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<h1 id="introduction">Introduction</h1>
<p>Welcome to the PyTorch API Reference.
Here you will find reference documentation for the built-in PyTorch packages.</p>
<h1 id="torch-nn">torch.nn</h1>
<h2 id="avgpool2d">AvgPool2d</h2>
<p>Applies a 2D average pooling over an input signal composed of several input</p>
<pre class="highlight python"><code><span class="n">The</span> <span class="n">output</span> <span class="n">value</span> <span class="n">of</span> <span class="n">the</span> <span class="n">layer</span> <span class="k">with</span> <span class="nb">input</span> <span class="p">(</span><span class="n">b</span> <span class="n">x</span> <span class="n">C</span> <span class="n">x</span> <span class="n">H</span> <span class="n">x</span> <span class="n">W</span><span class="p">)</span> <span class="ow">and</span> <span class="n">output</span> <span class="p">(</span><span class="n">b</span> <span class="n">x</span> <span class="n">C</span> <span class="n">x</span> <span class="n">oH</span> <span class="n">x</span> <span class="n">oW</span><span class="p">)</span>
<span class="n">can</span> <span class="n">be</span> <span class="n">precisely</span> <span class="n">described</span> <span class="k">as</span><span class="p">:</span>
<span class="n">output</span><span class="p">[</span><span class="n">b_i</span><span class="p">][</span><span class="n">c_i</span><span class="p">][</span><span class="n">h_i</span><span class="p">][</span><span class="n">w_i</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">K</span><span class="p">)</span> <span class="o">*</span> <span class="n">sum_</span><span class="p">{</span><span class="n">kh</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">KH</span><span class="p">}</span> <span class="n">sum_</span><span class="p">{</span><span class="n">kw</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">kW</span><span class="p">}</span> <span class="nb">input</span><span class="p">[</span><span class="n">b_i</span><span class="p">][</span><span class="n">c_i</span><span class="p">][</span><span class="n">stride_h</span> <span class="o">*</span> <span class="n">h_i</span> <span class="o">+</span> <span class="n">kh</span><span class="p">)][</span><span class="n">stride_w</span> <span class="o">*</span> <span class="n">w_i</span> <span class="o">+</span> <span class="n">kw</span><span class="p">)]</span>
</code></pre>
<pre class="highlight python"><code><span class="c"># pool of square window of size=3, stride=2</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">AvgPool2d</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">stride</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="c"># pool of non-square window</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">AvgPool2d</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">stride</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
<span class="nb">input</span> <span class="o">=</span> <span class="n">autograd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span> <span class="mi">32</span><span class="p">))</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">m</span><span class="o">.</span><span class="n">forward</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
</code></pre>
<p>planes. </p>
<h3 id="constructor-arguments">Constructor Arguments</h3>
<table><thead>
<tr>
<th>Parameter</th>
<th>Default</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>kernel_size</td>
<td></td>
<td>the size of the window. Can be a single number k (for a square kernel of k x k) or a tuple (kh x kw)</td>
</tr>
<tr>
<td>stride</td>
<td>kernel_size</td>
<td>the stride of the window. Can be a single number s or a tuple (sh x sw).</td>
</tr>
<tr>
<td>padding</td>
<td>0</td>
<td>implicit padding to be added. Can be a single number or a tuple.</td>
</tr>
<tr>
<td>ceil_mode</td>
<td></td>
<td>when True, will use “ceil” instead of “floor” to compute the output shape</td>
</tr>
</tbody></table>
<h3 id="expected-shape">Expected Shape</h3>
<table><thead>
<tr>
<th></th>
<th>Shape</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>input</td>
<td>[ * , * , *, * ]</td>
<td>Input is minibatch x channels x iH x iW</td>
</tr>
<tr>
<td>output</td>
<td>[ * , * , *, * ]</td>
<td>Output shape = minibatch x channels x floor((iH + 2*padH - kH) / sH + 1) x floor((iW + 2*padW - kW) / sW + 1)</td>
</tr>
</tbody></table>
<h2 id="avgpool3d">AvgPool3d</h2>
<p>Applies a 3D average pooling over an input signal composed of several input</p>
