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| <h1 id="symbol-and-automatic-differentiation">Symbol and Automatic Differentiation</h1> |
| |
| <p>The computational unit <code>NDArray</code> requires a way to construct neural networks. MXNet provides a symbolic interface, named Symbol, to do this. Symbol combines both flexibility and efficiency.</p> |
| |
| <h2 id="basic-composition-of-symbols">Basic Composition of Symbols</h2> |
| |
| <p>The following code creates a two-layer perceptron network:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">require</span><span class="p">(</span><span class="n">mxnet</span><span class="p">)</span><span class="w"> |
| </span><span class="n">net</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Variable</span><span class="p">(</span><span class="s2">"data"</span><span class="p">)</span><span class="w"> |
| </span><span class="n">net</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.FullyConnected</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">net</span><span class="p">,</span><span class="w"> </span><span class="n">name</span><span class="o">=</span><span class="s2">"fc1"</span><span class="p">,</span><span class="w"> </span><span class="n">num_hidden</span><span class="o">=</span><span class="m">128</span><span class="p">)</span><span class="w"> |
| </span><span class="n">net</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Activation</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">net</span><span class="p">,</span><span class="w"> </span><span class="n">name</span><span class="o">=</span><span class="s2">"relu1"</span><span class="p">,</span><span class="w"> </span><span class="n">act_type</span><span class="o">=</span><span class="s2">"relu"</span><span class="p">)</span><span class="w"> |
| </span><span class="n">net</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.FullyConnected</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">net</span><span class="p">,</span><span class="w"> </span><span class="n">name</span><span class="o">=</span><span class="s2">"fc2"</span><span class="p">,</span><span class="w"> </span><span class="n">num_hidden</span><span class="o">=</span><span class="m">64</span><span class="p">)</span><span class="w"> |
| </span><span class="n">net</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Softmax</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">net</span><span class="p">,</span><span class="w"> </span><span class="n">name</span><span class="o">=</span><span class="s2">"out"</span><span class="p">)</span><span class="w"> |
| </span><span class="nf">class</span><span class="p">(</span><span class="n">net</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang="">## [1] "Rcpp_MXSymbol" |
| ## attr(,"package") |
| ## [1] "mxnet" |
| </code></pre></div> |
| <p>Each symbol takes a (unique) string name. <em>Variable</em> often defines the inputs, |
| or free variables. Other symbols take a symbol as the input (<em>data</em>), |
| and may accept other hyper parameters, such as the number of hidden neurons (<em>num_hidden</em>) |
| or the activation type (<em>act_type</em>).</p> |
| |
| <p>A symbol can be viewed as a function that takes several arguments, whose |
| names are automatically generated and can be retrieved with the following command:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">arguments</span><span class="p">(</span><span class="n">net</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang="">## [1] "data" "fc1_weight" "fc1_bias" "fc2_weight" "fc2_bias" |
| ## [6] "out_label" |
| </code></pre></div> |
| <p>The arguments are the parameters need by each symbol:</p> |
| |
| <ul> |
| <li><em>data</em>: Input data needed by the variable <em>data</em></li> |
| <li><em>fc1_weight</em> and <em>fc1_bias</em>: The weight and bias for the first fully connected layer, <em>fc1</em></li> |
| <li><em>fc2_weight</em> and <em>fc2_bias</em>: The weight and bias for the second fully connected layer, <em>fc2</em></li> |
| <li><em>out_label</em>: The label needed by the loss</li> |
| </ul> |
| |
| <p>We can also specify the automatically generated names explicitly:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">data</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Variable</span><span class="p">(</span><span class="s2">"data"</span><span class="p">)</span><span class="w"> |
| </span><span class="n">w</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Variable</span><span class="p">(</span><span class="s2">"myweight"</span><span class="p">)</span><span class="w"> |
| </span><span class="n">net</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.FullyConnected</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">data</span><span class="p">,</span><span class="w"> </span><span class="n">weight</span><span class="o">=</span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="n">name</span><span class="o">=</span><span class="s2">"fc1"</span><span class="p">,</span><span class="w"> </span><span class="n">num_hidden</span><span class="o">=</span><span class="m">128</span><span class="p">)</span><span class="w"> |
| </span><span class="n">arguments</span><span class="p">(</span><span class="n">net</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang="">## [1] "data" "myweight" "fc1_bias" |
| </code></pre></div> |
| <h2 id="more-complicated-composition-of-symbols">More Complicated Composition of Symbols</h2> |
| |
| <p>MXNet provides well-optimized symbols for |
| commonly used layers in deep learning. You can also define new operators |
| in Python. The following example first performs an element-wise add between two |
