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Tracked 5-element CuArray{Float32,1}:
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-0.30535
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-0.618002</code></pre><p>The analogue <code>cpu</code> is also available for moving models and data back off of the GPU.</p><p>``` julia> x = rand(10) |> gpu 10-element CuArray{Float32,1}: 0.235164 ⋮ 0.192538</p><p>julia> x |> cpu 10-element Array{Float32,1}: 0.235164 ⋮ 0.192538 ```</p><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 & Loading</span></a></footer></article></body></html>
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-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> x = rand(10) |> gpu
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10-element CuArray{Float32,1}:
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0.235164
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⋮
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0.192538
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julia> x |> cpu
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10-element Array{Float32,1}:
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0.235164
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⋮
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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 & Loading</span></a></footer></article></body></html>
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@ -8,18 +8,18 @@ ga('create', 'UA-36890222-9', 'auto');
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ga('send', 'pageview');
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</script><link href="https://cdnjs.cloudflare.com/ajax/libs/normalize/4.2.0/normalize.min.css" rel="stylesheet" type="text/css"/><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.6.3/css/font-awesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/default.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.2.0/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link href="../assets/documenter.css" rel="stylesheet" type="text/css"/><link href="../../flux.css" rel="stylesheet" type="text/css"/></head><body><nav class="toc"><h1>Flux</h1><select id="version-selector" onChange="window.location.href=this.value" style="visibility: hidden"></select><form class="search" id="search-form" action="../search.html"><input id="search-query" name="q" type="text" placeholder="Search docs"/></form><ul><li><a class="toctext" href="../index.html">Home</a></li><li><span class="toctext">Building Models</span><ul><li><a class="toctext" href="basics.html">Basics</a></li><li><a class="toctext" href="recurrence.html">Recurrence</a></li><li><a class="toctext" href="regularisation.html">Regularisation</a></li><li class="current"><a class="toctext" href="layers.html">Model Reference</a><ul class="internal"><li><a class="toctext" href="#Basic-Layers-1">Basic Layers</a></li><li><a class="toctext" href="#Recurrent-Layers-1">Recurrent Layers</a></li><li><a class="toctext" href="#Activation-Functions-1">Activation Functions</a></li><li><a class="toctext" href="#Normalisation-and-Regularisation-1">Normalisation & Regularisation</a></li></ul></li></ul></li><li><span class="toctext">Training Models</span><ul><li><a class="toctext" href="../training/optimisers.html">Optimisers</a></li><li><a class="toctext" href="../training/training.html">Training</a></li></ul></li><li><a class="toctext" href="../data/onehot.html">One-Hot Encoding</a></li><li><a class="toctext" href="../gpu.html">GPU Support</a></li><li><a class="toctext" href="../saving.html">Saving & Loading</a></li><li><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><pre><code class="language-none">Chain
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Dense
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Conv2D</code></pre><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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/1c5f8e3534b4ffc1766b80bf4f073e467890b62d/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><pre><code class="language-none">LSTM(in::Integer, out::Integer, σ = tanh)</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><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/1c5f8e3534b4ffc1766b80bf4f073e467890b62d/src/layers/recurrent.jl#L151-L159">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><pre><code class="language-none">Recur(cell)</code></pre><p><code>Recur</code> takes a recurrent cell and makes it stateful, managing the hidden state in the background. <code>cell</code> should be a model of the form:</p><pre><code class="language-none">h, y = cell(h, x...)</code></pre><p>For example, here's a recurrent network that keeps a running total of its inputs.</p><pre><code class="language-julia">accum(h, x) = (h+x, x)
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Conv2D</code></pre><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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/d09eb8a8e7305b797044bf4857e2e38b3cc603d1/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><pre><code class="language-none">LSTM(in::Integer, out::Integer, σ = tanh)</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><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/d09eb8a8e7305b797044bf4857e2e38b3cc603d1/src/layers/recurrent.jl#L151-L159">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><pre><code class="language-none">Recur(cell)</code></pre><p><code>Recur</code> takes a recurrent cell and makes it stateful, managing the hidden state in the background. <code>cell</code> should be a model of the form:</p><pre><code class="language-none">h, y = cell(h, x...)</code></pre><p>For example, here's a recurrent network that keeps a running total of its inputs.</p><pre><code class="language-julia">accum(h, x) = (h+x, x)
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rnn = Flux.Recur(accum, 0)
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rnn(2) # 2
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rnn(3) # 3
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rnn.state # 5
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rnn.(1:10) # apply to a sequence
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rnn.state # 60</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/1c5f8e3534b4ffc1766b80bf4f073e467890b62d/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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/NNlib.jl/blob/35938a947f3a35f340861772a7f441169deadaa1/src/activation.jl#L1-L6">source</a></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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/NNlib.jl/blob/35938a947f3a35f340861772a7f441169deadaa1/src/activation.jl#L42-L47">source</a></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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/NNlib.jl/blob/35938a947f3a35f340861772a7f441169deadaa1/src/activation.jl#L51-L57">source</a></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><pre><code class="language-none">elu(x, α = 1) =
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rnn.state # 60</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/d09eb8a8e7305b797044bf4857e2e38b3cc603d1/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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/NNlib.jl/blob/35938a947f3a35f340861772a7f441169deadaa1/src/activation.jl#L1-L6">source</a></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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/NNlib.jl/blob/35938a947f3a35f340861772a7f441169deadaa1/src/activation.jl#L42-L47">source</a></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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/NNlib.jl/blob/35938a947f3a35f340861772a7f441169deadaa1/src/activation.jl#L51-L57">source</a></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><pre><code class="language-none">elu(x, α = 1) =