<pre class="highlight python"><code><span class="c"># pool of square window of size=3, stride=2</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">AvgPool3d</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">stride</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="c"># pool of non-square window</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">AvgPool3d</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">stride</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="nb">input</span> <span class="o">=</span> <span class="n">autograd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span><span class="mi">44</span><span class="p">,</span> <span class="mi">31</span><span class="p">))</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">m</span><span class="o">.</span><span class="n">forward</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
</code></pre>
<p>planes. </p>
<h3 id="constructor-arguments">Constructor Arguments</h3>
<table><thead>
<tr>
<th>Parameter</th>
<th>Default</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>kernel_size</td>
<td></td>
<td>the size of the window to take a average over. Can be a single number k (for a square kernel of k x k x k) or a tuple (kt x kh x kw)</td>
</tr>
<tr>
<td>stride</td>
<td>kernel_size</td>
<td>the stride of the window. Can be a single number s or a tuple (st x sh x sw).</td>
</tr>
</tbody></table>
<h3 id="expected-shape">Expected Shape</h3>
<table><thead>
<tr>
<th></th>
<th>Shape</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>input</td>
<td>[ * , * , *, *, * ]</td>
<td>Input is minibatch x channels x iT x iH x iW</td>
</tr>
<tr>
<td>output</td>
<td>[ * , * , *, *, * ]</td>
<td>Output shape = minibatch x channels x floor((iT + 2*padT - kT) / sT + 1) x floor((iH + 2*padH - kH) / sH + 1) x floor((iW + 2*padW - kW) / sW + 1)</td>
</tr>
</tbody></table>
<h2 id="batchnorm1d">BatchNorm1d</h2>
<p>Applies Batch Normalization over a 2d input that is seen as a mini-batch of 1d inputs</p>
<pre class="highlight python"><code> <span class="n">x</span> <span class="o">-</span> <span class="n">mean</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="o">-----------------------------</span> <span class="o">*</span> <span class="n">gamma</span> <span class="o">+</span> <span class="n">beta</span>
<span class="n">standard_deviation</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">+</span> <span class="n">eps</span>
</code></pre>
<pre class="highlight python"><code><span class="c"># With Learnable Parameters</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">BatchNorm1d</span><span class="p">(</span><span class="mi">100</span><span class="p">)</span>
<span class="c"># Without Learnable Parameters</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">BatchNorm1d</span><span class="p">(</span><span class="mi">100</span><span class="p">,</span> <span class="n">affine</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
<span class="nb">input</span> <span class="o">=</span> <span class="n">autograd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">100</span><span class="p">))</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">m</span><span class="o">.</span><span class="n">forward</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
</code></pre>
<p>The mean and standard-deviation are calculated per-dimension over
the mini-batches and gamma and beta are learnable parameter vectors
of size N (where N is the input size).</p>
<p>During training, this layer keeps a running estimate of its computed mean
and variance. The running sum is kept with a default momentum of 0.1
During evaluation, this running mean/variance is used for normalization.</p>
<h3 id="constructor-arguments">Constructor Arguments</h3>
<table><thead>
<tr>
<th>Parameter</th>
<th>Default</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>num_features</td>
<td></td>
<td>the size of each 1D input in the mini-batch</td>
</tr>
<tr>
<td>eps</td>
<td>1e-5</td>
<td>a value added to the denominator for numerical stability.</td>
</tr>
<tr>
<td>momentum</td>
<td>0.1</td>
<td>the value used for the running_mean and running_var computation.</td>
</tr>
<tr>
<td>affine</td>
<td></td>
<td>a boolean value that when set to true, gives the layer learnable affine parameters.</td>
</tr>
</tbody></table>
<h3 id="expected-shape">Expected Shape</h3>
<table><thead>
<tr>
<th></th>
<th>Shape</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>input</td>
<td>[ * , num_features ]</td>
<td>2D Tensor of nBatches x num_features</td>
</tr>
<tr>
<td>output</td>
<td>Same</td>
<td>Output has the same shape as input</td>
</tr>
</tbody></table>
<h3 id="returns">Returns</h3>
<p>a normalized tensor in the batch dimension</p>
<h2 id="batchnorm2d">BatchNorm2d</h2>
<p>Applies Batch Normalization over a 4d input that is seen as a mini-batch of 3d inputs</p>
<pre class="highlight python"><code> <span class="n">x</span> <span class="o">-</span> <span class="n">mean</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="o">-----------------------------</span> <span class="o">*</span> <span class="n">gamma</span> <span class="o">+</span> <span class="n">beta</span>