| symbols, then feeds them to the fully connected operator:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">lhs</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Variable</span><span class="p">(</span><span class="s2">"data1"</span><span class="p">)</span><span class="w"> |
| </span><span class="n">rhs</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Variable</span><span class="p">(</span><span class="s2">"data2"</span><span class="p">)</span><span class="w"> |
| </span><span class="n">net</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.FullyConnected</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">lhs</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">rhs</span><span class="p">,</span><span class="w"> </span><span class="n">name</span><span class="o">=</span><span class="s2">"fc1"</span><span class="p">,</span><span class="w"> </span><span class="n">num_hidden</span><span class="o">=</span><span class="m">128</span><span class="p">)</span><span class="w"> |
| </span><span class="n">arguments</span><span class="p">(</span><span class="n">net</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang="">## [1] "data1" "data2" "fc1_weight" "fc1_bias" |
| </code></pre></div> |
| <p>We can construct a symbol more flexibly than by using the single |
| forward composition, for example:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">net</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Variable</span><span class="p">(</span><span class="s2">"data"</span><span class="p">)</span><span class="w"> |
| </span><span class="n">net</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.FullyConnected</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">net</span><span class="p">,</span><span class="w"> </span><span class="n">name</span><span class="o">=</span><span class="s2">"fc1"</span><span class="p">,</span><span class="w"> </span><span class="n">num_hidden</span><span class="o">=</span><span class="m">128</span><span class="p">)</span><span class="w"> |
| </span><span class="n">net2</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.Variable</span><span class="p">(</span><span class="s2">"data2"</span><span class="p">)</span><span class="w"> |
| </span><span class="n">net2</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.symbol.FullyConnected</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="n">net2</span><span class="p">,</span><span class="w"> </span><span class="n">name</span><span class="o">=</span><span class="s2">"net2"</span><span class="p">,</span><span class="w"> </span><span class="n">num_hidden</span><span class="o">=</span><span class="m">128</span><span class="p">)</span><span class="w"> |
| </span><span class="n">composed.net</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.apply</span><span class="p">(</span><span class="n">net</span><span class="p">,</span><span class="w"> </span><span class="n">data</span><span class="o">=</span><span class="n">net2</span><span class="p">,</span><span class="w"> </span><span class="n">name</span><span class="o">=</span><span class="s2">"compose"</span><span class="p">)</span><span class="w"> |
| </span><span class="n">arguments</span><span class="p">(</span><span class="n">composed.net</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang="">## [1] "data2" "net2_weight" "net2_bias" "fc1_weight" "fc1_bias" |
| </code></pre></div> |
| <p>In the example, <em>net</em> is used as a function to apply to an existing symbol |
| <em>net</em>. The resulting <em>composed.net</em> will replace the original argument <em>data</em> with |
| <em>net2</em> instead.</p> |
| |
| <h2 id="training-a-neural-net">Training a Neural Net</h2> |
| |
| <p>The <a href="https://github.com/apache/mxnet/blob/master/R-package/R/model.R">model API</a> is a thin wrapper around the symbolic executors to support neural net training.</p> |
| |
| <p>We encourage you to read <a href="/api/python/symbol_in_pictures/symbol_in_pictures.md">Symbolic Configuration and Execution in Pictures for python package</a>for a detailed explanation of concepts in pictures.</p> |
| |
| <h2 id="how-efficient-is-the-symbolic-api">How Efficient Is the Symbolic API?</h2> |
| |
| <p>The Symbolic API brings the efficient C++ |
| operations in powerful toolkits, such as CXXNet and Caffe, together with the |
| flexible dynamic NDArray operations. All of the memory and computation resources are |
| allocated statically during bind operations, to maximize runtime performance and memory |
| utilization.</p> |
| |
| <p>The coarse-grained operators are equivalent to CXXNet layers, which are |
| extremely efficient. We also provide fine-grained operators for more flexible |
| composition. Because MXNet does more in-place memory allocation, it can |
| be more memory efficient than CXXNet and gets to the same runtime with |
| greater flexibility.</p> |
| |
| <h2 id="next-steps">Next Steps</h2> |
| |
| <ul> |
| <li><a href="/api/r/docs/tutorials/callback_function">Write and use callback functions</a></li> |
| <li><a href="/api/r/docs/tutorials/five_minutes_neural_network">Neural Networks with MXNet in Five Minutes</a></li> |
| <li><a href="/api/r/docs/tutorials/classify_real_image_with_pretrained_model">Classify Real-World Images with Pre-trained Model</a></li> |
| <li><a href="/api/r/docs/tutorials/mnist_competition">Handwritten Digits Classification Competition</a></li> |
| <li><a href="/api/r/docs/tutorials/char_rnn_model">Character Language Model using RNN</a></li> |
| </ul> |
| </div> |
| </div> |
| |
| </div> |
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