class="language-julia">Flux.train!(objective, params, data, opt)</code></pre><p>There are plenty of examples in the <a href="https://github.com/FluxML/model-zoo">model zoo</a>.</p><h2><a class="nav-anchor" id="Loss-Functions-1" href="#Loss-Functions-1">Loss Functions</a></h2><p>The objective function must return a number representing how far the model is from its target – the <em>loss</em> of the model. The <code>loss</code> function that we defined in <a href="../../models/basics/">basics</a> will work as an objective. We can also define an objective in terms of some model:</p><pre><code class="language-julia">m = Chain(
Dense(784, 32, σ),
Dense(32, 10), softmax)
@ -33,4 +33,4 @@ julia&gt; @epochs 2 Flux.train!(...)
evalcb() = @show(loss(test_x, test_y))
Flux.train!(objective, ps, data, opt,
cb = throttle(evalcb, 5))</code></pre><footer><hr/><a class="previous" href="optimisers.html"><span class="direction">Previous</span><span class="title">Optimisers</span></a><a class="next" href="../data/onehot.html"><span class="direction">Next</span><span class="title">One-Hot Encoding</span></a></footer></article></body></html>
cb = throttle(evalcb, 5))</code></pre><footer><hr/><a class="previous" href="../optimisers/"><span class="direction">Previous</span><span class="title">Optimisers</span></a><a class="next" href="../../data/onehot/"><span class="direction">Next</span><span class="title">One-Hot Encoding</span></a></footer></article></body></html>

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julia&gt; onehot(:b, [:a, :b, :c])
3-element Flux.OneHotVector:
false
true
false
julia&gt; onehot(:c, [:a, :b, :c])
3-element Flux.OneHotVector:
false
false
true</code></pre><p>The inverse is <code>onecold</code> (which can take a general probability distribution, as well as just booleans).</p><pre><code class="language-julia">julia&gt; onecold(ans, [:a, :b, :c])
:c
julia&gt; onecold([true, false, false], [:a, :b, :c])
:a
julia&gt; onecold([0.3, 0.2, 0.5], [:a, :b, :c])
:c</code></pre><h2><a class="nav-anchor" id="Batches-1" href="#Batches-1">Batches</a></h2><p><code>onehotbatch</code> creates a batch (matrix) of one-hot vectors, and <code>onecold</code> treats matrices as batches.</p><pre><code class="language-julia">julia&gt; using Flux: onehotbatch
julia&gt; onehotbatch([:b, :a, :b], [:a, :b, :c])
3×3 Flux.OneHotMatrix:
false true false
true false true
false false false
julia&gt; onecold(ans, [:a, :b, :c])
3-element Array{Symbol,1}:
:b
:a
:b</code></pre><p>Note that these operations returned <code>OneHotVector</code> and <code>OneHotMatrix</code> rather than <code>Array</code>s. <code>OneHotVector</code>s behave like normal vectors but avoid any unnecessary cost compared to using an integer index directly. For example, multiplying a matrix with a one-hot vector simply slices out the relevant row of the matrix under the hood.</p><footer><hr/><a class="previous" href="../training/training.html"><span class="direction">Previous</span><span class="title">Training</span></a><a class="next" href="../gpu.html"><span class="direction">Next</span><span class="title">GPU Support</span></a></footer></article></body></html>

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W = cu(rand(2, 5)) # a 2×5 CuArray
b = cu(rand(2))
predict(x) = W*x .+ b
loss(x, y) = sum((predict(x) .- y).^2)
x, y = cu(rand(5)), cu(rand(2)) # Dummy data
loss(x, y) # ~ 3</code></pre><p>Note that we convert both the parameters (<code>W</code>, <code>b</code>) and the data set (<code>x</code>, <code>y</code>) to cuda arrays. Taking derivatives and training works exactly as before.</p><p>If you define a structured model, like a <code>Dense</code> layer or <code>Chain</code>, you just need to convert the internal parameters. Flux provides <code>mapleaves</code>, which allows you to alter all parameters of a model at once.</p><pre><code class="language-julia">d = Dense(10, 5, σ)
d = mapleaves(cu, d)
d.W # Tracked CuArray
d(cu(rand(10))) # CuArray output
m = Chain(Dense(10, 5, σ), Dense(5, 2), softmax)
m = mapleaves(cu, m)
d(cu(rand(10)))</code></pre><p>As a convenience, Flux provides the <code>gpu</code> function to convert models and data to the GPU if one is available. By default, it&#39;ll do nothing, but loading <code>CuArrays</code> will cause it to move data to the GPU instead.</p><pre><code class="language-julia">julia&gt; using Flux, CuArrays
julia&gt; m = Dense(10,5) |&gt; gpu
Dense(10, 5)
julia&gt; x = rand(10) |&gt; gpu
10-element CuArray{Float32,1}:
0.800225
⋮
0.511655
julia&gt; m(x)
Tracked 5-element CuArray{Float32,1}:
-0.30535
⋮
-0.618002</code></pre><p>The analogue <code>cpu</code> is also available for moving models and data back off of the GPU.</p><pre><code class="language-julia">julia&gt; x = rand(10) |&gt; gpu
10-element CuArray{Float32,1}:
0.235164
⋮
0.192538
julia&gt; x |&gt; cpu
10-element Array{Float32,1}:
0.235164
⋮
0.192538</code></pre><footer><hr/><a class="previous" href="data/onehot.html"><span class="direction">Previous</span><span class="title">One-Hot Encoding</span></a><a class="next" href="saving.html"><span class="direction">Next</span><span class="title">Saving &amp; Loading</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="../models/basics.html">Basics</a></li><li><a class="toctext" href="../models/recurrence.html">Recurrence</a></li><li><a class="toctext" href="../models/regularisation.html">Regularisation</a></li><li><a class="toctext" href="../models/layers.html">Model Reference</a></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 &amp; Loading</a></li><li><span class="toctext">Internals</span><ul><li class="current"><a class="toctext" href="tracker.html">Backpropagation</a><ul class="internal"><li><a class="toctext" href="#Taking-Gradients-1">Taking Gradients</a></li><li><a class="toctext" href="#Tracked-Arrays-1">Tracked Arrays</a></li><li><a class="toctext" href="#Custom-Gradients-1">Custom Gradients</a></li><li><a class="toctext" href="#Tracked-Internals-1">Tracked Internals</a></li></ul></li></ul></li><li><a class="toctext" href="../community.html">Community</a></li></ul></nav><article id="docs"><header><nav><ul><li>Internals</li><li><a href="tracker.html">Backpropagation</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/internals/tracker.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Backpropagation</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Flux.Tracker-1" href="#Flux.Tracker-1">Flux.Tracker</a></h1><p>Backpropagation, or reverse-mode automatic differentiation, is handled by the <code>Flux.Tracker</code> module.</p><pre><code class="language-julia">julia&gt; using Flux.Tracker</code></pre><p>Here we discuss some more advanced uses of this module, as well as covering its internals.</p><h2><a class="nav-anchor" id="Taking-Gradients-1" href="#Taking-Gradients-1">Taking Gradients</a></h2><p>In the <a href="../models/basics.html">basics section</a> we covered basic usage of the <code>gradient</code> function.</p><pre><code class="language-julia">using Flux.Tracker
Tracker.gradient((a, b) -&gt; a*b, 2, 3) # (3.0 (tracked), 2.0 (tracked))</code></pre><p><code>gradient</code> is actually just a thin wrapper around the backpropagator-based interface, <code>forward</code>.</p><pre><code class="language-julia">using Flux.Tracker: forward
y, back = forward((a, b) -&gt; a*b, 2, 3) # (6.0 (tracked), Flux.Tracker.#9)
back(1) # (3.0 (tracked), 2.0 (tracked))</code></pre><p>The <code>forward</code> function returns two results. The first, <code>y</code>, is the original value of the function (perhaps with tracking applied). The second, <code>back</code>, is a new function which, given a sensitivity, returns the sensitivity of the inputs to <code>forward</code> (we call this a &quot;backpropagator&quot;). One use of this interface is to provide custom sensitivities when outputs are not scalar.</p><pre><code class="language-julia">julia&gt; y, back = forward((a, b) -&gt; a.*b, [1,2,3],[4,5,6])
(param([4.0, 10.0, 18.0]), Flux.Tracker.#9)
julia&gt; back([1,1,1])
(param([4.0, 5.0, 6.0]), param([1.0, 2.0, 3.0]))</code></pre><p>We can also take gradients in-place. This can be useful if you only care about first-order gradients.</p><pre><code class="language-julia">a, b = param(2), param(3)
c = a*b # 6.0 (tracked)
Tracker.back!(c)
Tracker.grad(a), Tracker.grad(b) # (3.0, 2.0)</code></pre><h2><a class="nav-anchor" id="Tracked-Arrays-1" href="#Tracked-Arrays-1">Tracked Arrays</a></h2><p>The <code>param</code> function converts a normal Julia array into a new object that, while behaving like an array, tracks extra information that allows us to calculate derivatives. For example, say we multiply two parameters:</p><pre><code class="language-julia">julia&gt; W = param([1 2; 3 4])
Tracked 2×2 Array{Float64,2}:
1.0 2.0
3.0 4.0
julia&gt; x = param([5, 6])
Tracked 2-element Array{Float64,1}:
5.0
6.0
julia&gt; y = W*x
Tracked 2-element Array{Float64,1}:
17.0
39.0</code></pre><p>The output <code>y</code> is also a <code>TrackedArray</code> object. We can now backpropagate sensitivities to <code>W</code> and <code>x</code> via the <code>back!</code> function, and see the gradients accumulated in the <code>W</code> and <code>x</code> tracked arrays:</p><pre><code class="language-julia">julia&gt; Tracker.back!(y, [1, -1])
julia&gt; W.grad
2×2 Array{Float64,2}:
5.0 6.0
-5.0 -6.0
julia&gt; x.grad
2-element Array{Float64,1}:
-2.0
-2.0</code></pre><p>You may sometimes want to drop derivative information and just get the plain value back. You can do this by calling <code>Tracker.data(W)</code>.</p><h2><a class="nav-anchor" id="Custom-Gradients-1" href="#Custom-Gradients-1">Custom Gradients</a></h2><p>We can hook in to the processes above to implement custom gradients for a function or kernel. For a toy example, imagine a custom implementation of <code>minus</code>:</p><pre><code class="language-julia">minus(a, b) = a - b</code></pre><p>Firstly, we must tell the tracker system to stop when it sees a call to <code>minus</code>, and record it. We can do this using dispatch:</p><pre><code class="language-julia">using Flux.Tracker: TrackedArray, track, @grad
minus(a::TrackedArray, b::TrackedArray) = track(minus, a, b)</code></pre><p><code>track</code> takes care of building a new <code>Tracked</code> object and recording the operation on the tape. We just need to provide a gradient definition.</p><pre><code class="language-julia">@grad function minus(a, b)
return minus(data(a), data(b)), Δ -&gt; (Δ, -Δ)
end</code></pre><p>This is essentially just a way of overloading the <code>forward</code> function we saw above. We strip tracking from <code>a</code> and <code>b</code> so that we are calling the original definition of <code>minus</code> (otherwise, we&#39;d just try to track the call again and hit an infinite regress).</p><p>Note that in the backpropagator we don&#39;t call <code>data(a)</code>; we <em>do</em> in fact want to track this, since nest AD will take a derivative through the backpropagator itself. For example, the gradient of <code>*</code> might look like this.</p><pre><code class="language-julia">@grad a * b = data(a)*data(b), Δ -&gt; (Δ*b, a*Δ)</code></pre><p>We can then calculate the first derivative of <code>minus</code> as follows:</p><pre><code class="language-julia">a = param([1,2,3])
b = param([3,2,1])
c = minus(a, b) # [-2.0 (tracked), 0.0 (tracked), 2.0 (tracked)]
Tracker.back!(c, 1)
Tracker.grad(a) # [1.00, 1.00, 1.00]
Tracker.grad(b) # [-1.00, -1.00, -1.00]</code></pre><p>For multi-argument functions with custom gradients, you likely want to catch not just <code>minus(::TrackedArray, ::TrackedArray)</code> but also <code>minus(::Array, TrackedArray)</code> and so on. To do so, just define those extra signatures as needed:</p><pre><code class="language-julia">minus(a::AbstractArray, b::TrackedArray) = Tracker.track(minus, a, b)
minus(a::TrackedArray, b::AbstractArray) = Tracker.track(minus, a, b)</code></pre><h2><a class="nav-anchor" id="Tracked-Internals-1" href="#Tracked-Internals-1">Tracked Internals</a></h2><p>All <code>Tracked*</code> objects (<code>TrackedArray</code>, <code>TrackedReal</code>) are light wrappers around the <code>Tracked</code> type, which you can access via the <code>.tracker</code> field.</p><pre><code class="language-julia">julia&gt; x.tracker
Flux.Tracker.Tracked{Array{Float64,1}}(0x00000000, Flux.Tracker.Call{Nothing,Tuple{}}(nothing, ()), true, [5.0, 6.0], [-2.0, -2.0])</code></pre><p>The <code>Tracker</code> stores the gradient of a given object, which we&#39;ve seen before.</p><pre><code class="language-julia">julia&gt; x.tracker.grad
2-element Array{Float64,1}:
-2.0
-2.0</code></pre><p>The tracker also contains a <code>Call</code> object, which simply represents a function call that was made at some point during the forward pass. For example, the <code>+</code> call would look like this:</p><pre><code class="language-julia">julia&gt; Tracker.Call(+, 1, 2)
Flux.Tracker.Call{Base.#+,Tuple{Int64,Int64}}(+, (1, 2))</code></pre><p>In the case of the <code>y</code> we produced above, we can see that it stores the call that produced it – that is, <code>W*x</code>.</p><pre><code class="language-julia">julia&gt; y.tracker.f