<span class="n">standard_deviation</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">+</span> <span class="n">eps</span>
</code></pre>
<pre class="highlight python"><code><span class="c"># With Learnable Parameters</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">BatchNorm2d</span><span class="p">(</span><span class="mi">100</span><span class="p">)</span>
<span class="c"># Without Learnable Parameters</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">BatchNorm2d</span><span class="p">(</span><span class="mi">100</span><span class="p">,</span> <span class="n">affine</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
<span class="nb">input</span> <span class="o">=</span> <span class="n">autograd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="mi">35</span><span class="p">,</span> <span class="mi">45</span><span class="p">))</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">m</span><span class="o">.</span><span class="n">forward</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
</code></pre>
<p>The mean and standard-deviation are calculated per-dimension over
the mini-batches and gamma and beta are learnable parameter vectors
of size N (where N is the input size).</p>
<p>During training, this layer keeps a running estimate of its computed mean
and variance. The running sum is kept with a default momentum of 0.1
During evaluation, this running mean/variance is used for normalization.</p>
<h3 id="constructor-arguments">Constructor Arguments</h3>
<table><thead>
<tr>
<th>Parameter</th>
<th>Default</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>num_features</td>
<td></td>
<td>num_features from an expected input of size batch_size x num_features x height x width</td>
</tr>
<tr>
<td>eps</td>
<td>1e-5</td>
<td>a value added to the denominator for numerical stability.</td>
</tr>
<tr>
<td>momentum</td>
<td>0.1</td>
<td>the value used for the running_mean and running_var computation.</td>
</tr>
<tr>
<td>affine</td>
<td></td>
<td>a boolean value that when set to true, gives the layer learnable affine parameters.</td>
</tr>
</tbody></table>
<h3 id="expected-shape">Expected Shape</h3>
<table><thead>
<tr>
<th></th>
<th>Shape</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>input</td>
<td>[ * , num_features , *, * ]</td>
<td>4D Tensor of batch_size x num_features x height x width</td>
</tr>
<tr>
<td>output</td>
<td>Same</td>
<td>Output has the same shape as input</td>
</tr>
</tbody></table>
<h3 id="returns">Returns</h3>
<p>a normalized tensor in the batch dimension</p>
<h2 id="batchnorm3d">BatchNorm3d</h2>
<p>Applies Batch Normalization over a 5d input that is seen as a mini-batch of 4d inputs</p>
<pre class="highlight python"><code> <span class="n">x</span> <span class="o">-</span> <span class="n">mean</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="o">-----------------------------</span> <span class="o">*</span> <span class="n">gamma</span> <span class="o">+</span> <span class="n">beta</span>
<span class="n">standard_deviation</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">+</span> <span class="n">eps</span>
</code></pre>
<pre class="highlight python"><code><span class="c"># With Learnable Parameters</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">BatchNorm3d</span><span class="p">(</span><span class="mi">100</span><span class="p">)</span>
<span class="c"># Without Learnable Parameters</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">BatchNorm3d</span><span class="p">(</span><span class="mi">100</span><span class="p">,</span> <span class="n">affine</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
<span class="nb">input</span> <span class="o">=</span> <span class="n">autograd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="mi">35</span><span class="p">,</span> <span class="mi">45</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">m</span><span class="o">.</span><span class="n">forward</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
</code></pre>
<p>The mean and standard-deviation are calculated per-dimension over
the mini-batches and gamma and beta are learnable parameter vectors
of size N (where N is the input size).</p>
<p>During training, this layer keeps a running estimate of its computed mean
and variance. The running sum is kept with a default momentum of 0.1
During evaluation, this running mean/variance is used for normalization.</p>
<h3 id="constructor-arguments">Constructor Arguments</h3>
<table><thead>
<tr>
<th>Parameter</th>
<th>Default</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>num_features</td>
<td></td>
<td>num_features from an expected input of size batch_size x num_features x height x width</td>
</tr>
<tr>
<td>eps</td>
<td>1e-5</td>
