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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" 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">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/layers.html">Layers</a></li></ul></li><li class="current"><a class="toctext" href="contributing.html">Contributing & Help</a><ul class="internal"></ul></li></ul></nav><article id="docs"><header><nav><ul><li><a href="contributing.html">Contributing & Help</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/tree/366efa92abb760d2ea5b15031fdcd99feee5b244/docs/src/contributing.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Contributing & Help</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Contributing-1" href="#Contributing-1">Contributing</a></h1><p>If you need help, please ask 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's <a href="https://gitter.im/FluxML/Lobby">Gitter</a>.</p><p>Right now, the best way to help out is to try out the examples and report any issues or missing features as you find them. The second best way is to help us spread the word, perhaps by <a href="https://github.com/MikeInnes/Flux.jl">starring the repo</a>.</p><p>If you're interested in hacking on Flux, most of the <a href="https://github.com/MikeInnes/Flux.jl/tree/master/src">code</a> is pretty straightforward. Adding new <a href="https://github.com/MikeInnes/Flux.jl/tree/master/src/layers">layer definitions</a> or cost functions is simple using the Flux DSL itself, and things like data utilities and training processes are all plain Julia code.</p><p>If you get stuck or need anything, let us know!</p><footer><hr/><a class="previous" href="models/layers.html"><span class="direction">Previous</span><span class="title">Layers</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" action="search.html"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li class="current"><a class="toctext" href="index.html">Home</a><ul class="internal"><li class="toplevel"><a class="toctext" href="#Installation-1">Installation</a></li></ul></li><li><span class="toctext">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/layers.html">Layers</a></li></ul></li><li><a class="toctext" href="contributing.html">Contributing & Help</a></li></ul></nav><article id="docs"><header><nav><ul><li><a href="index.html">Home</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/tree/366efa92abb760d2ea5b15031fdcd99feee5b244/docs/src/index.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Home</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Flux:-The-Julia-Machine-Learning-Library-1" href="#Flux:-The-Julia-Machine-Learning-Library-1">Flux: The Julia Machine Learning Library</a></h1><p>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. The whole stack is implemented in clean Julia code (right down to the <a href="https://github.com/FluxML/CuArrays.jl">GPU kernels</a>) and any part can be tweaked to your liking.</p><h1><a class="nav-anchor" id="Installation-1" href="#Installation-1">Installation</a></h1><p>Install <a href="https://julialang.org/downloads/">Julia 0.6.0 or later</a>, if you haven't already.</p><pre><code class="language-julia">Pkg.add("Flux")
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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" action="search.html"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li class="current"><a class="toctext" href="index.html">Home</a><ul class="internal"><li class="toplevel"><a class="toctext" href="#Installation-1">Installation</a></li></ul></li><li><span class="toctext">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/layers.html">Layer Reference</a></li></ul></li><li><a class="toctext" href="contributing.html">Contributing & Help</a></li></ul></nav><article id="docs"><header><nav><ul><li><a href="index.html">Home</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/tree/fedee95b14d0539fb366b3815c9c33d7fca7be24/docs/src/index.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Home</span><a class="fa fa-bars" href="#"></a></div></header><h1><a class="nav-anchor" id="Flux:-The-Julia-Machine-Learning-Library-1" href="#Flux:-The-Julia-Machine-Learning-Library-1">Flux: The Julia Machine Learning Library</a></h1><p>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. The whole stack is implemented in clean Julia code (right down to the <a href="https://github.com/FluxML/CuArrays.jl">GPU kernels</a>) and any part can be tweaked to your liking.</p><h1><a class="nav-anchor" id="Installation-1" href="#Installation-1">Installation</a></h1><p>Install <a href="https://julialang.org/downloads/">Julia 0.6.0 or later</a>, if you haven't already.</p><pre><code class="language-julia">Pkg.add("Flux")
