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<div class="section" id="torch-nn">
<h1>torch.nn<a class="headerlink" href="#torch-nn" title="Permalink to this headline">¶</a></h1>
<p>These are the basic building block for graphs</p>
<div class="contents local topic" id="id1">
<p class="topic-title">torch.nn</p>
<ul class="simple">
<li><p><a class="reference internal" href="#containers" id="id2">Containers</a></p></li>
<li><p><a class="reference internal" href="#convolution-layers" id="id3">Convolution Layers</a></p></li>
<li><p><a class="reference internal" href="#pooling-layers" id="id4">Pooling layers</a></p></li>
<li><p><a class="reference internal" href="#padding-layers" id="id5">Padding Layers</a></p></li>
<li><p><a class="reference internal" href="#non-linear-activations-weighted-sum-nonlinearity" id="id6">Non-linear Activations (weighted sum, nonlinearity)</a></p></li>
<li><p><a class="reference internal" href="#non-linear-activations-other" id="id7">Non-linear Activations (other)</a></p></li>
<li><p><a class="reference internal" href="#normalization-layers" id="id8">Normalization Layers</a></p></li>
<li><p><a class="reference internal" href="#recurrent-layers" id="id9">Recurrent Layers</a></p></li>
<li><p><a class="reference internal" href="#transformer-layers" id="id10">Transformer Layers</a></p></li>
<li><p><a class="reference internal" href="#linear-layers" id="id11">Linear Layers</a></p></li>
<li><p><a class="reference internal" href="#dropout-layers" id="id12">Dropout Layers</a></p></li>
<li><p><a class="reference internal" href="#sparse-layers" id="id13">Sparse Layers</a></p></li>
<li><p><a class="reference internal" href="#distance-functions" id="id14">Distance Functions</a></p></li>
<li><p><a class="reference internal" href="#loss-functions" id="id15">Loss Functions</a></p></li>
<li><p><a class="reference internal" href="#vision-layers" id="id16">Vision Layers</a></p></li>
<li><p><a class="reference internal" href="#shuffle-layers" id="id17">Shuffle Layers</a></p></li>
<li><p><a class="reference internal" href="#dataparallel-layers-multi-gpu-distributed" id="id18">DataParallel Layers (multi-GPU, distributed)</a></p></li>
<li><p><a class="reference internal" href="#utilities" id="id19">Utilities</a></p></li>
<li><p><a class="reference internal" href="#quantized-functions" id="id20">Quantized Functions</a></p></li>
<li><p><a class="reference internal" href="#lazy-modules-initialization" id="id21">Lazy Modules Initialization</a></p></li>
</ul>
</div>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><p id="torch.nn.parameter.Parameter"/><a class="reference internal" href="generated/torch.nn.parameter.Parameter.html#torch.nn.parameter.Parameter" title="torch.nn.parameter.Parameter"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Parameter</span></code></a></p></td>
<td><p>A kind of Tensor that is to be considered a module parameter.</p></td>
</tr>
<tr class="row-even"><td><p><p id="torch.nn.parameter.UninitializedParameter"/><a class="reference internal" href="generated/torch.nn.parameter.UninitializedParameter.html#torch.nn.parameter.UninitializedParameter" title="torch.nn.parameter.UninitializedParameter"><code class="xref py py-obj docutils literal notranslate"><span class="pre">UninitializedParameter</span></code></a></p></td>
<td><p>A parameter that is not initialized.</p></td>
</tr>
</tbody>
</table>
<div class="section" id="containers">
<h2><a class="toc-backref" href="#id1">Containers</a><a class="headerlink" href="#containers" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><p id="torch.nn.Module"/><a class="reference internal" href="generated/torch.nn.Module.html#torch.nn.Module" title="torch.nn.Module"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Module</span></code></a></p></td>
<td><p>Base class for all neural network modules.</p></td>
</tr>
<tr class="row-even"><td><p><p id="torch.nn.Sequential"/><a class="reference internal" href="generated/torch.nn.Sequential.html#torch.nn.Sequential" title="torch.nn.Sequential"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Sequential</span></code></a></p></td>
<td><p>A sequential container.</p></td>
</tr>
<tr class="row-odd"><td><p><p id="torch.nn.ModuleList"/><a class="reference internal" href="generated/torch.nn.ModuleList.html#torch.nn.ModuleList" title="torch.nn.ModuleList"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ModuleList</span></code></a></p></td>
<td><p>Holds submodules in a list.</p></td>
</tr>
<tr class="row-even"><td><p><p id="torch.nn.ModuleDict"/><a class="reference internal" href="generated/torch.nn.ModuleDict.html#torch.nn.ModuleDict" title="torch.nn.ModuleDict"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ModuleDict</span></code></a></p></td>
<td><p>Holds submodules in a dictionary.</p></td>
</tr>
<tr class="row-odd"><td><p><p id="torch.nn.ParameterList"/><a class="reference internal" href="generated/torch.nn.ParameterList.html#torch.nn.ParameterList" title="torch.nn.ParameterList"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ParameterList</span></code></a></p></td>