<td>a value added to the denominator for numerical stability.</td>
</tr>
<tr>
<td>momentum</td>
<td>0.1</td>
<td>the value used for the running_mean and running_var computation.</td>
</tr>
<tr>
<td>affine</td>
<td></td>
<td>a boolean value that when set to true, gives the layer learnable affine parameters.</td>
</tr>
</tbody></table>
<h3 id="expected-shape">Expected Shape</h3>
<table><thead>
<tr>
<th></th>
<th>Shape</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>input</td>
<td>[ * , num_features , * , * , * ]</td>
<td>5D Tensor of batch_size x num_features x depth x height x width</td>
</tr>
<tr>
<td>output</td>
<td>Same</td>
<td>Output has the same shape as input</td>
</tr>
</tbody></table>
<h3 id="returns">Returns</h3>
<p>a normalized tensor in the batch dimension</p>
<h2 id="container">Container</h2>
<p>This is the base container class for all neural networks you would define.</p>
<pre class="highlight python"><code><span class="c"># Example of using Container</span>
<span class="k">class</span> <span class="nc">Net</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">Container</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="nb">super</span><span class="p">(</span><span class="n">Net</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="n">__init__</span><span class="p">(</span>
<span class="n">conv1</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Conv2d</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span>
<span class="n">relu</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">ReLU</span><span class="p">()</span>
<span class="p">)</span>
<span class="k">def</span> <span class="nf">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="nb">input</span><span class="p">):</span>
<span class="n">output</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">conv1</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
<span class="k">return</span> <span class="n">output</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">Net</span><span class="p">()</span>
</code></pre>
<pre class="highlight python"><code><span class="c"># one can add modules to the container after construction</span>
<span class="n">model</span><span class="o">.</span><span class="n">add_module</span><span class="p">(</span><span class="s">'pool1'</span><span class="p">,</span> <span class="n">nn</span><span class="o">.</span><span class="n">MaxPool2d</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
</code></pre>
<p>You will subclass your container from this class.
In the constructor you define the modules that you would want to use,
and in the <strong>call</strong> function you use the constructed modules in
your operations.</p>
<p>To make it easier to understand, given is a small example.</p>
<p>One can also add new modules to a container after construction.
You can do this with the add_module function.</p>
<p>The container has one additional method <code class="prettyprint">parameters()</code> which
returns the list of learnable parameters in the container instance.</p>
<h2 id="conv1d">Conv1d</h2>
<p>Applies a 1D convolution over an input signal composed of several input</p>
<pre class="highlight python"><code><span class="n">The</span> <span class="n">output</span> <span class="n">value</span> <span class="n">of</span> <span class="n">the</span> <span class="n">layer</span> <span class="k">with</span> <span class="nb">input</span> <span class="p">(</span><span class="n">b</span> <span class="n">x</span> <span class="n">iC</span> <span class="n">x</span> <span class="n">W</span><span class="p">)</span> <span class="ow">and</span> <span class="n">output</span> <span class="p">(</span><span class="n">b</span> <span class="n">x</span> <span class="n">oC</span> <span class="n">x</span> <span class="n">oW</span><span class="p">)</span>
<span class="n">can</span> <span class="n">be</span> <span class="n">precisely</span> <span class="n">described</span> <span class="k">as</span><span class="p">:</span>
<span class="n">output</span><span class="p">[</span><span class="n">b_i</span><span class="p">][</span><span class="n">oc_i</span><span class="p">][</span><span class="n">w_i</span><span class="p">]</span> <span class="o">=</span> <span class="n">bias</span><span class="p">[</span><span class="n">oc_i</span><span class="p">]</span>
<span class="o">+</span> <span class="n">sum_iC</span> <span class="n">sum_</span><span class="p">{</span><span class="n">ow</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="n">oW</span><span class="o">-</span><span class="mi">1</span><span class="p">}</span> <span class="n">sum_</span><span class="p">{</span><span class="n">kw</span> <span class="o">=</span> <span class="mi">0</span> <span class="n">to</span> <span class="n">kW</span><span class="o">-</span><span class="mi">1</span><span class="p">}</span>