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Pkg.test("Flux") # Check things installed correctly</code></pre><p>Start with the <a href="basics.html">basics</a>. The <a href="https://github.com/FluxML/model-zoo/">model zoo</a> is also a good starting point for many common kinds of models.</p><footer><hr/><a class="next" href="models/basics.html"><span class="direction">Next</span><span class="title">Basics</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" 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">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="#Building-Layers-1">Building Layers</a></li><li><a class="toctext" href="#Stacking-It-Up-1">Stacking It Up</a></li></ul></li><li><a class="toctext" href="recurrence.html">Recurrence</a></li><li><a class="toctext" href="layers.html">Layers</a></li></ul></li><li><a class="toctext" href="../contributing.html">Contributing & Help</a></li></ul></nav><article id="docs"><header><nav><ul><li>Models</li><li><a href="basics.html">Basics</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/tree/366efa92abb760d2ea5b15031fdcd99feee5b244/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><h2><a class="nav-anchor" id="Taking-Gradients-1" href="#Taking-Gradients-1">Taking Gradients</a></h2><p>Consider a simple linear regression, which tries to predict an output array <code>y</code> from an input <code>x</code>. (It's a good idea to follow this example in the Julia repl.)</p><pre><code class="language-julia">W = rand(2, 5)
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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" 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">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="#Building-Layers-1">Building Layers</a></li><li><a class="toctext" href="#Stacking-It-Up-1">Stacking It Up</a></li></ul></li><li><a class="toctext" href="recurrence.html">Recurrence</a></li><li><a class="toctext" href="layers.html">Layer Reference</a></li></ul></li><li><a class="toctext" href="../contributing.html">Contributing & Help</a></li></ul></nav><article id="docs"><header><nav><ul><li>Models</li><li><a href="basics.html">Basics</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/tree/fedee95b14d0539fb366b3815c9c33d7fca7be24/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>Consider a simple linear regression, which tries to predict an output array <code>y</code> from an input <code>x</code>. (It's a good idea to follow this example in the Julia repl.)</p><pre><code class="language-julia">W = rand(2, 5)
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b = rand(2)
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predict(x) = W*x .+ b
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@ -22,9 +22,9 @@ l = loss(x, y)
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back!(l)</code></pre><p><code>loss(x, y)</code> returns the same number, but it's now a <em>tracked</em> value that records gradients as it goes along. Calling <code>back!</code> then calculates the gradient of <code>W</code> and <code>b</code>. We can see what this gradient is, and modify <code>W</code> to train the model.</p><pre><code class="language-julia">grad(W)
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W.data .-= grad(W)
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W.data .-= 0.1grad(W)
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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, not all models look like this – they might have millions of parameters or complex control flow, and Flux provides ways to manage this complexity. Let's see what that looks like.</p><h2><a class="nav-anchor" id="Building-Layers-1" href="#Building-Layers-1">Building Layers</a></h2><p>It'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))
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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, and there are ways to manage this complexity. Let's see what that looks like.</p><h2><a class="nav-anchor" id="Building-Layers-1" href="#Building-Layers-1">Building Layers</a></h2><p>It'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))
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b1 = param(rand(3))
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layer1(x) = W1 * x .+ b1
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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" 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">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="layers.html">Layers</a><ul class="internal"><li><a class="toctext" href="#Model-Layers-1">Model Layers</a></li></ul></li></ul></li><li><a class="toctext" href="../contributing.html">Contributing & Help</a></li></ul></nav><article id="docs"><header><nav><ul><li>Models</li><li><a href="layers.html">Layers</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/tree/366efa92abb760d2ea5b15031fdcd99feee5b244/docs/src/models/layers.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Layers</span><a class="fa fa-bars" href="#"></a></div></header><h2><a class="nav-anchor" id="Model-Layers-1" href="#Model-Layers-1">Model Layers</a></h2><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><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-none">m = Chain(x -> x^2, x -> x+1)
