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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 & Loading</a></li><li><a class="toctext" href="../../performance/">Performance Tips</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
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m = Dense(10, 5)
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loss(x, y) = crossentropy(softmax(m(x)), y)</code></pre><p>We can regularise this by taking the (L2) norm of the parameters, <code>m.W</code> and <code>m.b</code>.</p><pre><code class="language-julia">penalty() = norm(m.W) + norm(m.b)
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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> params(m)
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2-element Array{Any,1}:
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param([0.355408 0.533092; … 0.430459 0.171498])
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param([0.0, 0.0, 0.0, 0.0, 0.0])
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julia> sum(norm, params(m))
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26.01749952921026 (tracked)</code></pre><p>Here's a larger example with a multi-layer perceptron.</p><pre><code class="language-julia">m = Chain(
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Dense(28^2, 128, relu),
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Dense(128, 32, relu),
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Dense(32, 10), softmax)
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loss(x, y) = crossentropy(m(x), y) + sum(norm, params(m))
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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> c = Chain(Dense(10,5,σ),Dense(5,2),softmax)
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Chain(Dense(10, 5, NNlib.σ), Dense(5, 2), NNlib.softmax)
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julia> activations(c, rand(10))
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3-element Array{Any,1}:
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param([0.71068, 0.831145, 0.751219, 0.227116, 0.553074])
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param([0.0330606, -0.456104])
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param([0.61991, 0.38009])
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julia> sum(norm, ans)
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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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