<span class="n">weight</span><span class="p">[</span><span class="n">oc_i</span><span class="p">][</span><span class="n">ic_i</span><span class="p">][</span><span class="n">kw</span><span class="p">]</span> <span class="o">*</span> <span class="nb">input</span><span class="p">[</span><span class="n">b_i</span><span class="p">][</span><span class="n">ic_i</span><span class="p">][</span><span class="n">stride_w</span> <span class="o">*</span> <span class="n">ow</span> <span class="o">+</span> <span class="n">kw</span><span class="p">)]</span>
</code></pre>
<pre class="highlight python"><code><span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Conv1d</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">33</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">stride</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="nb">input</span> <span class="o">=</span> <span class="n">autograd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">50</span><span class="p">))</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">m</span><span class="o">.</span><span class="n">forward</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
</code></pre>
<p>planes. </p>
<p>Note that depending of the size of your kernel, several (of the last)
columns of the input might be lost. It is up to the user
to add proper padding.</p>
<h3 id="constructor-arguments">Constructor Arguments</h3>
<table><thead>
<tr>
<th>Parameter</th>
<th>Default</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>in_channels</td>
<td></td>
<td>The number of expected input channels in the image given as input</td>
</tr>
<tr>
<td>out_channels</td>
<td></td>
<td>The number of output channels the convolution layer will produce</td>
</tr>
<tr>
<td>kernel_size</td>
<td></td>
<td>the size of the convolving kernel.</td>
</tr>
<tr>
<td>stride</td>
<td></td>
<td>the stride of the convolving kernel.</td>
</tr>
</tbody></table>
<h3 id="expected-shape">Expected Shape</h3>
<table><thead>
<tr>
<th></th>
<th>Shape</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>input</td>
<td>[ * , in_channels , * ]</td>
<td>Input is minibatch x in_channels x iW</td>
</tr>
<tr>
<td>output</td>
<td>[ * , out_channels , * ]</td>
<td>Output shape is precisely minibatch x out_channels x floor((iW + 2*padW - kW) / dW + 1)</td>
</tr>
</tbody></table>
<p>Members:
weight: the learnable weights of the module of shape (out_channels x in_channels x kW)
bias: the learnable bias of the module of shape (out_channels)</p>
<h2 id="conv2d">Conv2d</h2>
<p>Applies a 2D convolution over an input image composed of several input</p>
<pre class="highlight python"><code><span class="n">The</span> <span class="n">output</span> <span class="n">value</span> <span class="n">of</span> <span class="n">the</span> <span class="n">layer</span> <span class="k">with</span> <span class="nb">input</span> <span class="p">(</span><span class="n">b</span> <span class="n">x</span> <span class="n">iC</span> <span class="n">x</span> <span class="n">H</span> <span class="n">x</span> <span class="n">W</span><span class="p">)</span> <span class="ow">and</span> <span class="n">output</span> <span class="p">(</span><span class="n">b</span> <span class="n">x</span> <span class="n">oC</span> <span class="n">x</span> <span class="n">oH</span> <span class="n">x</span> <span class="n">oW</span><span class="p">)</span>
<span class="n">can</span> <span class="n">be</span> <span class="n">precisely</span> <span class="n">described</span> <span class="k">as</span><span class="p">:</span>
<span class="n">output</span><span class="p">[</span><span class="n">b_i</span><span class="p">][</span><span class="n">oc_i</span><span class="p">][</span><span class="n">h_i</span><span class="p">][</span><span class="n">w_i</span><span class="p">]</span> <span class="o">=</span> <span class="n">bias</span><span class="p">[</span><span class="n">oc_i</span><span class="p">]</span>
<span class="o">+</span> <span class="n">sum_iC</span> <span class="n">sum_</span><span class="p">{</span><span class="n">oh</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="n">oH</span><span class="o">-</span><span class="mi">1</span><span class="p">}</span> <span class="n">sum_</span><span class="p">{</span><span class="n">ow</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="n">oW</span><span class="o">-</span><span class="mi">1</span><span class="p">}</span> <span class="n">sum_</span><span class="p">{</span><span class="n">kh</span> <span class="o">=</span> <span class="mi">0</span> <span class="n">to</span> <span class="n">kH</span><span class="o">-</span><span class="mi">1</span><span class="p">}</span> <span class="n">sum_</span><span class="p">{</span><span class="n">kw</span> <span class="o">=</span> <span class="mi">0</span> <span class="n">to</span> <span class="n">kW</span><span class="o">-</span><span class="mi">1</span><span class="p">}</span>