Flux.Tracker.Call{...}(*, (param([1.0 2.0; 3.0 4.0]), param([5.0, 6.0])))</code></pre><p>Notice that because the arguments to the call may also be tracked arrays, storing their own calls, this means that <code>Tracker</code> ends up forming a data structure that records everything that happened during the forward pass (often known as a <em>tape</em>).</p><p>When we call <code>back!(y, [1, -1])</code>, the sensitivities <code>[1, -1]</code> simply get forwarded to <code>y</code>&#39;s call (<code>*</code>), effectively calling</p><pre><code class="language-julia">Tracker.back(*, [1, -1], W, x)</code></pre><p>which in turn calculates the sensitivities of the arguments (<code>W</code> and <code>x</code>) and back-propagates through their calls. This is recursive, so it will walk the entire program graph and propagate gradients to the original model parameters.</p><footer><hr/><a class="previous" href="../saving.html"><span class="direction">Previous</span><span class="title">Saving &amp; Loading</span></a><a class="next" href="../community.html"><span class="direction">Next</span><span class="title">Community</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 class="current"><a class="toctext" href="regularisation.html">Regularisation</a><ul class="internal"></ul></li><li><a class="toctext" href="layers.html">Model Reference</a></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 &amp; 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="regularisation.html">Regularisation</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/regularisation.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Regularisation</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Regularisation-1" href="#Regularisation-1">Regularisation</a></h1><p>Applying regularisation to model parameters is straightforward. We just need to apply an appropriate regulariser, such as <code>norm</code>, to each model parameter and add the result to the overall loss.</p><p>For example, say we have a simple regression.</p><pre><code class="language-julia">using Flux: crossentropy
m = Dense(10, 5)
loss(x, y) = crossentropy(softmax(m(x)), y)</code></pre><p>We can regularise this by taking the (L2) norm of the parameters, <code>m.W</code> and <code>m.b</code>.</p><pre><code class="language-julia">penalty() = norm(m.W) + norm(m.b)
loss(x, y) = crossentropy(softmax(m(x)), y) + penalty()</code></pre><p>When working with layers, Flux provides the <code>params</code> function to grab all parameters at once. We can easily penalise everything with <code>sum(norm, params)</code>.</p><pre><code class="language-julia">julia&gt; params(m)
2-element Array{Any,1}:
param([0.355408 0.533092; … 0.430459 0.171498])
param([0.0, 0.0, 0.0, 0.0, 0.0])
julia&gt; sum(norm, params(m))
26.01749952921026 (tracked)</code></pre><p>Here&#39;s a larger example with a multi-layer perceptron.</p><pre><code class="language-julia">m = Chain(
Dense(28^2, 128, relu),
Dense(128, 32, relu),
Dense(32, 10), softmax)
loss(x, y) = crossentropy(m(x), y) + sum(norm, params(m))
loss(rand(28^2), rand(10))</code></pre><p>One can also easily add per-layer regularisation via the <code>activations</code> function:</p><pre><code class="language-julia">julia&gt; c = Chain(Dense(10,5,σ),Dense(5,2),softmax)
Chain(Dense(10, 5, NNlib.σ), Dense(5, 2), NNlib.softmax)
julia&gt; activations(c, rand(10))
3-element Array{Any,1}:
param([0.71068, 0.831145, 0.751219, 0.227116, 0.553074])
param([0.0330606, -0.456104])
param([0.61991, 0.38009])
julia&gt; sum(norm, ans)
2.639678767773633 (tracked)</code></pre><footer><hr/><a class="previous" href="recurrence.html"><span class="direction">Previous</span><span class="title">Recurrence</span></a><a class="next" href="layers.html"><span class="direction">Next</span><span class="title">Model Reference</span></a></footer></article></body></html>

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julia&gt; model = Chain(Dense(10,5,relu),Dense(5,2),softmax)
Chain(Dense(10, 5, NNlib.relu), Dense(5, 2), NNlib.softmax)
julia&gt; using BSON: @save
julia&gt; @save &quot;mymodel.bson&quot; model</code></pre><p>Load it again:</p><pre><code class="language-julia">julia&gt; using Flux
julia&gt; using BSON: @load
julia&gt; @load &quot;mymodel.bson&quot; model
julia&gt; model
Chain(Dense(10, 5, NNlib.relu), Dense(5, 2), NNlib.softmax)</code></pre><p>Models are just normal Julia structs, so it&#39;s fine to use any Julia storage format for this purpose. BSON.jl is particularly well supported and most likely to be forwards compatible (that is, models saved now will load in future versions of Flux).</p><div class="admonition note"><div class="admonition-title">Note</div><div class="admonition-text"><p>If a saved model&#39;s weights are stored on the GPU, the model will not load later on if there is no GPU support available. It&#39;s best to <a href="gpu.html">move your model to the CPU</a> with <code>cpu(model)</code> before saving it.</p></div></div><h2><a class="nav-anchor" id="Saving-Model-Weights-1" href="#Saving-Model-Weights-1">Saving Model Weights</a></h2><p>In some cases it may be useful to save only the model parameters themselves, and rebuild the model architecture in your code. You can use <code>params(model)</code> to get model parameters. You can also use <code>data.(params)</code> to remove tracking.</p><pre><code class="language-Julia">julia&gt; using Flux
julia&gt; model = Chain(Dense(10,5,relu),Dense(5,2),softmax)
Chain(Dense(10, 5, NNlib.relu), Dense(5, 2), NNlib.softmax)
julia&gt; weights = Tracker.data.(params(model));
julia&gt; using BSON: @save
julia&gt; @save &quot;mymodel.bson&quot; weights</code></pre><p>You can easily load parameters back into a model with <code>Flux.loadparams!</code>.</p><pre><code class="language-julia">julia&gt; using Flux
julia&gt; model = Chain(Dense(10,5,relu),Dense(5,2),softmax)
Chain(Dense(10, 5, NNlib.relu), Dense(5, 2), NNlib.softmax)
julia&gt; using BSON: @load
julia&gt; @load &quot;mymodel.bson&quot; weights
julia&gt; Flux.loadparams!(model, weights)</code></pre><p>The new <code>model</code> we created will now be identical to the one we saved parameters for.</p><h2><a class="nav-anchor" id="Checkpointing-1" href="#Checkpointing-1">Checkpointing</a></h2><p>In longer training runs it&#39;s a good idea to periodically save your model, so that you can resume if training is interrupted (for example, if there&#39;s a power cut). You can do this by saving the model in the <a href="training/training.html">callback provided to <code>train!</code></a>.</p><pre><code class="language-julia">using Flux: throttle
using BSON: @save
m = Chain(Dense(10,5,relu),Dense(5,2),softmax)
evalcb = throttle(30) do
# Show loss
@save &quot;model-checkpoint.bson&quot; model
end</code></pre><p>This will update the <code>&quot;model-checkpoint.bson&quot;</code> file every thirty seconds.</p><p>You can get more advanced by saving a series of models throughout training, for example</p><pre><code class="language-julia">@save &quot;model-$(now()).bson&quot; model</code></pre><p>will produce a series of models like <code>&quot;model-2018-03-06T02:57:10.41.bson&quot;</code>. You could also store the current test set loss, so that it&#39;s easy to (for example) revert to an older copy of the model if it starts to overfit.</p><pre><code class="language-julia">@save &quot;model-$(now()).bson&quot; model loss = testloss()</code></pre><p>You can even store optimiser state alongside the model, to resume training exactly where you left off.</p><pre><code class="language-julia">opt = ADAM(params(model))
@save &quot;model-$(now()).bson&quot; model opt</code></pre><footer><hr/><a class="previous" href="gpu.html"><span class="direction">Previous</span><span class="title">GPU Support</span></a><a class="next" href="internals/tracker.html"><span class="direction">Next</span><span class="title">Backpropagation</span></a></footer></article></body></html>

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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Search · Flux</title><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
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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="../models/basics.html">Basics</a></li><li><a class="toctext" href="../models/recurrence.html">Recurrence</a></li><li><a class="toctext" href="../models/regularisation.html">Regularisation</a></li><li><a class="toctext" href="../models/layers.html">Model Reference</a></li></ul></li><li><span class="toctext">Training Models</span><ul><li class="current"><a class="toctext" href="optimisers.html">Optimisers</a><ul class="internal"><li><a class="toctext" href="#Optimiser-Reference-1">Optimiser Reference</a></li></ul></li><li><a class="toctext" href="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 &amp; 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>Training Models</li><li><a href="optimisers.html">Optimisers</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/training/optimisers.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Optimisers</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Optimisers-1" href="#Optimisers-1">Optimisers</a></h1><p>Consider a <a href="../models/basics.html">simple linear regression</a>. We create some dummy data, calculate a loss, and backpropagate to calculate gradients for the parameters <code>W</code> and <code>b</code>.</p><pre><code class="language-julia">using Flux.Tracker
W = param(rand(2, 5))
b = param(rand(2))
predict(x) = W*x .+ b
loss(x, y) = sum((predict(x) .- y).^2)
x, y = rand(5), rand(2) # Dummy data
l = loss(x, y) # ~ 3
params = Params([W, b])
grads = Tracker.gradient(() -&gt; loss(x, y), params)</code></pre><p>We want to update each parameter, using the gradient, in order to improve (reduce) the loss. Here&#39;s one way to do that:</p><pre><code class="language-julia">using Flux.Tracker: grad, update!
η = 0.1 # Learning Rate
for p in (W, b)
update!(p, -η * grads[p])
end</code></pre><p>Running this will alter the parameters <code>W</code> and <code>b</code> and our loss should go down. Flux provides a more general way to do optimiser updates like this.</p><pre><code class="language-julia">opt = Descent(0.1) # Gradient descent with learning rate 0.1
for p in (W, b)
update!(opt, p, -η * grads[p])
end</code></pre><p>An optimiser <code>update!</code> accepts a parameter and a gradient, and updates the parameter according to the chosen rule. We can also pass <code>opt</code> to our <a href="training.html">training loop</a>, which will update all parameters of the model in a loop. However, we can now easily replace <code>Descent</code> with a more advanced optimiser such as <code>ADAM</code>.</p><h2><a class="nav-anchor" id="Optimiser-Reference-1" href="#Optimiser-Reference-1">Optimiser Reference</a></h2><p>All optimisers return an object that, when passed to <code>train!</code>, 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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border: 1px solid #c9c9c9;
border-radius: 1em;
font-size: .83em;
}
nav.toc > ul * {
margin: 0;
}
nav.toc ul {
color: #404040;
padding: 0;
list-style: none;
}
nav.toc ul .toctext {
color: inherit;
display: block;
}
nav.toc ul a:hover {
color: #fcfcfc;
background-color: #4e4a4a;
}
nav.toc ul.internal a {
color: inherit;
display: block;
}
nav.toc ul.internal a:hover {
background-color: #d6d6d6;
}
nav.toc ul.internal {
background-color: #e3e3e3;
box-shadow: inset -14px 0px 5px -12px rgb(210,210,210);
list-style: none;
}
nav.toc ul.internal li.toplevel {
border-top: 1px solid #909090;
font-weight: bold;
}
nav.toc ul.internal li.toplevel:first-child {
border-top: none;
}
nav.toc .toctext {
padding-top: 0.3em;
padding-bottom: 0.3em;
padding-right: 1em;
}
nav.toc ul .toctext {
padding-left: 1em;
}
nav.toc ul ul .toctext {
padding-left: 2em;
}
nav.toc ul ul ul .toctext {
padding-left: 3em;
}
nav.toc li.current > .toctext {
border-top: 1px solid #c9c9c9;
border-bottom: 1px solid #c9c9c9;
color: #404040;
font-weight: bold;
background-color: white;
}
article {
margin-left: 20em;
min-width: 20em;
max-width: 48em;
padding: 2em;
}
article > header {}
article > header div#topbar {
display: none;
}
article > header nav ul {
display: inline-block;
list-style: none;
margin: 0;
padding: 0;
}
article > header nav li {
display: inline-block;
padding-right: 0.2em;
}
article > header nav li:before {
content: "»";
padding-right: 0.2em;
}
article > header .edit-page {
float: right;
}
article > footer {}
article > footer a.prev {
float: left;
}
article > footer a.next {
float: right;
}
article > footer a .direction:after {
content: ": ";
}
article hr {
margin: 1em 0;
}
article section.docstring {
border: 1px solid #ddd;
margin: 0.5em 0;
padding: 0.5em;
border-radius: 3px;
}
article section.docstring .docstring-header {
margin-bottom: 1em;
}
article section.docstring .docstring-binding {
color: #333;
font-weight: bold;
}
article section.docstring .docstring-category {
font-style: italic;
}
article section.docstring a.source-link {
display: block;
font-weight: bold;
}
.nav-anchor,
.nav-anchor:hover,
.nav-anchor:visited {
color: #333;
}
/*
* Admonitions
*
* Colors (title, body)
* warning: #f0b37e #ffedcc (orange)
* note: #6ab0de #e7f2fa (blue)
* tip: #1abc9c #dbfaf4 (green)
*/
.admonition {
border-radius: 3px;
background-color: #eeeeee;
}
.admonition-title {
border-radius: 3px 3px 0 0;
background-color: #9b9b9b;
padding: 0.15em 0.5em;
}
.admonition-text {
padding: 0.5em;
}
.admonition-text > :first-child {
margin-top: 0;
}
.admonition-text > :last-child {
margin-bottom: 0;
}
.admonition > .admonition-title:before {
font-family: "FontAwesome";
margin-right: 5px;
content: "\f06a";
}
.admonition.warning > .admonition-title {
background-color: #f0b37e;
}
.admonition.warning {
background-color: #ffedcc;
}
.admonition.note > .admonition-title {
background-color: #6ab0de;
}
.admonition.note {
background-color: #e7f2fa;
}
.admonition.tip > .admonition-title {
background-color: #1abc9c;
}
.admonition.tip {
background-color: #dbfaf4;
}
/* footnotes */
.footnote {
padding-left: 0.8em;
border-left: 2px solid #ccc;
}
/* Search page */
#search-results .category {
font-size: smaller;
}
/* Overriding the <code> block style of highligh.js.