|
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</script><link href="https://cdnjs.cloudflare.com/ajax/libs/normalize/4.2.0/normalize.min.css" rel="stylesheet" type="text/css"/><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.6.3/css/font-awesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/default.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.2.0/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link href="../assets/documenter.css" rel="stylesheet" type="text/css"/><link href="../../flux.css" rel="stylesheet" type="text/css"/></head><body><nav class="toc"><h1>Flux</h1><select id="version-selector" onChange="window.location.href=this.value" style="visibility: hidden"></select><form class="search" 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">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="layers.html">Layer Reference</a><ul class="internal"><li><a class="toctext" href="#Model-Layers-1">Model Layers</a></li></ul></li></ul></li><li><a class="toctext" href="../contributing.html">Contributing & Help</a></li></ul></nav><article id="docs"><header><nav><ul><li>Models</li><li><a href="layers.html">Layer Reference</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/tree/fedee95b14d0539fb366b3815c9c33d7fca7be24/docs/src/models/layers.md"><span class="fa"></span> Edit on GitHub</a></nav><hr/><div id="topbar"><span>Layer Reference</span><a class="fa fa-bars" href="#"></a></div></header><h2><a class="nav-anchor" id="Model-Layers-1" href="#Model-Layers-1">Model Layers</a></h2><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><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-none">m = Chain(x -> x^2, x -> x+1)
|
||||
m(5) == 26
|
||||
|
||||
m = Chain(Dense(10, 5), Dense(5, 2))
|
||||
x = rand(10)
|
||||
m(x) = m[2](m[1](x))</code></pre><p><code>Chain</code> also supports indexing and slicing, e.g. <code>m[2]</code> or <code>m[1:end-1]</code>.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/tree/366efa92abb760d2ea5b15031fdcd99feee5b244/src/layers/basic.jl#L1-L15">source</a><br/></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><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></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/tree/366efa92abb760d2ea5b15031fdcd99feee5b244/src/layers/basic.jl#L39-L45">source</a><br/></section><footer><hr/><a class="previous" href="recurrence.html"><span class="direction">Previous</span><span class="title">Recurrence</span></a><a class="next" href="../contributing.html"><span class="direction">Next</span><span class="title">Contributing & Help</span></a></footer></article></body></html>
|
||||
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>.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/tree/fedee95b14d0539fb366b3815c9c33d7fca7be24/src/layers/basic.jl#L1-L15">source</a><br/></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><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>in</code>.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/tree/fedee95b14d0539fb366b3815c9c33d7fca7be24/src/layers/basic.jl#L39-L48">source</a><br/></section><footer><hr/><a class="previous" href="recurrence.html"><span class="direction">Previous</span><span class="title">Recurrence</span></a><a class="next" href="../contributing.html"><span class="direction">Next</span><span class="title">Contributing & Help</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" 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">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"></ul></li><li><a class="toctext" href="layers.html">Layers</a></li></ul></li><li><a class="toctext" href="../contributing.html">Contributing & Help</a></li></ul></nav><article id="docs"><header><nav><ul><li>Models</li><li><a href="recurrence.html">Recurrence</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/tree/366efa92abb760d2ea5b15031fdcd99feee5b244/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><footer><hr/><a class="previous" href="basics.html"><span class="direction">Previous</span><span class="title">Basics</span></a><a class="next" href="layers.html"><span class="direction">Next</span><span class="title">Layers</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" 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">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="layers.html">Layer Reference</a></li></ul></li><li><a class="toctext" href="../contributing.html">Contributing & Help</a></li></ul></nav><article id="docs"><header><nav><ul><li>Models</li><li><a href="recurrence.html">Recurrence</a></li></ul><a class="edit-page" href="https://github.com/FluxML/Flux.jl/tree/fedee95b14d0539fb366b3815c9c33d7fca7be24/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><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 ...