<span class="n">weight</span><span class="p">[</span><span class="n">oc_i</span><span class="p">][</span><span class="n">ic_i</span><span class="p">][</span><span class="n">kh</span><span class="p">][</span><span class="n">kw</span><span class="p">]</span> <span class="o">*</span> <span class="nb">input</span><span class="p">[</span><span class="n">b_i</span><span class="p">][</span><span class="n">ic_i</span><span class="p">][</span><span class="n">stride_h</span> <span class="o">*</span> <span class="n">oh</span> <span class="o">+</span> <span class="n">kh</span><span class="p">)][</span><span class="n">stride_w</span> <span class="o">*</span> <span class="n">ow</span> <span class="o">+</span> <span class="n">kw</span><span class="p">)]</span>
</code></pre>
<pre class="highlight python"><code><span class="c"># With square kernels and equal stride</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Conv2d</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">33</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">stride</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="c"># non-square kernels and unequal stride and with padding</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Conv2d</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">33</span><span class="p">,</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="n">stride</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">padding</span><span class="o">=</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="c"># non-square kernels and unequal stride and with padding and dilation</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Conv2d</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">33</span><span class="p">,</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="n">stride</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">padding</span><span class="o">=</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">dilation</span><span class="o">=</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
<span class="nb">input</span> <span class="o">=</span> <span class="n">autograd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span> <span class="mi">100</span><span class="p">))</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">m</span><span class="o">.</span><span class="n">forward</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
</code></pre>
<p>planes. </p>
<p>Note that depending of the size of your kernel, several (of the last)
columns or rows of the input image might be lost. It is up to the user
to add proper padding in images.</p>
<h3 id="constructor-arguments">Constructor Arguments</h3>
<table><thead>
<tr>
<th>Parameter</th>
<th>Default</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>in_channels</td>
<td></td>
<td>The number of expected input channels in the image given as input</td>
</tr>
<tr>
<td>out_channels</td>
<td></td>
<td>The number of output channels the convolution layer will produce</td>
</tr>
<tr>
<td>kernel_size</td>
<td></td>
<td>the size of the convolving kernel. Can be a single number k (for a square kernel of k x k) or a tuple (kh x kw)</td>
</tr>
<tr>
<td>stride</td>
<td>1</td>
<td>the stride of the convolving kernel. Can be a single number s or a tuple (sh x sw).</td>
</tr>
<tr>
<td>padding</td>
<td>0</td>
<td>implicit zero padding on the input. Can be a single number s or a tuple.</td>
</tr>
<tr>
<td>dilation</td>
<td>None</td>
<td>If given, will do dilated (or atrous) convolutions. Can be a single number s or a tuple.</td>
</tr>
<tr>
<td>no_bias</td>
<td>False</td>
<td>If set to true, the layer will not learn an additive bias.</td>
</tr>
</tbody></table>
<h3 id="expected-shape">Expected Shape</h3>
<table><thead>
<tr>
<th></th>
<th>Shape</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>input</td>
<td>[ * , in_channels , * , * ]</td>
<td>Input is minibatch x in_channels x iH x iW</td>
</tr>
<tr>
<td>output</td>
<td>[ * , out_channels , * , * ]</td>
<td>Output shape is precisely minibatch x out_channels x floor((iH + 2*padH - kH) / dH + 1) x floor((iW + 2*padW - kW) / dW + 1)</td>
</tr>
</tbody></table>
<p>Members:
weight: the learnable weights of the module of shape (out_channels x in_channels x kH x kW)
bias: the learnable bias of the module of shape (out_channels)</p>
<h2 id="conv3d">Conv3d</h2>
<p>Applies a 3D convolution over an input image composed of several input</p>
<pre class="highlight python"><code><span class="c"># With square kernels and equal stride</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Conv3d</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">33</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">stride</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="c"># non-square kernels and unequal stride and with padding</span>