* We have to override the padding and the background-color, since we style this
* part ourselves. Specifically, we style the <pre> surrounding the <code>, while
* highlight.js applies the .hljs style directly to the <code> tag.
*/
.hljs {
background-color: transparent;
padding: 0;
}
@media only screen and (max-width: 768px) {
nav.toc {
position: fixed;
overflow-y: scroll;
width: 16em;
left: -16em;
-webkit-overflow-scrolling: touch;
-webkit-transition-property: left; /* Safari */
-webkit-transition-duration: 0.3s; /* Safari */
transition-property: left;
transition-duration: 0.3s;
-webkit-transition-timing-function: ease-out; /* Safari */
transition-timing-function: ease-out;
z-index: 2;
}
nav.toc.show {
left: 0;
}
article {
margin-left: 0;
padding: 3em 0.9em 0 0.9em; /* top right bottom left */
overflow-wrap: break-word;
}
article > header {
position: fixed;
left: 0;
z-index: 1;
}
article > header nav, hr {
display: none;
}
article > header div#topbar {
display: block; /* is mobile */
position: fixed;
width: 100%;
height: 1.5em;
padding-top: 1em;
padding-bottom: 1em;
background-color: #fcfcfc;
box-shadow: 0 1px 3px rgba(0,0,0,.26);
top: 0;
-webkit-transition-property: top; /* Safari */
-webkit-transition-duration: 0.3s; /* Safari */
transition-property: top;
transition-duration: 0.3s;
}
article > header div#topbar.headroom--unpinned.headroom--not-top.headroom--not-bottom {
top: -4em;
-webkit-transition-property: top; /* Safari */
-webkit-transition-duration: 0.7s; /* Safari */
transition-property: top;
transition-duration: 0.7s;
}
article > header div#topbar span {
position: fixed;
width: 80%;
height: 1.5em;
margin-top: -0.1em;
margin-left: 0.9em;
font-size: 1.2em;
overflow: hidden;
}
article > header div#topbar a.fa-bars {
float: right;
padding: 0.6em;
margin-top: -0.6em;
margin-right: 0.3em;
font-size: 1.5em;
}
article > header div#topbar a.fa-bars:visited {
color: #3091d1;
}
article table {
overflow-x: auto;
display: block;
}
article div.MathJax_Display {
overflow: scroll;
}
article span.MathJax {
overflow: hidden;
}
}
@media only screen and (max-width: 320px) {
body {
font-size: 15px;
}
}

129
stable/assets/documenter.js
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@ -1,129 +0,0 @@
/*
* Part of Documenter.jl
* https://github.com/JuliaDocs/Documenter.jl
*
* License: MIT
*/
requirejs.config({
paths: {
'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.1.1/jquery.min',
'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.0/jquery-ui.min',
'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.9.3/headroom.min',
'mathjax': 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS_HTML',
'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/highlight.min',
'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/languages/julia.min',
'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/languages/julia-repl.min',
},
shim: {
'mathjax' : {
exports: "MathJax"
},
'highlight-julia': ['highlight'],
'highlight-julia-repl': ['highlight'],
}
});
// Load MathJax
require(['mathjax'], function(MathJax) {
MathJax.Hub.Config({
"tex2jax": {
inlineMath: [['$','$'], ['\\(','\\)']],
processEscapes: true
}
});
MathJax.Hub.Config({
config: ["MMLorHTML.js"],
jax: [
"input/TeX",
"output/HTML-CSS",
"output/NativeMML"
],
extensions: [
"MathMenu.js",
"MathZoom.js",
"TeX/AMSmath.js",
"TeX/AMSsymbols.js",
"TeX/autobold.js",
"TeX/autoload-all.js"
]
});
MathJax.Hub.Config({
TeX: { equationNumbers: { autoNumber: "AMS" } }
});
})
require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($, hljs) {
$(document).ready(function() {
hljs.initHighlighting();
})
})
// update the version selector with info from the siteinfo.js and ../versions.js files
require(['jquery'], function($) {
$(document).ready(function() {
var version_selector = $("#version-selector");
// add the current version to the selector based on siteinfo.js, but only if the selector is empty
if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) {
var option = $("<option value='#' selected='selected'>" + DOCUMENTER_CURRENT_VERSION + "</option>");
version_selector.append(option);
}
if (typeof DOC_VERSIONS !== 'undefined') {
var existing_versions = $('#version-selector > option');
var existing_versions_texts = existing_versions.map(function(i,x){return x.text});
DOC_VERSIONS.forEach(function(each) {
var version_url = documenterBaseURL + "/../" + each;
var existing_id = $.inArray(each, existing_versions_texts);
// if not already in the version selector, add it as a new option,
// otherwise update the old option with the URL and enable it
if (existing_id == -1) {
var option = $("<option value='" + version_url + "'>" + each + "</option>");
version_selector.append(option);
} else {
var option = existing_versions[existing_id];
option.value = version_url;
option.disabled = false;
}
});
}
// only show the version selector if the selector has been populated
if ($('#version-selector > option').length > 0) {
version_selector.css("visibility", "visible");
}
})
})
// mobile
require(['jquery', 'headroom'], function($, Headroom) {
$(document).ready(function() {
var navtoc = $("nav.toc");
$("nav.toc li.current a.toctext").click(function() {
navtoc.toggleClass('show');
});
$("article > header div#topbar a.fa-bars").click(function(ev) {
ev.preventDefault();
navtoc.toggleClass('show');
if (navtoc.hasClass('show')) {
var title = $("article > header div#topbar span").text();
$("nav.toc ul li a:contains('" + title + "')").focus();
}
});
$("article#docs").bind('click', function(ev) {
if ($(ev.target).is('div#topbar a.fa-bars')) {
return;
}
if (navtoc.hasClass('show')) {
navtoc.removeClass('show');
}
});
if ($("article > header div#topbar").css('display') == 'block') {
var headroom = new Headroom(document.querySelector("article > header div#topbar"), {"tolerance": {"up": 10, "down": 10}});
headroom.init();
}
})
})

250
stable/assets/search.js
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@ -1,250 +0,0 @@
/*
* Part of Documenter.jl
* https://github.com/JuliaDocs/Documenter.jl
*
* License: MIT
*/
// parseUri 1.2.2
// (c) Steven Levithan <stevenlevithan.com>
// MIT License
function parseUri (str) {
var o = parseUri.options,
m = o.parser[o.strictMode ? "strict" : "loose"].exec(str),
uri = {},
i = 14;
while (i--) uri[o.key[i]] = m[i] || "";
uri[o.q.name] = {};
uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) {
if ($1) uri[o.q.name][$1] = $2;
});
return uri;
};
parseUri.options = {
strictMode: false,
key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"],
q: {
name: "queryKey",
parser: /(?:^|&)([^&=]*)=?([^&]*)/g
},
parser: {
strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/,
loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/
}
};
requirejs.config({
paths: {
'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.1.1/jquery.min',
'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.1/lunr.min',
'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.4/lodash.min',
}
});
var currentScript = document.currentScript;
require(["jquery", "lunr", "lodash"], function($, lunr, _) {
$("#search-form").submit(function(e) {
e.preventDefault()
})
// list below is the lunr 2.1.3 list minus the intersect with names(Base)
// (all, any, get, in, is, which) and (do, else, for, let, where, while, with)
// ideally we'd just filter the original list but it's not available as a variable
lunr.stopWordFilter = lunr.generateStopWordFilter([
'a',
'able',
'about',
'across',
'after',
'almost',
'also',
'am',
'among',
'an',
'and',
'are',
'as',
'at',
'be',
'because',
'been',
'but',
'by',
'can',
'cannot',
'could',
'dear',
'did',
'does',
'either',
'ever',
'every',
'from',
'got',
'had',
'has',
'have',
'he',
'her',
'hers',
'him',
'his',
'how',
'however',
'i',
'if',
'into',
'it',
'its',
'just',
'least',
'like',
'likely',
'may',
'me',
'might',
'most',
'must',
'my',
'neither',
'no',
'nor',
'not',
'of',
'off',
'often',
'on',
'only',
'or',
'other',
'our',
'own',
'rather',
'said',
'say',
'says',
'she',
'should',
'since',
'so',
'some',
'than',
'that',
'the',
'their',
'them',
'then',
'there',
'these',
'they',
'this',
'tis',
'to',
'too',
'twas',
'us',
'wants',
'was',
'we',
'were',
'what',
'when',
'who',
'whom',
'why',
'will',
'would',
'yet',
'you',
'your'
])
// add . as a separator, because otherwise "title": "Documenter.Anchors.add!"