|
||||
y₁, h = f(x₁, h)
|
||||
y₂, h = f(x₂, h)
|
||||
y₃, h = f(x₃, h)
|
||||
# ...</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's interpretation of the word "bank" should change if the previous input was "river" rather than "investment".)</p><p>Flux'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 and hidden state are the same. By convention, the hidden state is the first input and output.</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'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="models/layers.html">layer reference</a>. The hand-written example above can be replaced with:</p><pre><code class="language-julia">using Flux
|
||||
|
||||
m = Flux.RNNCell(10, 5)
|
||||
|
||||
x = rand(10) # dummy data
|
||||
h = rand(5) # initial hidden state
|
||||
|
||||
h, y = rnn(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'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'll see that it's simply a wrapped cell.</p><pre><code class="language-julia">julia> 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">map(m, seq) # returns a list of 5-element vectors</code></pre><p>To make this a bit more convenient, Flux has the <code>Seq</code> type. This is just a list, but tagged so that we know it's meant to be used as a sequence of data points.</p><pre><code class="language-julia">seq = Seq([rand(10) for i = 1:10])
|
||||
m(seq) # returns a new Seq of length 10</code></pre><p>When we apply the model <code>m</code> to a seq, it gets mapped over every item in the sequence in order. This is just like the code above, but often more convenient.</p><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 the entire history. For example, if we call the model on 100 inputs, calling <code>back!</code> will 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><footer><hr/><a class="previous" href="basics.html"><span class="direction">Previous</span><span class="title">Basics</span></a><a class="next" href="layers.html"><span class="direction">Next</span><span class="title">Layer Reference</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" 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">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/layers.html">Layers</a></li></ul></li><li><a class="toctext" href="contributing.html">Contributing & Help</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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|
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"text": "Consider a simple linear regression, which tries to predict an output array y from an input x. (It's a good idea to follow this example in the Julia repl.)W = rand(2, 5)\nb = 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\nloss(x, y) # ~ 3To improve the prediction we can take the gradients of W and b with respect to the loss function and perform gradient descent. We could calculate gradients by hand, but Flux will do it for us if we tell it that W and b are trainable parameters.using Flux.Tracker: param, back!, data, grad\n\nW = param(W)\nb = param(b)\n\nl = loss(x, y)\n\nback!(l)loss(x, y) returns the same number, but it's now a tracked value that records gradients as it goes along. Calling back! then calculates the gradient of W and b. We can see what this gradient is, and modify W to train the model.grad(W)\n\nW.data .-= grad(W)\n\nloss(x, y) # ~ 2.5The loss has decreased a little, meaning that our prediction x is closer to the target y. If we have some data we can already try training the model.All deep learning in Flux, however complex, is a simple generalisation of this example. Of course, not all models look like this – they might have millions of parameters or complex control flow, and Flux provides ways to manage this complexity. Let's see what that looks like."
|
||||
"text": "Consider a simple linear regression, which tries to predict an output array y from an input x. (It's a good idea to follow this example in the Julia repl.)W = rand(2, 5)\nb = 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\nloss(x, y) # ~ 3To improve the prediction we can take the gradients of W and b with respect to the loss function and perform gradient descent. We could calculate gradients by hand, but Flux will do it for us if we tell it that W and b are trainable parameters.using Flux.Tracker: param, back!, data, grad\n\nW = param(W)\nb = param(b)\n\nl = loss(x, y)\n\nback!(l)loss(x, y) returns the same number, but it's now a tracked value that records gradients as it goes along. Calling back! then calculates the gradient of W and b. We can see what this gradient is, and modify W to train the model.grad(W)\n\nW.data .-= 0.1grad(W)\n\nloss(x, y) # ~ 2.5The loss has decreased a little, meaning that our prediction x is closer to the target y. If we have some data we can already try training the model.All deep learning in Flux, however complex, is a simple generalisation of this example. Of course, models can look very different – they might have millions of parameters or complex control flow, and there are ways to manage this complexity. Let's see what that looks like."