<span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Conv3d</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span> <span class="mi">33</span><span class="p">,</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">stride</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">padding</span><span class="o">=</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
<span class="nb">input</span> <span class="o">=</span> <span class="n">autograd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span> <span class="mi">100</span><span class="p">))</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">m</span><span class="o">.</span><span class="n">forward</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
</code></pre>
<p>planes. </p>
<p>Note that depending of the size of your kernel, several (of the last)
columns or rows of the input image might be lost. It is up to the user
to add proper padding in images.</p>
<h3 id="constructor-arguments">Constructor Arguments</h3>
<table><thead>
<tr>
<th>Parameter</th>
<th>Default</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>in_channels</td>
<td></td>
<td>The number of expected input channels in the image given as input</td>
</tr>
<tr>
<td>out_channels</td>
<td></td>
<td>The number of output channels the convolution layer will produce</td>
</tr>
<tr>
<td>kernel_size</td>
<td></td>
<td>the size of the convolving kernel. Can be a single number k (for a square kernel of k x k x k) or a tuple (kt x kh x kw)</td>
</tr>
<tr>
<td>stride</td>
<td>1</td>
<td>the stride of the convolving kernel. Can be a single number s or a tuple (kt x sh x sw).</td>
</tr>
<tr>
<td>padding</td>
<td>0</td>
<td>implicit zero padding on the input. Can be a single number s or a tuple.</td>
</tr>
<tr>
<td>no_bias</td>
<td>False</td>
<td>If set to true, the layer will not learn an additive bias.</td>
</tr>
</tbody></table>
<h3 id="expected-shape">Expected Shape</h3>
<table><thead>
<tr>
<th></th>
<th>Shape</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>input</td>
<td>[ * , in_channels , * , * , * ]</td>
<td>Input is minibatch x in_channels x iT x iH x iW</td>
</tr>
<tr>
<td>output</td>
<td>[ * , out_channels , * , * , * ]</td>
<td>Output shape is precisely minibatch x out_channels x floor((iT + 2*padT - kT) / dT + 1) x floor((iH + 2*padH - kH) / dH + 1) x floor((iW + 2*padW - kW) / dW + 1)</td>
</tr>
</tbody></table>
<p>Members:
weight: the learnable weights of the module of shape (out_channels x in_channels x kT x kH x kW)
bias: the learnable bias of the module of shape (out_channels)</p>
<h2 id="dropout">Dropout</h2>
<p>Randomly zeroes some of the elements of the input tensor.</p>
<pre class="highlight python"><code><span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Dropout</span><span class="p">(</span><span class="n">p</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>
<span class="nb">input</span> <span class="o">=</span> <span class="n">autograd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">16</span><span class="p">))</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">m</span><span class="o">.</span><span class="n">forward</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
</code></pre>
<p>The elements to zero are randomized on every forward call.</p>
<h3 id="constructor-arguments">Constructor Arguments</h3>
<table><thead>
<tr>
<th>Parameter</th>
<th>Default</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>p</td>
<td>0.5</td>
<td>probability of an element to be zeroed.</td>
</tr>
<tr>
<td>inplace</td>
<td>false</td>
<td>If set to True, will do this operation in-place.</td>
</tr>
</tbody></table>
<h3 id="expected-shape">Expected Shape</h3>
<table><thead>
<tr>
<th></th>
<th>Shape</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>input</td>
<td>Any</td>
<td>Input can be of any shape</td>
</tr>
<tr>
<td>output</td>
<td>Same</td>
<td>Output is of the same shape as input</td>
</tr>
</tbody></table>
<h2 id="dropout2d">Dropout2d</h2>
<p>Randomly zeroes whole channels of the input tensor.</p>
<pre class="highlight python"><code><span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Dropout2d</span><span class="p">(</span><span class="n">p</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>
<span class="nb">input</span> <span class="o">=</span> <span class="n">autograd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">32</span><span class="p">,</span> <span class="mi">32</span><span class="p">))</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">m</span><span class="o">.</span><span class="n">forward</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
</code></pre>
<p>The input is 4D (batch x channels, height, width) and each channel
is of size (1, height, width).
The channels to zero are randomized on every forward call.