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x > 0 ? x : α * (exp(x) - 1)</code></pre><p>Exponential Linear Unit activation function. See <a href="https://arxiv.org/abs/1511.07289">Fast and Accurate Deep Network Learning by Exponential Linear Units</a>. You can also specify the coefficient explicitly, e.g. <code>elu(x, 1)</code>.</p></div><a class="source-link" target="_blank" href="https://github.com/FluxML/NNlib.jl/blob/35938a947f3a35f340861772a7f441169deadaa1/src/activation.jl#L60-L67">source</a></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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/NNlib.jl/blob/35938a947f3a35f340861772a7f441169deadaa1/src/activation.jl#L70-L75">source</a></section><h2><a class="nav-anchor" id="Normalisation-and-Regularisation-1" href="#Normalisation-and-Regularisation-1">Normalisation & Regularisation</a></h2><p>These layers don't affect the structure of the network but may improve training times or reduce overfitting.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.testmode!" href="#Flux.testmode!"><code>Flux.testmode!</code></a> — <span class="docstring-category">Function</span>.</div><div><pre><code class="language-none">testmode!(m)
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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><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/1c5f8e3534b4ffc1766b80bf4f073e467890b62d/src/layers/normalisation.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><pre><code class="language-none">BatchNorm(dims...; λ = identity,
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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><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/d09eb8a8e7305b797044bf4857e2e38b3cc603d1/src/layers/normalisation.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><pre><code class="language-none">BatchNorm(dims...; λ = identity,
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initβ = zeros, initγ = ones, ϵ = 1e-8, momentum = .1)</code></pre><p>Batch Normalization Layer for <a href="layers.html#Flux.Dense"><code>Dense</code></a> layer.</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>In the example of MNIST, in order to normalize the input of other layer, put the <code>BatchNorm</code> layer before activation function.</p><pre><code class="language-julia">m = Chain(
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Dense(28^2, 64),
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BatchNorm(64, λ = relu),
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Dense(64, 10),
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BatchNorm(10),
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softmax)</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/1c5f8e3534b4ffc1766b80bf4f073e467890b62d/src/layers/normalisation.jl#L70-L91">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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/1c5f8e3534b4ffc1766b80bf4f073e467890b62d/src/layers/normalisation.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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/1c5f8e3534b4ffc1766b80bf4f073e467890b62d/src/layers/normalisation.jl#L47-L54">source</a></section><footer><hr/><a class="previous" href="regularisation.html"><span class="direction">Previous</span><span class="title">Regularisation</span></a><a class="next" href="../training/optimisers.html"><span class="direction">Next</span><span class="title">Optimisers</span></a></footer></article></body></html>
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softmax)</code></pre></div><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/d09eb8a8e7305b797044bf4857e2e38b3cc603d1/src/layers/normalisation.jl#L70-L91">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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/d09eb8a8e7305b797044bf4857e2e38b3cc603d1/src/layers/normalisation.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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/d09eb8a8e7305b797044bf4857e2e38b3cc603d1/src/layers/normalisation.jl#L47-L54">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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@ -405,7 +405,7 @@ var documenterSearchIndex = {"docs": [
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"page": "GPU Support",
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"title": "GPU Support",
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"category": "section",
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"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.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 10-element CuArray{Float32,1}: 0.235164 ⋮ 0.192538julia> x |> cpu 10-element Array{Float32,1}: 0.235164 ⋮ 0.192538 ```"
|
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"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.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"
|
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},
|
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|
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{
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@ -24,4 +24,4 @@ end</code></pre><p>If we call <code>update</code>, the parameters <code>W</code>
|
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Dense(10, 5, σ),
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Dense(5, 2), softmax)</code></pre><p>Instead of having to write <code>[m[1].W, m[1].b, ...]</code>, Flux provides a params function <code>params(m)</code> that returns a list of all parameters in the model for you.</p><p>For the update step, there's nothing whatsoever wrong with writing the loop above – it'll work just fine – but Flux provides various <em>optimisers</em> that make it more convenient.</p><pre><code class="language-julia">opt = SGD([W, b], 0.1) # Gradient descent with learning rate 0.1
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opt() # Carry out the update, modifying `W` and `b`.</code></pre><p>An optimiser takes a parameter list and returns a function that does the same thing as <code>update</code> above. We can pass either <code>opt</code> or <code>update</code> to our <a href="training.html">training loop</a>, which will then run the optimiser after every mini-batch of data.</p><h2><a class="nav-anchor" id="Optimiser-Reference-1" href="#Optimiser-Reference-1">Optimiser Reference</a></h2><p>All optimisers return a function that, when called, will update the parameters passed to it.</p><section class="docstring"><div class="docstring-header"><a class="docstring-binding" id="Flux.Optimise.SGD" href="#Flux.Optimise.SGD"><code>Flux.Optimise.SGD</code></a> — <span class="docstring-category">Function</span>.</div><div><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><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/1c5f8e3534b4ffc1766b80bf4f073e467890b62d/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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/1c5f8e3534b4ffc1766b80bf4f073e467890b62d/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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/1c5f8e3534b4ffc1766b80bf4f073e467890b62d/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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/1c5f8e3534b4ffc1766b80bf4f073e467890b62d/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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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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/d09eb8a8e7305b797044bf4857e2e38b3cc603d1/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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/d09eb8a8e7305b797044bf4857e2e38b3cc603d1/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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/d09eb8a8e7305b797044bf4857e2e38b3cc603d1/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><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><a class="source-link" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/d09eb8a8e7305b797044bf4857e2e38b3cc603d1/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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