// would not find anything if searching for "add!", only for the entire qualification
lunr.tokenizer.separator = /[\s\-\.]+/
// custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
lunr.trimmer = function (token) {
return token.update(function (s) {
return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '')
})
}
lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter')
lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer')
var index = lunr(function () {
this.ref('location')
this.field('title')
this.field('text')
documenterSearchIndex['docs'].forEach(function(e) {
this.add(e)
}, this)
})
var store = {}
documenterSearchIndex['docs'].forEach(function(e) {
store[e.location] = {title: e.title, category: e.category}
})
$(function(){
function update_search(querystring) {
tokens = lunr.tokenizer(querystring)
results = index.query(function (q) {
tokens.forEach(function (t) {
q.term(t.toString(), {
fields: ["title"],
boost: 100,
usePipeline: false,
editDistance: 0,
wildcard: lunr.Query.wildcard.NONE
})
q.term(t.toString(), {
fields: ["title"],
boost: 10,
usePipeline: false,
editDistance: 2,
wildcard: lunr.Query.wildcard.NONE
})
q.term(t.toString(), {
fields: ["text"],
boost: 1,
usePipeline: true,
editDistance: 0,
wildcard: lunr.Query.wildcard.NONE
})
})
})
$('#search-info').text("Number of results: " + results.length)
$('#search-results').empty()
results.forEach(function(result) {
data = store[result.ref]
link = $('<a>')
link.text(data.title)
link.attr('href', documenterBaseURL+'/'+result.ref)
cat = $('<span class="category">('+data.category+')</span>')
li = $('<li>').append(link).append(" ").append(cat)
$('#search-results').append(li)
})
}
function update_search_box() {
querystring = $('#search-query').val()
update_search(querystring)
}
$('#search-query').keyup(_.debounce(update_search_box, 250))
$('#search-query').change(update_search_box)
search_query_uri = parseUri(window.location).queryKey["q"]
if(search_query_uri !== undefined) {
search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20'))
$("#search-query").val(search_query)
}
update_search_box();
})
})

9
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@ -1,9 +0,0 @@
<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Community · Flux</title><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-36890222-9', 'auto');
ga('send', 'pageview');
</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="models/basics.html">Basics</a></li><li><a class="toctext" href="models/recurrence.html">Recurrence</a></li><li><a class="toctext" href="models/regularisation.html">Regularisation</a></li><li><a class="toctext" href="models/layers.html">Model Reference</a></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 &amp; Loading</a></li><li><span class="toctext">Internals</span><ul><li><a class="toctext" href="internals/tracker.html">Backpropagation</a></li></ul></li><li class="current"><a class="toctext" href="community.html">Community</a><ul class="internal"></ul></li></ul></nav><article id="docs"><header><nav><ul><li><a href="community.html">Community</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/community.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Community</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Community-1" href="#Community-1">Community</a></h1><p>All Flux users are welcome to join our community on the <a href="https://discourse.julialang.org/">Julia forum</a>, the <a href="https://discourse.julialang.org/t/announcing-a-julia-slack/4866">slack</a> (channel #machine-learning), or Flux&#39;s <a href="https://gitter.im/FluxML/Lobby">Gitter</a>. If you have questions or issues we&#39;ll try to help you out.</p><p>If you&#39;re interested in hacking on Flux, the <a href="https://github.com/FluxML/Flux.jl">source code</a> is open and easy to understand – it&#39;s all just the same Julia code you work with normally. You might be interested in our <a href="https://github.com/FluxML/Flux.jl/issues?q=is%3Aopen+is%3Aissue+label%3A%22help+wanted%22">intro issues</a> to get started.</p><footer><hr/><a class="previous" href="internals/tracker.html"><span class="direction">Previous</span><span class="title">Backpropagation</span></a></footer></article></body></html>

40
stable/data/onehot.html
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@ -1,40 +0,0 @@
<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>One-Hot Encoding · Flux</title><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-36890222-9', 'auto');
ga('send', 'pageview');
</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="../models/basics.html">Basics</a></li><li><a class="toctext" href="../models/recurrence.html">Recurrence</a></li><li><a class="toctext" href="../models/regularisation.html">Regularisation</a></li><li><a class="toctext" href="../models/layers.html">Model Reference</a></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 class="current"><a class="toctext" href="onehot.html">One-Hot Encoding</a><ul class="internal"><li><a class="toctext" href="#Batches-1">Batches</a></li></ul></li><li><a class="toctext" href="../gpu.html">GPU Support</a></li><li><a class="toctext" href="../saving.html">Saving &amp; 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><a href="onehot.html">One-Hot Encoding</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/data/onehot.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>One-Hot Encoding</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="One-Hot-Encoding-1" href="#One-Hot-Encoding-1">One-Hot Encoding</a></h1><p>It&#39;s common to encode categorical variables (like <code>true</code>, <code>false</code> or <code>cat</code>, <code>dog</code>) in &quot;one-of-k&quot; or <a href="https://en.wikipedia.org/wiki/One-hot">&quot;one-hot&quot;</a> form. Flux provides the <code>onehot</code> function to make this easy.</p><pre><code class="language-none">julia&gt; using Flux: onehot, onecold
julia&gt; onehot(:b, [:a, :b, :c])
3-element Flux.OneHotVector:
false
true
false
julia&gt; onehot(:c, [:a, :b, :c])
3-element Flux.OneHotVector:
false
false
true</code></pre><p>The inverse is <code>onecold</code> (which can take a general probability distribution, as well as just booleans).</p><pre><code class="language-julia">julia&gt; onecold(ans, [:a, :b, :c])
:c
julia&gt; onecold([true, false, false], [:a, :b, :c])
:a
julia&gt; onecold([0.3, 0.2, 0.5], [:a, :b, :c])
:c</code></pre><h2><a class="nav-anchor" id="Batches-1" href="#Batches-1">Batches</a></h2><p><code>onehotbatch</code> creates a batch (matrix) of one-hot vectors, and <code>onecold</code> treats matrices as batches.</p><pre><code class="language-julia">julia&gt; using Flux: onehotbatch
julia&gt; onehotbatch([:b, :a, :b], [:a, :b, :c])
3×3 Flux.OneHotMatrix:
false true false
true false true
false false false
julia&gt; onecold(ans, [:a, :b, :c])
3-element Array{Symbol,1}:
:b
:a
:b</code></pre><p>Note that these operations returned <code>OneHotVector</code> and <code>OneHotMatrix</code> rather than <code>Array</code>s. <code>OneHotVector</code>s behave like normal vectors but avoid any unnecessary cost compared to using an integer index directly. For example, multiplying a matrix with a one-hot vector simply slices out the relevant row of the matrix under the hood.</p><footer><hr/><a class="previous" href="../training/training.html"><span class="direction">Previous</span><span class="title">Training</span></a><a class="next" href="../gpu.html"><span class="direction">Next</span><span class="title">GPU Support</span></a></footer></article></body></html>

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W = cu(rand(2, 5)) # a 2×5 CuArray
b = cu(rand(2))
predict(x) = W*x .+ b
loss(x, y) = sum((predict(x) .- y).^2)
x, y = cu(rand(5)), cu(rand(2)) # Dummy data
loss(x, y) # ~ 3</code></pre><p>Note that we convert both the parameters (<code>W</code>, <code>b</code>) and the data set (<code>x</code>, <code>y</code>) to cuda arrays. Taking derivatives and training works exactly as before.</p><p>If you define a structured model, like a <code>Dense</code> layer or <code>Chain</code>, you just need to convert the internal parameters. Flux provides <code>mapleaves</code>, which allows you to alter all parameters of a model at once.</p><pre><code class="language-julia">d = Dense(10, 5, σ)
d = mapleaves(cu, d)
d.W # Tracked CuArray
d(cu(rand(10))) # CuArray output
m = Chain(Dense(10, 5, σ), Dense(5, 2), softmax)
m = mapleaves(cu, m)
d(cu(rand(10)))</code></pre><p>As a convenience, Flux provides the <code>gpu</code> function to convert models and data to the GPU if one is available. By default, it&#39;ll do nothing, but loading <code>CuArrays</code> will cause it to move data to the GPU instead.</p><pre><code class="language-julia">julia&gt; using Flux, CuArrays
julia&gt; m = Dense(10,5) |&gt; gpu
Dense(10, 5)
julia&gt; x = rand(10) |&gt; gpu
10-element CuArray{Float32,1}:
0.800225
⋮
0.511655
julia&gt; m(x)
Tracked 5-element CuArray{Float32,1}:
-0.30535
⋮
-0.618002</code></pre><p>The analogue <code>cpu</code> is also available for moving models and data back off of the GPU.</p><pre><code class="language-julia">julia&gt; x = rand(10) |&gt; gpu
10-element CuArray{Float32,1}:
0.235164
⋮
0.192538
julia&gt; x |&gt; cpu
10-element Array{Float32,1}:
0.235164
⋮
0.192538</code></pre><footer><hr/><a class="previous" href="data/onehot.html"><span class="direction">Previous</span><span class="title">One-Hot Encoding</span></a><a class="next" href="saving.html"><span class="direction">Next</span><span class="title">Saving &amp; Loading</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 class="current"><a class="toctext" href="basics.html">Basics</a><ul class="internal"><li><a class="toctext" href="#Taking-Gradients-1">Taking Gradients</a></li><li><a class="toctext" href="#Simple-Models-1">Simple Models</a></li><li><a class="toctext" href="#Building-Layers-1">Building Layers</a></li><li><a class="toctext" href="#Stacking-It-Up-1">Stacking It Up</a></li><li><a class="toctext" href="#Layer-helpers-1">Layer helpers</a></li></ul></li><li><a class="toctext" href="recurrence.html">Recurrence</a></li><li><a class="toctext" href="regularisation.html">Regularisation</a></li><li><a class="toctext" href="layers.html">Model Reference</a></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 &amp; 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="basics.html">Basics</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/basics.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Basics</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Model-Building-Basics-1" href="#Model-Building-Basics-1">Model-Building Basics</a></h1><h2><a class="nav-anchor" id="Taking-Gradients-1" href="#Taking-Gradients-1">Taking Gradients</a></h2><p>Flux&#39;s core feature is taking gradients of Julia code. The <code>gradient</code> function takes another Julia function <code>f</code> and a set of arguments, and returns the gradient with respect to each argument. (It&#39;s a good idea to try pasting these examples in the Julia terminal.)</p><pre><code class="language-julia">using Flux.Tracker
f(x) = 3x^2 + 2x + 1
# df/dx = 6x + 2
df(x) = Tracker.gradient(f, x)[1]
df(2) # 14.0 (tracked)
# d²f/dx² = 6
d2f(x) = Tracker.gradient(df, x)[1]
d2f(2) # 6.0 (tracked)</code></pre><p>(We&#39;ll learn more about why these numbers show up as <code>(tracked)</code> below.)</p><p>When a function has many parameters, we can pass them all in explicitly:</p><pre><code class="language-julia">f(W, b, x) = W * x + b
Tracker.gradient(f, 2, 3, 4)
(4.0 (tracked), 1.0, 2.0 (tracked))</code></pre><p>But machine learning models can have <em>hundreds</em> of parameters! Flux offers a nice way to handle this. We can tell Flux to treat something as a parameter via <code>param</code>. Then we can collect these together and tell <code>gradient</code> to collect the gradients of all of them at once.</p><pre><code class="language-julia">W = param(2) # 2.0 (tracked)
b = param(3) # 3.0 (tracked)
f(x) = W * x + b
params = Params([W, b])
grads = Tracker.gradient(() -&gt; f(4), params)
grads[W] # 4.0
grads[b] # 1.0</code></pre><p>There are a few things to notice here. Firstly, <code>W</code> and <code>b</code> now show up as <em>tracked</em>. Tracked things behave like normal numbers or arrays, but keep records of everything you do with them, allowing Flux to calculate their gradients. <code>gradient</code> takes a zero-argument function; no arguments are necessary because the <code>Params</code> tell it what to differentiate.</p><p>This will come in really handy when dealing with big, complicated models. For now, though, let&#39;s start with something simple.</p><h2><a class="nav-anchor" id="Simple-Models-1" href="#Simple-Models-1">Simple Models</a></h2><p>Consider a simple linear regression, which tries to predict an output array <code>y</code> from an input <code>x</code>.</p><pre><code class="language-julia">W = rand(2, 5)
b = rand(2)
predict(x) = W*x .+ b
function loss(x, y)
ŷ = predict(x)
sum((y .- ŷ).^2)
end
x, y = rand(5), rand(2) # Dummy data
loss(x, y) # ~ 3</code></pre><p>To improve the prediction we can take the gradients of <code>W</code> and <code>b</code> with respect to the loss and perform gradient descent. Let&#39;s tell Flux that <code>W</code> and <code>b</code> are parameters, just like we did above.</p><pre><code class="language-julia">using Flux.Tracker
W = param(W)
b = param(b)
gs = Tracker.gradient(() -&gt; loss(x, y), Params([W, b]))</code></pre><p>Now that we have gradients, we can pull them out and update <code>W</code> to train the model. The <code>update!(W, Δ)</code> function applies <code>W = W + Δ</code>, which we can use for gradient descent.</p><pre><code class="language-julia">using Flux.Tracker: update!
Δ = gs[W]
# Update the parameter and reset the gradient
update!(W, -0.1Δ)
loss(x, y) # ~ 2.5</code></pre><p>The loss has decreased a little, meaning that our prediction <code>x</code> is closer to the target <code>y</code>. If we have some data we can already try <a href="../training/training.html">training the model</a>.</p><p>All deep learning in Flux, however complex, is a simple generalisation of this example. Of course, models can <em>look</em> very different – they might have millions of parameters or complex control flow. Let&#39;s see how Flux handles more complex models.</p><h2><a class="nav-anchor" id="Building-Layers-1" href="#Building-Layers-1">Building Layers</a></h2><p>It&#39;s common to create more complex models than the linear regression above. For example, we might want to have two linear layers with a nonlinearity like <a href="https://en.wikipedia.org/wiki/Sigmoid_function">sigmoid</a> (<code>σ</code>) in between them. In the above style we could write this as:</p><pre><code class="language-julia">W1 = param(rand(3, 5))
b1 = param(rand(3))
layer1(x) = W1 * x .+ b1
W2 = param(rand(2, 3))
b2 = param(rand(2))
layer2(x) = W2 * x .+ b2
model(x) = layer2(σ.(layer1(x)))
model(rand(5)) # =&gt; 2-element vector</code></pre><p>This works but is fairly unwieldy, with a lot of repetition – especially as we add more layers. One way to factor this out is to create a function that returns linear layers.</p><pre><code class="language-julia">function linear(in, out)
W = param(randn(out, in))
b = param(randn(out))
x -&gt; W * x .+ b
end
linear1 = linear(5, 3) # we can access linear1.W etc
linear2 = linear(3, 2)
model(x) = linear2(σ.(linear1(x)))
model(rand(5)) # =&gt; 2-element vector</code></pre><p>Another (equivalent) way is to create a struct that explicitly represents the affine layer.</p><pre><code class="language-julia">struct Affine
W
b
end
Affine(in::Integer, out::Integer) =
Affine(param(randn(out, in)), param(randn(out)))
# Overload call, so the object can be used as a function
(m::Affine)(x) = m.W * x .+ m.b
a = Affine(10, 5)
a(rand(10)) # =&gt; 5-element vector</code></pre><p>Congratulations! You just built the <code>Dense</code> layer that comes with Flux. Flux has many interesting layers available, but they&#39;re all things you could have built yourself very easily.</p><p>(There is one small difference with <code>Dense</code> – for convenience it also takes an activation function, like <code>Dense(10, 5, σ)</code>.)</p><h2><a class="nav-anchor" id="Stacking-It-Up-1" href="#Stacking-It-Up-1">Stacking It Up</a></h2><p>It&#39;s pretty common to write models that look something like:</p><pre><code class="language-julia">layer1 = Dense(10, 5, σ)