<td><p>Holds parameters in a list.</p></td>
</tr>
<tr class="row-even"><td><p><p id="torch.nn.ParameterDict"/><a class="reference internal" href="generated/torch.nn.ParameterDict.html#torch.nn.ParameterDict" title="torch.nn.ParameterDict"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ParameterDict</span></code></a></p></td>
<td><p>Holds parameters in a dictionary.</p></td>
</tr>
</tbody>
</table>
<p>Global Hooks For Module</p>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><p id="torch.nn.modules.module.register_module_forward_pre_hook"/><a class="reference internal" href="generated/torch.nn.modules.module.register_module_forward_pre_hook.html#torch.nn.modules.module.register_module_forward_pre_hook" title="torch.nn.modules.module.register_module_forward_pre_hook"><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_module_forward_pre_hook</span></code></a></p></td>
<td><p>Registers a forward pre-hook common to all modules.</p></td>
</tr>
<tr class="row-even"><td><p><p id="torch.nn.modules.module.register_module_forward_hook"/><a class="reference internal" href="generated/torch.nn.modules.module.register_module_forward_hook.html#torch.nn.modules.module.register_module_forward_hook" title="torch.nn.modules.module.register_module_forward_hook"><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_module_forward_hook</span></code></a></p></td>
<td><p>Registers a global forward hook for all the modules</p></td>
</tr>
<tr class="row-odd"><td><p><p id="torch.nn.modules.module.register_module_backward_hook"/><a class="reference internal" href="generated/torch.nn.modules.module.register_module_backward_hook.html#torch.nn.modules.module.register_module_backward_hook" title="torch.nn.modules.module.register_module_backward_hook"><code class="xref py py-obj docutils literal notranslate"><span class="pre">register_module_backward_hook</span></code></a></p></td>
<td><p>Registers a backward hook common to all the modules.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="convolution-layers">
<h2><a class="toc-backref" href="#id1">Convolution Layers</a><a class="headerlink" href="#convolution-layers" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.Conv1d.html#torch.nn.Conv1d" title="torch.nn.Conv1d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Conv1d</span></code></a></p></td>
<td><p>Applies a 1D convolution over an input signal composed of several input planes.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.Conv2d.html#torch.nn.Conv2d" title="torch.nn.Conv2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Conv2d</span></code></a></p></td>
<td><p>Applies a 2D convolution over an input signal composed of several input planes.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.Conv3d.html#torch.nn.Conv3d" title="torch.nn.Conv3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Conv3d</span></code></a></p></td>
<td><p>Applies a 3D convolution over an input signal composed of several input planes.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.ConvTranspose1d.html#torch.nn.ConvTranspose1d" title="torch.nn.ConvTranspose1d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.ConvTranspose1d</span></code></a></p></td>
<td><p>Applies a 1D transposed convolution operator over an input image composed of several input planes.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.ConvTranspose2d.html#torch.nn.ConvTranspose2d" title="torch.nn.ConvTranspose2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.ConvTranspose2d</span></code></a></p></td>
<td><p>Applies a 2D transposed convolution operator over an input image composed of several input planes.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.ConvTranspose3d.html#torch.nn.ConvTranspose3d" title="torch.nn.ConvTranspose3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.ConvTranspose3d</span></code></a></p></td>
<td><p>Applies a 3D transposed convolution operator over an input image composed of several input planes.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.LazyConv1d.html#torch.nn.LazyConv1d" title="torch.nn.LazyConv1d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.LazyConv1d</span></code></a></p></td>
<td><p>A <a class="reference internal" href="generated/torch.nn.Conv1d.html#torch.nn.Conv1d" title="torch.nn.Conv1d"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.nn.Conv1d</span></code></a> module with lazy initialization of the <code class="docutils literal notranslate"><span class="pre">in_channels</span></code> argument of the <code class="xref py py-class docutils literal notranslate"><span class="pre">Conv1d</span></code> that is inferred from the <code class="docutils literal notranslate"><span class="pre">input.size(1)</span></code>.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.LazyConv2d.html#torch.nn.LazyConv2d" title="torch.nn.LazyConv2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.LazyConv2d</span></code></a></p></td>