|
||||
},
|
||||
|
||||
{
|
||||
@ -64,33 +72,65 @@ var documenterSearchIndex = {"docs": [
|
||||
"text": ""
|
||||
},
|
||||
|
||||
{
|
||||
"location": "models/recurrence.html#Recurrent-Cells-1",
|
||||
"page": "Recurrence",
|
||||
"title": "Recurrent Cells",
|
||||
"category": "section",
|
||||
"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 ...\ny₁, h = f(x₁, h)\ny₂, h = f(x₂, h)\ny₃, h = f(x₃, h)\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 and hidden state are the same. By convention, the hidden state is the first input and output.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\nm = Flux.RNNCell(10, 5)\n\nx = rand(10) # dummy data\nh = rand(5) # initial hidden state\n\nh, y = rnn(h, x)"
|
||||
},
|
||||
|
||||
{
|
||||
"location": "models/recurrence.html#Stateful-Models-1",
|
||||
"page": "Recurrence",
|
||||
"title": "Stateful Models",
|
||||
"category": "section",
|
||||
"text": "For the most part, we don't want to manage hidden states ourselves, but to treat our models as being stateful. Flux provides the Recur wrapper to do this.x = rand(10)\nh = rand(5)\n\nm = Flux.Recur(rnn, h)\n\ny = m(x)The Recur wrapper stores the state between runs in the m.state field.If you use the RNN(10, 5) constructor – as opposed to RNNCell – you'll see that it's simply a wrapped cell.julia> RNN(10, 5)\nRecur(RNNCell(Dense(15, 5)))"
|
||||
},
|
||||
|
||||
{
|
||||
"location": "models/recurrence.html#Sequences-1",
|
||||
"page": "Recurrence",
|
||||
"title": "Sequences",
|
||||
"category": "section",
|
||||
"text": "Often we want to work with sequences of inputs, rather than individual xs.seq = [rand(10) for i = 1:10]With Recur, applying our model to each element of a sequence is trivial:map(m, seq) # returns a list of 5-element vectorsTo make this a bit more convenient, Flux has the Seq type. This is just a list, but tagged so that we know it's meant to be used as a sequence of data points.seq = Seq([rand(10) for i = 1:10])\nm(seq) # returns a new Seq of length 10When we apply the model m to a seq, it gets mapped over every item in the sequence in order. This is just like the code above, but often more convenient."
|
||||
},
|
||||
|
||||
{
|
||||
"location": "models/recurrence.html#Truncating-Gradients-1",
|
||||
"page": "Recurrence",
|
||||
"title": "Truncating Gradients",
|
||||
"category": "section",
|
||||
"text": "By default, calculating the gradients in a recurrent layer involves the entire history. For example, if we call the model on 100 inputs, calling back! will 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.To avoid this we can truncate the gradient calculation, forgetting the history.truncate!(m)Calling truncate! wipes the slate clean, so we can call the model with more inputs without building up an expensive gradient computation."
|
||||
},
|
||||
|
||||
{
|
||||
"location": "models/layers.html#",
|
||||
"page": "Layers",
|
||||
"title": "Layers",
|
||||
"page": "Layer Reference",
|
||||
"title": "Layer Reference",
|
||||
"category": "page",
|
||||
"text": ""
|
||||
},
|
||||
|
||||
{
|
||||
"location": "models/layers.html#Flux.Chain",
|
||||
"page": "Layers",
|
||||
"page": "Layer 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].\n\n\n\n"
|
||||
"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].\n\n\n\n"
|
||||
},
|
||||
|
||||
{
|
||||
"location": "models/layers.html#Flux.Dense",
|
||||
"page": "Layers",
|
||||
"page": "Layer 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\n\n\n"
|
||||
"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 in.\n\n\n\n"
|
||||
},
|
||||
|
||||
{
|
||||
"location": "models/layers.html#Model-Layers-1",
|
||||
"page": "Layers",
|
||||
"page": "Layer Reference",
|
||||
"title": "Model Layers",
|
||||
"category": "section",
|
||||
"text": "Chain\nDense"
|
||||
@ -105,9 +145,9 @@ var documenterSearchIndex = {"docs": [
|
||||
},
|
||||
|
||||
{
|
||||
"location": "contributing.html#Contributing-1",
|
||||
"location": "contributing.html#Contributing-and-Help-1",
|
||||
"page": "Contributing & Help",
|
||||
"title": "Contributing",
|
||||
"title": "Contributing & Help",
|
||||
"category": "section",
|
||||
"text": "If you need help, please ask on the Julia forum, the slack (channel #machine-learning), or Flux's Gitter.Right now, the best way to help out is to try out the examples and report any issues or missing features as you find them. The second best way is to help us spread the word, perhaps by starring the repo.If you're interested in hacking on Flux, most of the code is pretty straightforward. Adding new layer definitions or cost functions is simple using the Flux DSL itself, and things like data utilities and training processes are all plain Julia code.If you get stuck or need anything, let us know!"
|
||||
},
|
||||
|
||||
Loading…
Reference in New Issue
Block a user