# ...
model(x) = layer3(layer2(layer1(x)))</code></pre><p>For long chains, it might be a bit more intuitive to have a list of layers, like this:</p><pre><code class="language-julia">using Flux
layers = [Dense(10, 5, σ), Dense(5, 2), softmax]
model(x) = foldl((x, m) -&gt; m(x), layers, init = x)
model(rand(10)) # =&gt; 2-element vector</code></pre><p>Handily, this is also provided for in Flux:</p><pre><code class="language-julia">model2 = Chain(
Dense(10, 5, σ),
Dense(5, 2),
softmax)
model2(rand(10)) # =&gt; 2-element vector</code></pre><p>This quickly starts to look like a high-level deep learning library; yet you can see how it falls out of simple abstractions, and we lose none of the power of Julia code.</p><p>A nice property of this approach is that because &quot;models&quot; are just functions (possibly with trainable parameters), you can also see this as simple function composition.</p><pre><code class="language-julia">m = Dense(5, 2) ∘ Dense(10, 5, σ)
m(rand(10))</code></pre><p>Likewise, <code>Chain</code> will happily work with any Julia function.</p><pre><code class="language-julia">m = Chain(x -&gt; x^2, x -&gt; x+1)
m(5) # =&gt; 26</code></pre><h2><a class="nav-anchor" id="Layer-helpers-1" href="#Layer-helpers-1">Layer helpers</a></h2><p>Flux provides a set of helpers for custom layers, which you can enable by calling</p><pre><code class="language-julia">Flux.@treelike Affine</code></pre><p>This enables a useful extra set of functionality for our <code>Affine</code> layer, such as <a href="../training/optimisers.html">collecting its parameters</a> or <a href="../gpu.html">moving it to the GPU</a>.</p><footer><hr/><a class="previous" href="../index.html"><span class="direction">Previous</span><span class="title">Home</span></a><a class="next" href="recurrence.html"><span class="direction">Next</span><span class="title">Recurrence</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="#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 &amp; 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 &amp; 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 -&gt; x^2, x -&gt; 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/9d563820f8f2f5ae91364afc1e9f371f75466e77/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&gt; d = Dense(5, 2)
Dense(5, 2)
julia&gt; 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/9d563820f8f2f5ae91364afc1e9f371f75466e77/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=&gt;out)
Conv(size, in=&gt;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/9d563820f8f2f5ae91364afc1e9f371f75466e77/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/9d563820f8f2f5ae91364afc1e9f371f75466e77/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/9d563820f8f2f5ae91364afc1e9f371f75466e77/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/9d563820f8f2f5ae91364afc1e9f371f75466e77/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/9d563820f8f2f5ae91364afc1e9f371f75466e77/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/9d563820f8f2f5ae91364afc1e9f371f75466e77/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&#39;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/9d563820f8f2f5ae91364afc1e9f371f75466e77/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 &gt; 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 &amp; Regularisation</a></h2><p>These layers don&#39;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/9d563820f8f2f5ae91364afc1e9f371f75466e77/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&#39;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/9d563820f8f2f5ae91364afc1e9f371f75466e77/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/9d563820f8f2f5ae91364afc1e9f371f75466e77/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/9d563820f8f2f5ae91364afc1e9f371f75466e77/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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</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 class="current"><a class="toctext" href="recurrence.html">Recurrence</a><ul class="internal"><li><a class="toctext" href="#Recurrent-Cells-1">Recurrent Cells</a></li><li><a class="toctext" href="#Stateful-Models-1">Stateful Models</a></li><li><a class="toctext" href="#Sequences-1">Sequences</a></li><li><a class="toctext" href="#Truncating-Gradients-1">Truncating Gradients</a></li></ul></li><li><a class="toctext" href="regularisation.html">Regularisation</a></li><li><a class="toctext" href="layers.html">Model Reference</a></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 &amp; 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="recurrence.html">Recurrence</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/models/recurrence.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Recurrence</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Recurrent-Models-1" href="#Recurrent-Models-1">Recurrent Models</a></h1><h2><a class="nav-anchor" id="Recurrent-Cells-1" href="#Recurrent-Cells-1">Recurrent Cells</a></h2><p>In the simple feedforward case, our model <code>m</code> is a simple function from various inputs <code>xᵢ</code> to predictions <code>yᵢ</code>. (For example, each <code>x</code> might be an MNIST digit and each <code>y</code> a digit label.) Each prediction is completely independent of any others, and using the same <code>x</code> will always produce the same <code>y</code>.</p><pre><code class="language-julia">y₁ = f(x₁)
y₂ = f(x₂)
y₃ = f(x₃)
# ...</code></pre><p>Recurrent networks introduce a <em>hidden state</em> that gets carried over each time we run the model. The model now takes the old <code>h</code> as an input, and produces a new <code>h</code> as output, each time we run it.</p><pre><code class="language-julia">h = # ... initial state ...
h, y₁ = f(h, x₁)
h, y₂ = f(h, x₂)
h, y₃ = f(h, x₃)
# ...</code></pre><p>Information stored in <code>h</code> is preserved for the next prediction, allowing it to function as a kind of memory. This also means that the prediction made for a given <code>x</code> depends on all the inputs previously fed into the model.</p><p>(This might be important if, for example, each <code>x</code> represents one word of a sentence; the model&#39;s interpretation of the word &quot;bank&quot; should change if the previous input was &quot;river&quot; rather than &quot;investment&quot;.)</p><p>Flux&#39;s RNN support closely follows this mathematical perspective. The most basic RNN is as close as possible to a standard <code>Dense</code> layer, and the output is also the hidden state.</p><pre><code class="language-julia">Wxh = randn(5, 10)
Whh = randn(5, 5)
b = randn(5)
function rnn(h, x)
h = tanh.(Wxh * x .+ Whh * h .+ b)
return h, h
end
x = rand(10) # dummy data
h = rand(5) # initial hidden state
h, y = rnn(h, x)</code></pre><p>If you run the last line a few times, you&#39;ll notice the output <code>y</code> changing slightly even though the input <code>x</code> is the same.</p><p>We sometimes refer to functions like <code>rnn</code> above, which explicitly manage state, as recurrent <em>cells</em>. There are various recurrent cells available, which are documented in the <a href="layers.html">layer reference</a>. The hand-written example above can be replaced with:</p><pre><code class="language-julia">using Flux
rnn2 = Flux.RNNCell(10, 5)
x = rand(10) # dummy data
h = rand(5) # initial hidden state
h, y = rnn2(h, x)</code></pre><h2><a class="nav-anchor" id="Stateful-Models-1" href="#Stateful-Models-1">Stateful Models</a></h2><p>For the most part, we don&#39;t want to manage hidden states ourselves, but to treat our models as being stateful. Flux provides the <code>Recur</code> wrapper to do this.</p><pre><code class="language-julia">x = rand(10)
h = rand(5)
m = Flux.Recur(rnn, h)
y = m(x)</code></pre><p>The <code>Recur</code> wrapper stores the state between runs in the <code>m.state</code> field.</p><p>If you use the <code>RNN(10, 5)</code> constructor – as opposed to <code>RNNCell</code> – you&#39;ll see that it&#39;s simply a wrapped cell.</p><pre><code class="language-julia">julia&gt; RNN(10, 5)
Recur(RNNCell(Dense(15, 5)))</code></pre><h2><a class="nav-anchor" id="Sequences-1" href="#Sequences-1">Sequences</a></h2><p>Often we want to work with sequences of inputs, rather than individual <code>x</code>s.</p><pre><code class="language-julia">seq = [rand(10) for i = 1:10]</code></pre><p>With <code>Recur</code>, applying our model to each element of a sequence is trivial:</p><pre><code class="language-julia">m.(seq) # returns a list of 5-element vectors</code></pre><p>This works even when we&#39;ve chain recurrent layers into a larger model.</p><pre><code class="language-julia">m = Chain(LSTM(10, 15), Dense(15, 5))
m.(seq)</code></pre><h2><a class="nav-anchor" id="Truncating-Gradients-1" href="#Truncating-Gradients-1">Truncating Gradients</a></h2><p>By default, calculating the gradients in a recurrent layer involves its entire history. For example, if we call the model on 100 inputs, we&#39;ll have to calculate the gradient for those 100 calls. If we then calculate another 10 inputs we have to calculate 110 gradients – this accumulates and quickly becomes expensive.</p><p>To avoid this we can <em>truncate</em> the gradient calculation, forgetting the history.</p><pre><code class="language-julia">truncate!(m)</code></pre><p>Calling <code>truncate!</code> wipes the slate clean, so we can call the model with more inputs without building up an expensive gradient computation.</p><p><code>truncate!</code> makes sense when you are working with multiple chunks of a large sequence, but we may also want to work with a set of independent sequences. In this case the hidden state should be completely reset to its original value, throwing away any accumulated information. <code>reset!</code> does this for you.</p><footer><hr/><a class="previous" href="basics.html"><span class="direction">Previous</span><span class="title">Basics</span></a><a class="next" href="regularisation.html"><span class="direction">Next</span><span class="title">Regularisation</span></a></footer></article></body></html>

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m = Dense(10, 5)
loss(x, y) = crossentropy(softmax(m(x)), y)</code></pre><p>We can regularise this by taking the (L2) norm of the parameters, <code>m.W</code> and <code>m.b</code>.</p><pre><code class="language-julia">penalty() = norm(m.W) + norm(m.b)
loss(x, y) = crossentropy(softmax(m(x)), y) + penalty()</code></pre><p>When working with layers, Flux provides the <code>params</code> function to grab all parameters at once. We can easily penalise everything with <code>sum(norm, params)</code>.</p><pre><code class="language-julia">julia&gt; params(m)
2-element Array{Any,1}:
param([0.355408 0.533092; … 0.430459 0.171498])
param([0.0, 0.0, 0.0, 0.0, 0.0])
julia&gt; sum(norm, params(m))
26.01749952921026 (tracked)</code></pre><p>Here&#39;s a larger example with a multi-layer perceptron.</p><pre><code class="language-julia">m = Chain(
Dense(28^2, 128, relu),
Dense(128, 32, relu),
Dense(32, 10), softmax)
loss(x, y) = crossentropy(m(x), y) + sum(norm, params(m))
loss(rand(28^2), rand(10))</code></pre><p>One can also easily add per-layer regularisation via the <code>activations</code> function:</p><pre><code class="language-julia">julia&gt; c = Chain(Dense(10,5,σ),Dense(5,2),softmax)
Chain(Dense(10, 5, NNlib.σ), Dense(5, 2), NNlib.softmax)
julia&gt; activations(c, rand(10))
3-element Array{Any,1}:
param([0.71068, 0.831145, 0.751219, 0.227116, 0.553074])
param([0.0330606, -0.456104])
param([0.61991, 0.38009])
julia&gt; sum(norm, ans)
2.639678767773633 (tracked)</code></pre><footer><hr/><a class="previous" href="recurrence.html"><span class="direction">Previous</span><span class="title">Recurrence</span></a><a class="next" href="layers.html"><span class="direction">Next</span><span class="title">Model Reference</span></a></footer></article></body></html>

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"text": "Flux is a library for machine learning. It comes \"batteries-included\" with many useful tools built in, but also lets you use the full power of the Julia language where you need it. We follow a few key principles:Doing the obvious thing. Flux has relatively few explicit APIs for features like regularisation or embeddings. Instead, writing down the mathematical form will work – and be fast.\nYou could have written Flux. All of it, from LSTMs to GPU kernels, is straightforward Julia code. When in doubt, it’s well worth looking at the source. If you need something different, you can easily roll your own.\nPlay nicely with others. Flux works well with Julia libraries from data frames and images to differential equation solvers, so you can easily build complex data processing pipelines that integrate Flux models."
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"text": "Download Julia 1.0 or later, if you haven\'t already. You can add Flux from using Julia\'s package manager, by typing ] add Flux in the Julia prompt.If you have CUDA you can also run ] add CuArrays to get GPU support; see here for more details."
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"text": "Flux\'s core feature is taking gradients of Julia code. The gradient function takes another Julia function f and a set of arguments, and returns the gradient with respect to each argument. (It\'s a good idea to try pasting these examples in the Julia terminal.)using Flux.Tracker\n\nf(x) = 3x^2 + 2x + 1\n\n# df/dx = 6x + 2\ndf(x) = Tracker.gradient(f, x)[1]\n\ndf(2) # 14.0 (tracked)\n\n# d²f/dx² = 6\nd2f(x) = Tracker.gradient(df, x)[1]\n\nd2f(2) # 6.0 (tracked)(We\'ll learn more about why these numbers show up as (tracked) below.)When a function has many parameters, we can pass them all in explicitly:f(W, b, x) = W * x + b\n\nTracker.gradient(f, 2, 3, 4)\n(4.0 (tracked), 1.0, 2.0 (tracked))But machine learning models can have hundreds of parameters! Flux offers a nice way to handle this. We can tell Flux to treat something as a parameter via param. Then we can collect these together and tell gradient to collect the gradients of all of them at once.W = param(2) # 2.0 (tracked)\nb = param(3) # 3.0 (tracked)\n\nf(x) = W * x + b\n\nparams = Params([W, b])\ngrads = Tracker.gradient(() -> f(4), params)\n\ngrads[W] # 4.0\ngrads[b] # 1.0There are a few things to notice here. Firstly, W and b now show up as tracked. Tracked things behave like normal numbers or arrays, but keep records of everything you do with them, allowing Flux to calculate their gradients. gradient takes a zero-argument function; no arguments are necessary because the Params tell it what to differentiate.This will come in really handy when dealing with big, complicated models. For now, though, let\'s start with something simple."