<td><p>A <a class="reference internal" href="generated/torch.nn.Conv2d.html#torch.nn.Conv2d" title="torch.nn.Conv2d"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.nn.Conv2d</span></code></a> module with lazy initialization of the <code class="docutils literal notranslate"><span class="pre">in_channels</span></code> argument of the <code class="xref py py-class docutils literal notranslate"><span class="pre">Conv2d</span></code> that is inferred from the <code class="docutils literal notranslate"><span class="pre">input.size(1)</span></code>.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.LazyConv3d.html#torch.nn.LazyConv3d" title="torch.nn.LazyConv3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.LazyConv3d</span></code></a></p></td>
<td><p>A <a class="reference internal" href="generated/torch.nn.Conv3d.html#torch.nn.Conv3d" title="torch.nn.Conv3d"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.nn.Conv3d</span></code></a> module with lazy initialization of the <code class="docutils literal notranslate"><span class="pre">in_channels</span></code> argument of the <code class="xref py py-class docutils literal notranslate"><span class="pre">Conv3d</span></code> that is inferred from the <code class="docutils literal notranslate"><span class="pre">input.size(1)</span></code>.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.LazyConvTranspose1d.html#torch.nn.LazyConvTranspose1d" title="torch.nn.LazyConvTranspose1d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.LazyConvTranspose1d</span></code></a></p></td>
<td><p>A <a class="reference internal" href="generated/torch.nn.ConvTranspose1d.html#torch.nn.ConvTranspose1d" title="torch.nn.ConvTranspose1d"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.nn.ConvTranspose1d</span></code></a> module with lazy initialization of the <code class="docutils literal notranslate"><span class="pre">in_channels</span></code> argument of the <code class="xref py py-class docutils literal notranslate"><span class="pre">ConvTranspose1d</span></code> that is inferred from the <code class="docutils literal notranslate"><span class="pre">input.size(1)</span></code>.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.LazyConvTranspose2d.html#torch.nn.LazyConvTranspose2d" title="torch.nn.LazyConvTranspose2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.LazyConvTranspose2d</span></code></a></p></td>
<td><p>A <a class="reference internal" href="generated/torch.nn.ConvTranspose2d.html#torch.nn.ConvTranspose2d" title="torch.nn.ConvTranspose2d"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.nn.ConvTranspose2d</span></code></a> module with lazy initialization of the <code class="docutils literal notranslate"><span class="pre">in_channels</span></code> argument of the <code class="xref py py-class docutils literal notranslate"><span class="pre">ConvTranspose2d</span></code> that is inferred from the <code class="docutils literal notranslate"><span class="pre">input.size(1)</span></code>.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.LazyConvTranspose3d.html#torch.nn.LazyConvTranspose3d" title="torch.nn.LazyConvTranspose3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.LazyConvTranspose3d</span></code></a></p></td>
<td><p>A <a class="reference internal" href="generated/torch.nn.ConvTranspose3d.html#torch.nn.ConvTranspose3d" title="torch.nn.ConvTranspose3d"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.nn.ConvTranspose3d</span></code></a> module with lazy initialization of the <code class="docutils literal notranslate"><span class="pre">in_channels</span></code> argument of the <code class="xref py py-class docutils literal notranslate"><span class="pre">ConvTranspose3d</span></code> that is inferred from the <code class="docutils literal notranslate"><span class="pre">input.size(1)</span></code>.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.Unfold.html#torch.nn.Unfold" title="torch.nn.Unfold"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Unfold</span></code></a></p></td>
<td><p>Extracts sliding local blocks from a batched input tensor.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.Fold.html#torch.nn.Fold" title="torch.nn.Fold"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Fold</span></code></a></p></td>
<td><p>Combines an array of sliding local blocks into a large containing tensor.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="pooling-layers">
<h2><a class="toc-backref" href="#id1">Pooling layers</a><a class="headerlink" href="#pooling-layers" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.MaxPool1d.html#torch.nn.MaxPool1d" title="torch.nn.MaxPool1d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.MaxPool1d</span></code></a></p></td>
<td><p>Applies a 1D max pooling over an input signal composed of several input planes.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.MaxPool2d.html#torch.nn.MaxPool2d" title="torch.nn.MaxPool2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.MaxPool2d</span></code></a></p></td>