Usually the input comes from Conv2d modules.</p>
<p>As described in the paper “Efficient Object Localization Using Convolutional
Networks” (http:arxiv.org/abs/1411.4280), if adjacent pixels within
feature maps are strongly correlated (as is normally the case in early
convolution layers) then iid dropout will not regularize the activations
and will otherwise just result in an effective learning rate decrease.
In this case, nn.Dropout2d will help promote independence between
feature maps and should be used instead.</p>
<h3 id="constructor-arguments">Constructor Arguments</h3>
<table><thead>
<tr>
<th>Parameter</th>
<th>Default</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>p</td>
<td>0.5</td>
<td>probability of an element to be zeroed.</td>
</tr>
<tr>
<td>inplace</td>
<td>false</td>
<td>If set to True, will do this operation in-place.</td>
</tr>
</tbody></table>
<h3 id="expected-shape">Expected Shape</h3>
<table><thead>
<tr>
<th></th>
<th>Shape</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>input</td>
<td>[*, *, *, *]</td>
<td>Input can be of any sizes of 4D shape</td>
</tr>
<tr>
<td>output</td>
<td>Same</td>
<td>Output is of the same shape as input</td>
</tr>
</tbody></table>
<h2 id="dropout3d">Dropout3d</h2>
<p>Randomly zeroes whole channels of the input tensor.</p>
<pre class="highlight python"><code><span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Dropout3d</span><span class="p">(</span><span class="n">p</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>
<span class="nb">input</span> <span class="o">=</span> <span class="n">autograd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">32</span><span class="p">,</span> <span class="mi">32</span><span class="p">))</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">m</span><span class="o">.</span><span class="n">forward</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
</code></pre>
<p>The input is 5D (batch x channels, depth, height, width) and each channel
is of size (1, depth, height, width).
The channels to zero are randomized on every forward call.
Usually the input comes from Conv3d modules.</p>
<h3 id="constructor-arguments">Constructor Arguments</h3>
<table><thead>
<tr>
<th>Parameter</th>
<th>Default</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>p</td>
<td>0.5</td>
<td>probability of an element to be zeroed.</td>
</tr>
<tr>
<td>inplace</td>
<td>false</td>
<td>If set to True, will do this operation in-place.</td>
</tr>
</tbody></table>
<h3 id="expected-shape">Expected Shape</h3>
<table><thead>
<tr>
<th></th>
<th>Shape</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>input</td>
<td>[*, *, *, *, *]</td>
<td>Input can be of any sizes of 5D shape</td>
</tr>
<tr>
<td>output</td>
<td>Same</td>
<td>Output is of the same shape as input</td>
</tr>
</tbody></table>
<h2 id="elu">ELU</h2>
<p>Applies element-wise, ELU(x) = max(0,x) + min(0, alpha * (exp(x) - 1))</p>
<pre class="highlight python"><code><span class="n">m</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">ELU</span><span class="p">()</span>
<span class="nb">input</span> <span class="o">=</span> <span class="n">autograd</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">))</span>
<span class="k">print</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="n">m</span><span class="o">.</span><span class="n">forward</span><span class="p">(</span><span class="nb">input</span><span class="p">))</span>
</code></pre>
<h3 id="constructor-arguments">Constructor Arguments</h3>
<table><thead>
<tr>
<th>Parameter</th>
<th>Default</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>alpha</td>
<td>1.0</td>
<td>the alpha value for the ELU formulation.</td>
</tr>
<tr>
<td>inplace</td>
<td></td>
<td>can optionally do the operation in-place</td>
</tr>
</tbody></table>
<h3 id="expected-shape">Expected Shape</h3>
<table><thead>
<tr>
<th></th>
<th>Shape</th>
<th>Description</th>
</tr>
</thead><tbody>
<tr>
<td>input</td>
<td>Any</td>
<td>Tensor of any size and dimension</td>
</tr>
<tr>
<td>output</td>
<td>Same</td>
<td>Output has the same shape as input</td>
</tr>
</tbody></table>
<h3 id="returns">Returns</h3>
<p>a Tensor of the same dimension and shape as the input</p>
<p><img src="image/elu.png" ></p>
<h2 id="embedding">Embedding</h2>