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"text": "It\'s pretty common to write models that look something like:layer1 = Dense(10, 5, σ)\n# ...\nmodel(x) = layer3(layer2(layer1(x)))For long chains, it might be a bit more intuitive to have a list of layers, like this:using Flux\n\nlayers = [Dense(10, 5, σ), Dense(5, 2), softmax]\n\nmodel(x) = foldl((x, m) -> m(x), layers, init = x)\n\nmodel(rand(10)) # => 2-element vectorHandily, this is also provided for in Flux:model2 = Chain(\n Dense(10, 5, σ),\n Dense(5, 2),\n softmax)\n\nmodel2(rand(10)) # => 2-element vectorThis quickly starts to look like a high-level deep learning library; yet you can see how it falls out of simple abstractions, and we lose none of the power of Julia code.A nice property of this approach is that because \"models\" are just functions (possibly with trainable parameters), you can also see this as simple function composition.m = Dense(5, 2) ∘ Dense(10, 5, σ)\n\nm(rand(10))Likewise, Chain will happily work with any Julia function.m = Chain(x -> x^2, x -> x+1)\n\nm(5) # => 26"
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"text": "In the simple feedforward case, our model m is a simple function from various inputs xᵢ to predictions yᵢ. (For example, each x might be an MNIST digit and each y a digit label.) Each prediction is completely independent of any others, and using the same x will always produce the same y.y₁ = f(x₁)\ny₂ = f(x₂)\ny₃ = f(x₃)\n# ...Recurrent networks introduce a hidden state that gets carried over each time we run the model. The model now takes the old h as an input, and produces a new h as output, each time we run it.h = # ... initial state ...\nh, y₁ = f(h, x₁)\nh, y₂ = f(h, x₂)\nh, y₃ = f(h, x₃)\n# ...Information stored in h is preserved for the next prediction, allowing it to function as a kind of memory. This also means that the prediction made for a given x depends on all the inputs previously fed into the model.(This might be important if, for example, each x represents one word of a sentence; the model\'s interpretation of the word \"bank\" should change if the previous input was \"river\" rather than \"investment\".)Flux\'s RNN support closely follows this mathematical perspective. The most basic RNN is as close as possible to a standard Dense layer, and the output is also the hidden state.Wxh = randn(5, 10)\nWhh = randn(5, 5)\nb = randn(5)\n\nfunction rnn(h, x)\n h = tanh.(Wxh * x .+ Whh * h .+ b)\n return h, h\nend\n\nx = rand(10) # dummy data\nh = rand(5) # initial hidden state\n\nh, y = rnn(h, x)If you run the last line a few times, you\'ll notice the output y changing slightly even though the input x is the same.We sometimes refer to functions like rnn above, which explicitly manage state, as recurrent cells. There are various recurrent cells available, which are documented in the layer reference. The hand-written example above can be replaced with:using Flux\n\nrnn2 = Flux.RNNCell(10, 5)\n\nx = rand(10) # dummy data\nh = rand(5) # initial hidden state\n\nh, y = rnn2(h, x)"
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"text": "Applying regularisation to model parameters is straightforward. We just need to apply an appropriate regulariser, such as norm, to each model parameter and add the result to the overall loss.For example, say we have a simple regression.using Flux: crossentropy\nm = Dense(10, 5)\nloss(x, y) = crossentropy(softmax(m(x)), y)We can regularise this by taking the (L2) norm of the parameters, m.W and m.b.penalty() = norm(m.W) + norm(m.b)\nloss(x, y) = crossentropy(softmax(m(x)), y) + penalty()When working with layers, Flux provides the params function to grab all parameters at once. We can easily penalise everything with sum(norm, params).julia> params(m)\n2-element Array{Any,1}:\n param([0.355408 0.533092; … 0.430459 0.171498])\n param([0.0, 0.0, 0.0, 0.0, 0.0])\n\njulia> sum(norm, params(m))\n26.01749952921026 (tracked)Here\'s a larger example with a multi-layer perceptron.m = Chain(\n Dense(28^2, 128, relu),\n Dense(128, 32, relu),\n Dense(32, 10), softmax)\n\nloss(x, y) = crossentropy(m(x), y) + sum(norm, params(m))\n\nloss(rand(28^2), rand(10))One can also easily add per-layer regularisation via the activations function:julia> c = Chain(Dense(10,5,σ),Dense(5,2),softmax)\nChain(Dense(10, 5, NNlib.σ), Dense(5, 2), NNlib.softmax)\n\njulia> activations(c, rand(10))\n3-element Array{Any,1}:\n param([0.71068, 0.831145, 0.751219, 0.227116, 0.553074])\n param([0.0330606, -0.456104])\n param([0.61991, 0.38009])\n\njulia> sum(norm, ans)\n2.639678767773633 (tracked)"
},
{
"location": "models/layers.html#",
"page": "Model Reference",
"title": "Model Reference",
"category": "page",
"text": ""
},
{
"location": "models/layers.html#Flux.Chain",
"page": "Model Reference",
"title": "Flux.Chain",
"category": "type",
"text": "Chain(layers...)\n\nChain multiple layers / functions together, so that they are called in sequence on a given input.\n\nm = Chain(x -> x^2, x -> x+1)\nm(5) == 26\n\nm = Chain(Dense(10, 5), Dense(5, 2))\nx = rand(10)\nm(x) == m[2](m[1](x))\n\nChain also supports indexing and slicing, e.g. m[2] or m[1:end-1]. m[1:3](x) will calculate the output of the first three layers.\n\n\n\n\n\n"
},
{
"location": "models/layers.html#Flux.Dense",
"page": "Model Reference",
"title": "Flux.Dense",
"category": "type",
"text": "Dense(in::Integer, out::Integer, σ = identity)\n\nCreates a traditional Dense layer with parameters W and b.\n\ny = σ.(W * x .+ b)\n\nThe input x must be a vector of length in, or a batch of vectors represented as an in × N matrix. The out y will be a vector or batch of length out.\n\njulia> d = Dense(5, 2)\nDense(5, 2)\n\njulia> d(rand(5))\nTracked 2-element Array{Float64,1}:\n 0.00257447\n -0.00449443\n\n\n\n\n\n"
},
{
"location": "models/layers.html#Flux.Conv",
"page": "Model Reference",
"title": "Flux.Conv",
"category": "type",
"text": "Conv(size, in=>out)\nConv(size, in=>out, relu)\n\nStandard convolutional layer. size should be a tuple like (2, 2). in and out specify the number of input and output channels respectively.\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, stride and dilation.\n\n\n\n\n\n"
},
{
"location": "models/layers.html#Flux.MaxPool",
"page": "Model Reference",
"title": "Flux.MaxPool",
"category": "type",
"text": "MaxPool(k)\n\nMax pooling layer. k stands for the size of the window for each dimension of the input.\n\nTakes the keyword arguments pad and stride.\n\n\n\n\n\n"
},
{
"location": "models/layers.html#Flux.MeanPool",
"page": "Model Reference",
"title": "Flux.MeanPool",
"category": "type",
"text": "MeanPool(k)\n\nMean pooling layer. k stands for the size of the window for each dimension of the input.\n\nTakes the keyword arguments pad and stride.\n\n\n\n\n\n"
},
{
"location": "models/layers.html#Basic-Layers-1",
"page": "Model Reference",
"title": "Basic Layers",
"category": "section",
"text": "These core layers form the foundation of almost all neural networks.Chain\nDense\nConv\nMaxPool\nMeanPool"
},
{
"location": "models/layers.html#Flux.RNN",
"page": "Model Reference",
"title": "Flux.RNN",
"category": "function",
"text": "RNN(in::Integer, out::Integer, σ = tanh)\n\nThe most basic recurrent layer; essentially acts as a Dense layer, but with the output fed back into the input each time step.\n\n\n\n\n\n"
},
{
"location": "models/layers.html#Flux.LSTM",
"page": "Model Reference",
"title": "Flux.LSTM",
"category": "function",
"text": "LSTM(in::Integer, out::Integer)\n\nLong Short Term Memory recurrent layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.\n\nSee this article for a good overview of the internals.\n\n\n\n\n\n"
},
{
"location": "models/layers.html#Flux.GRU",
"page": "Model Reference",
"title": "Flux.GRU",
"category": "function",
"text": "GRU(in::Integer, out::Integer)\n\nGated Recurrent Unit layer. Behaves like an RNN but generally exhibits a longer memory span over sequences.\n\nSee this article for a good overview of the internals.\n\n\n\n\n\n"
},
{
"location": "models/layers.html#Flux.Recur",
"page": "Model Reference",
"title": "Flux.Recur",
"category": "type",
"text": "Recur(cell)\n\nRecur takes a recurrent cell and makes it stateful, managing the hidden state in the background. cell should be a model of the form:\n\nh, y = cell(h, x...)\n\nFor example, here\'s a recurrent network that keeps a running total of its inputs.\n\naccum(h, x) = (h+x, x)\nrnn = Flux.Recur(accum, 0)\nrnn(2) # 2\nrnn(3) # 3\nrnn.state # 5\nrnn.(1:10) # apply to a sequence\nrnn.state # 60\n\n\n\n\n\n"
},
{
"location": "models/layers.html#Recurrent-Layers-1",
"page": "Model Reference",
"title": "Recurrent Layers",
"category": "section",
"text": "Much like the core layers above, but can be used to process sequence data (as well as other kinds of structured data).RNN\nLSTM\nGRU\nFlux.Recur"
},
{
"location": "models/layers.html#NNlib.σ",
"page": "Model Reference",
"title": "NNlib.σ",
"category": "function",
"text": "σ(x) = 1 / (1 + exp(-x))\n\nClassic sigmoid activation function.\n\n\n\n\n\n"
},
{
"location": "models/layers.html#NNlib.relu",
"page": "Model Reference",
"title": "NNlib.relu",
"category": "function",
"text": "relu(x) = max(0, x)\n\nRectified Linear Unit activation function.\n\n\n\n\n\n"
},
{
"location": "models/layers.html#NNlib.leakyrelu",
"page": "Model Reference",
"title": "NNlib.leakyrelu",
"category": "function",
"text": "leakyrelu(x) = max(0.01x, x)\n\nLeaky Rectified Linear Unit activation function. You can also specify the coefficient explicitly, e.g. leakyrelu(x, 0.01).\n\n\n\n\n\n"
},
{
"location": "models/layers.html#NNlib.elu",
"page": "Model Reference",
"title": "NNlib.elu",
"category": "function",
"text": "elu(x, α = 1) =\n x > 0 ? x : α * (exp(x) - 1)\n\nExponential Linear Unit activation function. See Fast and Accurate Deep Network Learning by Exponential Linear Units. You can also specify the coefficient explicitly, e.g. elu(x, 1).\n\n\n\n\n\n"
},
{
"location": "models/layers.html#NNlib.swish",
"page": "Model Reference",
"title": "NNlib.swish",
"category": "function",
"text": "swish(x) = x * σ(x)\n\nSelf-gated actvation function. See Swish: a Self-Gated Activation Function.\n\n\n\n\n\n"
},
{
"location": "models/layers.html#Activation-Functions-1",
"page": "Model Reference",
"title": "Activation Functions",
"category": "section",
"text": "Non-linearities that go between layers of your model. Most of these functions are defined in NNlib but are available by default in Flux.Note that, unless otherwise stated, activation functions operate on scalars. To apply them to an array you can call σ.(xs), relu.(xs) and so on.σ\nrelu\nleakyrelu\nelu\nswish"
},
{
"location": "models/layers.html#Flux.testmode!",
"page": "Model Reference",
"title": "Flux.testmode!",
"category": "function",
"text": "testmode!(m)\ntestmode!(m, false)\n\nPut layers like Dropout and BatchNorm into testing mode (or back to training mode with false).\n\n\n\n\n\n"
},
{
"location": "models/layers.html#Flux.BatchNorm",
"page": "Model Reference",
"title": "Flux.BatchNorm",
"category": "type",
"text": "BatchNorm(channels::Integer, σ = identity;\n initβ = zeros, initγ = ones,\n ϵ = 1e-8, momentum = .1)\n\nBatch Normalization layer. The channels input should be the size of the channel dimension in your data (see below).\n\nGiven an array with N dimensions, call the N-1th the channel dimension. (For a batch of feature vectors this is just the data dimension, for WHCN images it\'s the usual channel dimension.)\n\nBatchNorm computes the mean and variance for each each W×H×1×N slice and shifts them to have a new mean and variance (corresponding to the learnable, per-channel bias and scale parameters).\n\nSee Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift.\n\nExample:\n\nm = Chain(\n Dense(28^2, 64),\n BatchNorm(64, relu),\n Dense(64, 10),\n BatchNorm(10),\n softmax)\n\n\n\n\n\n"
},
{
"location": "models/layers.html#Flux.Dropout",
"page": "Model Reference",
"title": "Flux.Dropout",
"category": "type",
"text": "Dropout(p)\n\nA Dropout layer. For each input, either sets that input to 0 (with probability p) or scales it by 1/(1-p). This is used as a regularisation, i.e. it reduces overfitting during training.\n\nDoes nothing to the input once in testmode!.\n\n\n\n\n\n"
},
{
"location": "models/layers.html#Flux.LayerNorm",
"page": "Model Reference",
"title": "Flux.LayerNorm",
"category": "type",
"text": "LayerNorm(h::Integer)\n\nA normalisation layer designed to be used with recurrent hidden states of size h. Normalises the mean/stddev of each input before applying a per-neuron gain/bias.\n\n\n\n\n\n"
},
{
"location": "models/layers.html#Normalisation-and-Regularisation-1",
"page": "Model Reference",
"title": "Normalisation & Regularisation",
"category": "section",
"text": "These layers don\'t affect the structure of the network but may improve training times or reduce overfitting.Flux.testmode!\nBatchNorm\nDropout\nLayerNorm"
},
{
"location": "training/optimisers.html#",
"page": "Optimisers",
"title": "Optimisers",
"category": "page",
"text": ""
},
{
"location": "training/optimisers.html#Optimisers-1",
"page": "Optimisers",
"title": "Optimisers",
"category": "section",
"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."
},
{
"location": "training/optimisers.html#Flux.Optimise.SGD",
"page": "Optimisers",
"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"
},
{
"location": "training/optimisers.html#Flux.Optimise.Momentum",
"page": "Optimisers",
"title": "Flux.Optimise.Momentum",
"category": "function",
"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"
},
{
"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"
},
{
"location": "training/optimisers.html#Flux.Optimise.ADAM",
"page": "Optimisers",
"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"
},
{
"location": "training/optimisers.html#Optimiser-Reference-1",
"page": "Optimisers",
"title": "Optimiser Reference",
"category": "section",
"text": "All optimisers return a function that, when called, will update the parameters passed to it.SGD\nMomentum\nNesterov\nADAM"
},
{
"location": "training/training.html#",
"page": "Training",
"title": "Training",
"category": "page",
"text": ""
},
{
"location": "training/training.html#Training-1",
"page": "Training",
"title": "Training",
"category": "section",
"text": "To actually train a model we need three things:A objective function, that evaluates how well a model is doing given some input data.\nA collection of data points that will be provided to the objective function.\nAn optimiser that will update the model parameters appropriately.With these we can call Flux.train!:Flux.train!(objective, data, opt)There are plenty of examples in the model zoo."
},
{
"location": "training/training.html#Loss-Functions-1",
"page": "Training",
"title": "Loss Functions",
"category": "section",
"text": "The objective function must return a number representing how far the model is from its target – the loss of the model. The loss function that we defined in basics will work as an objective. We can also define an objective in terms of some model:m = Chain(\n Dense(784, 32, σ),\n Dense(32, 10), softmax)\n\nloss(x, y) = Flux.mse(m(x), y)\n\n# later\nFlux.train!(loss, data, opt)The objective will almost always be defined in terms of some cost function that measures the distance of the prediction m(x) from the target y. Flux has several of these built in, like mse for mean squared error or crossentropy for cross entropy loss, but you can calculate it however you want."
},
{
"location": "training/training.html#Datasets-1",
"page": "Training",
"title": "Datasets",
"category": "section",
"text": "The data argument provides a collection of data to train with (usually a set of inputs x and target outputs y). For example, here\'s a dummy data set with only one data point:x = rand(784)\ny = rand(10)\ndata = [(x, y)]Flux.train! will call loss(x, y), calculate gradients, update the weights and then move on to the next data point if there is one. We can train the model on the same data three times:data = [(x, y), (x, y), (x, y)]\n# Or equivalently\ndata = Iterators.repeated((x, y), 3)It\'s common to load the xs and ys separately. In this case you can use zip:xs = [rand(784), rand(784), rand(784)]\nys = [rand( 10), rand( 10), rand( 10)]\ndata = zip(xs, ys)Note that, by default, train! only loops over the data once (a single \"epoch\"). A convenient way to run multiple epochs from the REPL is provided by @epochs.julia> using Flux: @epochs\n\njulia> @epochs 2 println(\"hello\")\nINFO: Epoch 1\nhello\nINFO: Epoch 2\nhello\n\njulia> @epochs 2 Flux.train!(...)\n# Train for two epochs"
},
{
"location": "training/training.html#Callbacks-1",
"page": "Training",
"title": "Callbacks",
"category": "section",
"text": "train! takes an additional argument, cb, that\'s used for callbacks so that you can observe the training process. For example:train!(objective, data, opt, cb = () -> println(\"training\"))Callbacks are called for every batch of training data. You can slow this down using Flux.throttle(f, timeout) which prevents f from being called more than once every timeout seconds.A more typical callback might look like this:test_x, test_y = # ... create single batch of test data ...\nevalcb() = @show(loss(test_x, test_y))\n\nFlux.train!(objective, data, opt,\n cb = throttle(evalcb, 5))"
},
{
"location": "data/onehot.html#",
"page": "One-Hot Encoding",
"title": "One-Hot Encoding",
"category": "page",
"text": ""
},
{
"location": "data/onehot.html#One-Hot-Encoding-1",
"page": "One-Hot Encoding",
"title": "One-Hot Encoding",
"category": "section",
"text": "It\'s common to encode categorical variables (like true, false or cat, dog) in \"one-of-k\" or \"one-hot\" form. Flux provides the onehot function to make this easy.julia> using Flux: onehot, onecold\n\njulia> onehot(:b, [:a, :b, :c])\n3-element Flux.OneHotVector:\n false\n true\n false\n\njulia> onehot(:c, [:a, :b, :c])\n3-element Flux.OneHotVector:\n false\n false\n trueThe inverse is onecold (which can take a general probability distribution, as well as just booleans).julia> onecold(ans, [:a, :b, :c])\n:c\n\njulia> onecold([true, false, false], [:a, :b, :c])\n:a\n\njulia> onecold([0.3, 0.2, 0.5], [:a, :b, :c])\n:c"
},
{
"location": "data/onehot.html#Batches-1",
"page": "One-Hot Encoding",
"title": "Batches",
"category": "section",
"text": "onehotbatch creates a batch (matrix) of one-hot vectors, and onecold treats matrices as batches.julia> using Flux: onehotbatch\n\njulia> onehotbatch([:b, :a, :b], [:a, :b, :c])\n3×3 Flux.OneHotMatrix:\n false true false\n true false true\n false false false\n\njulia> onecold(ans, [:a, :b, :c])\n3-element Array{Symbol,1}:\n :b\n :a\n :bNote that these operations returned OneHotVector and OneHotMatrix rather than Arrays. OneHotVectors behave like normal vectors but avoid any unnecessary cost compared to using an integer index directly. For example, multiplying a matrix with a one-hot vector simply slices out the relevant row of the matrix under the hood."
},
{
"location": "gpu.html#",
"page": "GPU Support",
"title": "GPU Support",
"category": "page",
"text": ""
},
{
"location": "gpu.html#GPU-Support-1",
"page": "GPU Support",
"title": "GPU Support",
"category": "section",
"text": "Support for array operations on other hardware backends, like GPUs, is provided by external packages like CuArrays. Flux is agnostic to array types, so we simply need to move model weights and data to the GPU and Flux will handle it.For example, we can use CuArrays (with the cu converter) to run our basic example on an NVIDIA GPU.(Note that you need to build Julia 0.6 from source and have CUDA available to use CuArrays – please see the CUDAnative.jl instructions for more details.)using CuArrays\n\nW = cu(rand(2, 5)) # a 2×5 CuArray\nb = cu(rand(2))\n\npredict(x) = W*x .+ b\nloss(x, y) = sum((predict(x) .- y).^2)\n\nx, y = cu(rand(5)), cu(rand(2)) # Dummy data\nloss(x, y) # ~ 3Note that we convert both the parameters (W, b) and the data set (x, y) to cuda arrays. Taking derivatives and training works exactly as before.If you define a structured model, like a Dense layer or Chain, you just need to convert the internal parameters. Flux provides mapleaves, which allows you to alter all parameters of a model at once.d = Dense(10, 5, σ)\nd = mapleaves(cu, d)\nd.W # Tracked CuArray\nd(cu(rand(10))) # CuArray output\n\nm = Chain(Dense(10, 5, σ), Dense(5, 2), softmax)\nm = mapleaves(cu, m)\nd(cu(rand(10)))As a convenience, Flux provides the gpu function to convert models and data to the GPU if one is available. By default, it\'ll do nothing, but loading CuArrays will cause it to move data to the GPU instead.julia> using Flux, CuArrays\n\njulia> m = Dense(10,5) |> gpu\nDense(10, 5)\n\njulia> x = rand(10) |> gpu\n10-element CuArray{Float32,1}:\n 0.800225\n ⋮\n 0.511655\n\njulia> m(x)\nTracked 5-element CuArray{Float32,1}:\n -0.30535\n ⋮\n -0.618002The analogue cpu is also available for moving models and data back off of the GPU.julia> x = rand(10) |> gpu\n10-element CuArray{Float32,1}:\n 0.235164\n ⋮\n 0.192538\n\njulia> x |> cpu\n10-element Array{Float32,1}:\n 0.235164\n ⋮\n 0.192538"
},
{
"location": "saving.html#",
"page": "Saving & Loading",
"title": "Saving & Loading",
"category": "page",
"text": ""
},
{
"location": "saving.html#Saving-and-Loading-Models-1",
"page": "Saving & Loading",
"title": "Saving and Loading Models",
"category": "section",
"text": "You may wish to save models so that they can be loaded and run in a later session. The easiest way to do this is via BSON.jl.Save a model:julia> using Flux\n\njulia> model = Chain(Dense(10,5,relu),Dense(5,2),softmax)\nChain(Dense(10, 5, NNlib.relu), Dense(5, 2), NNlib.softmax)\n\njulia> using BSON: @save\n\njulia> @save \"mymodel.bson\" modelLoad it again:julia> using Flux\n\njulia> using BSON: @load\n\njulia> @load \"mymodel.bson\" model\n\njulia> model\nChain(Dense(10, 5, NNlib.relu), Dense(5, 2), NNlib.softmax)Models are just normal Julia structs, so it\'s fine to use any Julia storage format for this purpose. BSON.jl is particularly well supported and most likely to be forwards compatible (that is, models saved now will load in future versions of Flux).note: Note\nIf a saved model\'s weights are stored on the GPU, the model will not load later on if there is no GPU support available. It\'s best to move your model to the CPU with cpu(model) before saving it."
},
{
"location": "saving.html#Saving-Model-Weights-1",
"page": "Saving & Loading",
"title": "Saving Model Weights",
"category": "section",
"text": "In some cases it may be useful to save only the model parameters themselves, and rebuild the model architecture in your code. You can use params(model) to get model parameters. You can also use data.(params) to remove tracking.julia> using Flux\n\njulia> model = Chain(Dense(10,5,relu),Dense(5,2),softmax)\nChain(Dense(10, 5, NNlib.relu), Dense(5, 2), NNlib.softmax)\n\njulia> weights = Tracker.data.(params(model));\n\njulia> using BSON: @save\n\njulia> @save \"mymodel.bson\" weightsYou can easily load parameters back into a model with Flux.loadparams!.julia> using Flux\n\njulia> model = Chain(Dense(10,5,relu),Dense(5,2),softmax)\nChain(Dense(10, 5, NNlib.relu), Dense(5, 2), NNlib.softmax)\n\njulia> using BSON: @load\n\njulia> @load \"mymodel.bson\" weights\n\njulia> Flux.loadparams!(model, weights)The new model we created will now be identical to the one we saved parameters for."
},
{
"location": "saving.html#Checkpointing-1",
"page": "Saving & Loading",
"title": "Checkpointing",
"category": "section",
"text": "In longer training runs it\'s a good idea to periodically save your model, so that you can resume if training is interrupted (for example, if there\'s a power cut). You can do this by saving the model in the callback provided to train!.using Flux: throttle\nusing BSON: @save\n\nm = Chain(Dense(10,5,relu),Dense(5,2),softmax)\n\nevalcb = throttle(30) do\n # Show loss\n @save \"model-checkpoint.bson\" model\nendThis will update the \"model-checkpoint.bson\" file every thirty seconds.You can get more advanced by saving a series of models throughout training, for example@save \"model-$(now()).bson\" modelwill produce a series of models like \"model-2018-03-06T02:57:10.41.bson\". You could also store the current test set loss, so that it\'s easy to (for example) revert to an older copy of the model if it starts to overfit.@save \"model-$(now()).bson\" model loss = testloss()You can even store optimiser state alongside the model, to resume training exactly where you left off.opt = ADAM(params(model))\n@save \"model-$(now()).bson\" model opt"
},
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"location": "internals/tracker.html#",
"page": "Backpropagation",
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"text": ""
},
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"location": "internals/tracker.html#Flux.Tracker-1",
"page": "Backpropagation",
"title": "Flux.Tracker",
"category": "section",
"text": "Backpropagation, or reverse-mode automatic differentiation, is handled by the Flux.Tracker module.julia> using Flux.TrackerHere we discuss some more advanced uses of this module, as well as covering its internals."
},
{
"location": "internals/tracker.html#Taking-Gradients-1",
"page": "Backpropagation",
"title": "Taking Gradients",
"category": "section",
"text": "In the basics section we covered basic usage of the gradient function.using Flux.Tracker\n\nTracker.gradient((a, b) -> a*b, 2, 3) # (3.0 (tracked), 2.0 (tracked))gradient is actually just a thin wrapper around the backpropagator-based interface, forward.using Flux.Tracker: forward\n\ny, back = forward((a, b) -> a*b, 2, 3) # (6.0 (tracked), Flux.Tracker.#9)\n\nback(1) # (3.0 (tracked), 2.0 (tracked))The forward function returns two results. The first, y, is the original value of the function (perhaps with tracking applied). The second, back, is a new function which, given a sensitivity, returns the sensitivity of the inputs to forward (we call this a \"backpropagator\"). One use of this interface is to provide custom sensitivities when outputs are not scalar.julia> y, back = forward((a, b) -> a.*b, [1,2,3],[4,5,6])\n(param([4.0, 10.0, 18.0]), Flux.Tracker.#9)\n\njulia> back([1,1,1])\n(param([4.0, 5.0, 6.0]), param([1.0, 2.0, 3.0]))We can also take gradients in-place. This can be useful if you only care about first-order gradients.a, b = param(2), param(3)\n\nc = a*b # 6.0 (tracked)\n\nTracker.back!(c)\n\nTracker.grad(a), Tracker.grad(b) # (3.0, 2.0)"
},
{
"location": "internals/tracker.html#Tracked-Arrays-1",
"page": "Backpropagation",
"title": "Tracked Arrays",
"category": "section",
"text": "The param function converts a normal Julia array into a new object that, while behaving like an array, tracks extra information that allows us to calculate derivatives. For example, say we multiply two parameters:julia> W = param([1 2; 3 4])\nTracked 2×2 Array{Float64,2}:\n 1.0 2.0\n 3.0 4.0\n\njulia> x = param([5, 6])\nTracked 2-element Array{Float64,1}:\n 5.0\n 6.0\n\njulia> y = W*x\nTracked 2-element Array{Float64,1}:\n 17.0\n 39.0The output y is also a TrackedArray object. We can now backpropagate sensitivities to W and x via the back! function, and see the gradients accumulated in the W and x tracked arrays:julia> Tracker.back!(y, [1, -1])\n\njulia> W.grad\n2×2 Array{Float64,2}:\n 5.0 6.0\n-5.0 -6.0\n\njulia> x.grad\n2-element Array{Float64,1}:\n -2.0\n -2.0You may sometimes want to drop derivative information and just get the plain value back. You can do this by calling Tracker.data(W)."
},
{
"location": "internals/tracker.html#Custom-Gradients-1",
"page": "Backpropagation",
"title": "Custom Gradients",
"category": "section",
"text": "We can hook in to the processes above to implement custom gradients for a function or kernel. For a toy example, imagine a custom implementation of minus:minus(a, b) = a - bFirstly, we must tell the tracker system to stop when it sees a call to minus, and record it. We can do this using dispatch:using Flux.Tracker: TrackedArray, track, @grad\n\nminus(a::TrackedArray, b::TrackedArray) = track(minus, a, b)track takes care of building a new Tracked object and recording the operation on the tape. We just need to provide a gradient definition.@grad function minus(a, b)\n return minus(data(a), data(b)), Δ -> (Δ, -Δ)\nendThis is essentially just a way of overloading the forward function we saw above. We strip tracking from a and b so that we are calling the original definition of minus (otherwise, we\'d just try to track the call again and hit an infinite regress).Note that in the backpropagator we don\'t call data(a); we do in fact want to track this, since nest AD will take a derivative through the backpropagator itself. For example, the gradient of * might look like this.@grad a * b = data(a)*data(b), Δ -> (Δ*b, a*Δ)We can then calculate the first derivative of minus as follows:a = param([1,2,3])\nb = param([3,2,1])\n\nc = minus(a, b) # [-2.0 (tracked), 0.0 (tracked), 2.0 (tracked)]\n\nTracker.back!(c, 1)\nTracker.grad(a) # [1.00, 1.00, 1.00]\nTracker.grad(b) # [-1.00, -1.00, -1.00]For multi-argument functions with custom gradients, you likely want to catch not just minus(::TrackedArray, ::TrackedArray) but also minus(::Array, TrackedArray) and so on. To do so, just define those extra signatures as needed:minus(a::AbstractArray, b::TrackedArray) = Tracker.track(minus, a, b)\nminus(a::TrackedArray, b::AbstractArray) = Tracker.track(minus, a, b)"
},
{
"location": "internals/tracker.html#Tracked-Internals-1",
"page": "Backpropagation",
"title": "Tracked Internals",
"category": "section",
"text": "All Tracked* objects (TrackedArray, TrackedReal) are light wrappers around the Tracked type, which you can access via the .tracker field.julia> x.tracker\nFlux.Tracker.Tracked{Array{Float64,1}}(0x00000000, Flux.Tracker.Call{Nothing,Tuple{}}(nothing, ()), true, [5.0, 6.0], [-2.0, -2.0])The Tracker stores the gradient of a given object, which we\'ve seen before.julia> x.tracker.grad\n2-element Array{Float64,1}:\n -2.0\n -2.0The tracker also contains a Call object, which simply represents a function call that was made at some point during the forward pass. For example, the + call would look like this:julia> Tracker.Call(+, 1, 2)\nFlux.Tracker.Call{Base.#+,Tuple{Int64,Int64}}(+, (1, 2))In the case of the y we produced above, we can see that it stores the call that produced it – that is, W*x.julia> y.tracker.f\nFlux.Tracker.Call{...}(*, (param([1.0 2.0; 3.0 4.0]), param([5.0, 6.0])))Notice that because the arguments to the call may also be tracked arrays, storing their own calls, this means that Tracker ends up forming a data structure that records everything that happened during the forward pass (often known as a tape).When we call back!(y, [1, -1]), the sensitivities [1, -1] simply get forwarded to y\'s call (*), effectively callingTracker.back(*, [1, -1], W, x)which in turn calculates the sensitivities of the arguments (W and x) and back-propagates through their calls. This is recursive, so it will walk the entire program graph and propagate gradients to the original model parameters."
},
{
"location": "community.html#",
"page": "Community",
"title": "Community",
"category": "page",
"text": ""
},
{
"location": "community.html#Community-1",
"page": "Community",
"title": "Community",
"category": "section",
"text": "All Flux users are welcome to join our community on the Julia forum, the slack (channel #machine-learning), or Flux\'s Gitter. If you have questions or issues we\'ll try to help you out.If you\'re interested in hacking on Flux, the source code is open and easy to understand – it\'s all just the same Julia code you work with normally. You might be interested in our intro issues to get started."
},
]}

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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Optimisers · Flux</title><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
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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="../models/basics.html">Basics</a></li><li><a class="toctext" href="../models/recurrence.html">Recurrence</a></li><li><a class="toctext" href="../models/regularisation.html">Regularisation</a></li><li><a class="toctext" href="../models/layers.html">Model Reference</a></li></ul></li><li><span class="toctext">Training Models</span><ul><li class="current"><a class="toctext" href="optimisers.html">Optimisers</a><ul class="internal"><li><a class="toctext" href="#Optimiser-Reference-1">Optimiser Reference</a></li></ul></li><li><a class="toctext" href="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 &amp; 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>Training Models</li><li><a href="optimisers.html">Optimisers</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/training/optimisers.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Optimisers</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Optimisers-1" href="#Optimisers-1">Optimisers</a></h1><p>Consider a <a href="../models/basics.html">simple linear regression</a>. We create some dummy data, calculate a loss, and backpropagate to calculate gradients for the parameters <code>W</code> and <code>b</code>.</p><pre><code class="language-julia">using Flux.Tracker
W = param(rand(2, 5))
b = param(rand(2))
predict(x) = W*x .+ b
loss(x, y) = sum((predict(x) .- y).^2)
x, y = rand(5), rand(2) # Dummy data
l = loss(x, y) # ~ 3
params = Params([W, b])
grads = Tracker.gradient(() -&gt; loss(x, y), params)</code></pre><p>We want to update each parameter, using the gradient, in order to improve (reduce) the loss. Here&#39;s one way to do that:</p><pre><code class="language-julia">using Flux.Tracker: grad, update!
function sgd()
η = 0.1 # Learning Rate
for p in (W, b)
update!(p, -η * grads[p])
end
end</code></pre><p>If we call <code>sgd</code>, the parameters <code>W</code> and <code>b</code> will change and our loss should go down.</p><p>There are two pieces here: one is that we need a list of trainable parameters for the model (<code>[W, b]</code> in this case), and the other is the update step. In this case the update is simply gradient descent (<code>x .-= η .* Δ</code>), but we might choose to do something more advanced, like adding momentum.</p><p>In this case, getting the variables is trivial, but you can imagine it&#39;d be more of a pain with some complex stack of layers.</p><pre><code class="language-julia">m = Chain(
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&#39;s nothing whatsoever wrong with writing the loop above – it&#39;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><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/9d563820f8f2f5ae91364afc1e9f371f75466e77/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/9d563820f8f2f5ae91364afc1e9f371f75466e77/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/9d563820f8f2f5ae91364afc1e9f371f75466e77/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/9d563820f8f2f5ae91364afc1e9f371f75466e77/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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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Training · Flux</title><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
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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="../models/basics.html">Basics</a></li><li><a class="toctext" href="../models/recurrence.html">Recurrence</a></li><li><a class="toctext" href="../models/regularisation.html">Regularisation</a></li><li><a class="toctext" href="../models/layers.html">Model Reference</a></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="optimisers.html">Optimisers</a></li><li class="current"><a class="toctext" href="training.html">Training</a><ul class="internal"><li><a class="toctext" href="#Loss-Functions-1">Loss Functions</a></li><li><a class="toctext" href="#Datasets-1">Datasets</a></li><li><a class="toctext" href="#Callbacks-1">Callbacks</a></li></ul></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 &amp; 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>Training Models</li><li><a href="training.html">Training</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/training/training.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Training</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Training-1" href="#Training-1">Training</a></h1><p>To actually train a model we need three things:</p><ul><li>A <em>objective function</em>, that evaluates how well a model is doing given some input data.</li><li>A collection of data points that will be provided to the objective function.</li><li>An <a href="optimisers.html">optimiser</a> that will update the model parameters appropriately.</li></ul><p>With these we can call <code>Flux.train!</code>:</p><pre><code class="language-julia">Flux.train!(objective, data, opt)</code></pre><p>There are plenty of examples in the <a href="https://github.com/FluxML/model-zoo">model zoo</a>.</p><h2><a class="nav-anchor" id="Loss-Functions-1" href="#Loss-Functions-1">Loss Functions</a></h2><p>The objective function must return a number representing how far the model is from its target – the <em>loss</em> of the model. The <code>loss</code> function that we defined in <a href="../models/basics.html">basics</a> will work as an objective. We can also define an objective in terms of some model:</p><pre><code class="language-julia">m = Chain(
Dense(784, 32, σ),
Dense(32, 10), softmax)
loss(x, y) = Flux.mse(m(x), y)
# later
Flux.train!(loss, data, opt)</code></pre><p>The objective will almost always be defined in terms of some <em>cost function</em> that measures the distance of the prediction <code>m(x)</code> from the target <code>y</code>. Flux has several of these built in, like <code>mse</code> for mean squared error or <code>crossentropy</code> for cross entropy loss, but you can calculate it however you want.</p><h2><a class="nav-anchor" id="Datasets-1" href="#Datasets-1">Datasets</a></h2><p>The <code>data</code> argument provides a collection of data to train with (usually a set of inputs <code>x</code> and target outputs <code>y</code>). For example, here&#39;s a dummy data set with only one data point:</p><pre><code class="language-julia">x = rand(784)
y = rand(10)
data = [(x, y)]</code></pre><p><code>Flux.train!</code> will call <code>loss(x, y)</code>, calculate gradients, update the weights and then move on to the next data point if there is one. We can train the model on the same data three times:</p><pre><code class="language-julia">data = [(x, y), (x, y), (x, y)]
# Or equivalently
data = Iterators.repeated((x, y), 3)</code></pre><p>It&#39;s common to load the <code>x</code>s and <code>y</code>s separately. In this case you can use <code>zip</code>:</p><pre><code class="language-julia">xs = [rand(784), rand(784), rand(784)]
ys = [rand( 10), rand( 10), rand( 10)]
data = zip(xs, ys)</code></pre><p>Note that, by default, <code>train!</code> only loops over the data once (a single &quot;epoch&quot;). A convenient way to run multiple epochs from the REPL is provided by <code>@epochs</code>.</p><pre><code class="language-julia">julia&gt; using Flux: @epochs
julia&gt; @epochs 2 println(&quot;hello&quot;)
INFO: Epoch 1
hello
INFO: Epoch 2
hello
julia&gt; @epochs 2 Flux.train!(...)
# Train for two epochs</code></pre><h2><a class="nav-anchor" id="Callbacks-1" href="#Callbacks-1">Callbacks</a></h2><p><code>train!</code> takes an additional argument, <code>cb</code>, that&#39;s used for callbacks so that you can observe the training process. For example:</p><pre><code class="language-julia">train!(objective, data, opt, cb = () -&gt; println(&quot;training&quot;))</code></pre><p>Callbacks are called for every batch of training data. You can slow this down using <code>Flux.throttle(f, timeout)</code> which prevents <code>f</code> from being called more than once every <code>timeout</code> seconds.</p><p>A more typical callback might look like this:</p><pre><code class="language-julia">test_x, test_y = # ... create single batch of test data ...
evalcb() = @show(loss(test_x, test_y))
Flux.train!(objective, data, opt,
cb = throttle(evalcb, 5))</code></pre><footer><hr/><a class="previous" href="optimisers.html"><span class="direction">Previous</span><span class="title">Optimisers</span></a><a class="next" href="../data/onehot.html"><span class="direction">Next</span><span class="title">One-Hot Encoding</span></a></footer></article></body></html>

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