<td><p>Applies a 2D max pooling over an input signal composed of several input planes.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.MaxPool3d.html#torch.nn.MaxPool3d" title="torch.nn.MaxPool3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.MaxPool3d</span></code></a></p></td>
<td><p>Applies a 3D max pooling over an input signal composed of several input planes.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.MaxUnpool1d.html#torch.nn.MaxUnpool1d" title="torch.nn.MaxUnpool1d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.MaxUnpool1d</span></code></a></p></td>
<td><p>Computes a partial inverse of <code class="xref py py-class docutils literal notranslate"><span class="pre">MaxPool1d</span></code>.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.MaxUnpool2d.html#torch.nn.MaxUnpool2d" title="torch.nn.MaxUnpool2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.MaxUnpool2d</span></code></a></p></td>
<td><p>Computes a partial inverse of <code class="xref py py-class docutils literal notranslate"><span class="pre">MaxPool2d</span></code>.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.MaxUnpool3d.html#torch.nn.MaxUnpool3d" title="torch.nn.MaxUnpool3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.MaxUnpool3d</span></code></a></p></td>
<td><p>Computes a partial inverse of <code class="xref py py-class docutils literal notranslate"><span class="pre">MaxPool3d</span></code>.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.AvgPool1d.html#torch.nn.AvgPool1d" title="torch.nn.AvgPool1d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.AvgPool1d</span></code></a></p></td>
<td><p>Applies a 1D average pooling over an input signal composed of several input planes.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.AvgPool2d.html#torch.nn.AvgPool2d" title="torch.nn.AvgPool2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.AvgPool2d</span></code></a></p></td>
<td><p>Applies a 2D average pooling over an input signal composed of several input planes.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.AvgPool3d.html#torch.nn.AvgPool3d" title="torch.nn.AvgPool3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.AvgPool3d</span></code></a></p></td>
<td><p>Applies a 3D average pooling over an input signal composed of several input planes.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.FractionalMaxPool2d.html#torch.nn.FractionalMaxPool2d" title="torch.nn.FractionalMaxPool2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.FractionalMaxPool2d</span></code></a></p></td>
<td><p>Applies a 2D fractional max pooling over an input signal composed of several input planes.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.LPPool1d.html#torch.nn.LPPool1d" title="torch.nn.LPPool1d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.LPPool1d</span></code></a></p></td>
<td><p>Applies a 1D power-average pooling over an input signal composed of several input planes.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.LPPool2d.html#torch.nn.LPPool2d" title="torch.nn.LPPool2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.LPPool2d</span></code></a></p></td>
<td><p>Applies a 2D power-average pooling over an input signal composed of several input planes.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.AdaptiveMaxPool1d.html#torch.nn.AdaptiveMaxPool1d" title="torch.nn.AdaptiveMaxPool1d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.AdaptiveMaxPool1d</span></code></a></p></td>
<td><p>Applies a 1D adaptive max pooling over an input signal composed of several input planes.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.AdaptiveMaxPool2d.html#torch.nn.AdaptiveMaxPool2d" title="torch.nn.AdaptiveMaxPool2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.AdaptiveMaxPool2d</span></code></a></p></td>
<td><p>Applies a 2D adaptive max pooling over an input signal composed of several input planes.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.AdaptiveMaxPool3d.html#torch.nn.AdaptiveMaxPool3d" title="torch.nn.AdaptiveMaxPool3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.AdaptiveMaxPool3d</span></code></a></p></td>
<td><p>Applies a 3D adaptive max pooling over an input signal composed of several input planes.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.AdaptiveAvgPool1d.html#torch.nn.AdaptiveAvgPool1d" title="torch.nn.AdaptiveAvgPool1d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.AdaptiveAvgPool1d</span></code></a></p></td>
<td><p>Applies a 1D adaptive average pooling over an input signal composed of several input planes.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.AdaptiveAvgPool2d.html#torch.nn.AdaptiveAvgPool2d" title="torch.nn.AdaptiveAvgPool2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.AdaptiveAvgPool2d</span></code></a></p></td>
<td><p>Applies a 2D adaptive average pooling over an input signal composed of several input planes.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.AdaptiveAvgPool3d.html#torch.nn.AdaptiveAvgPool3d" title="torch.nn.AdaptiveAvgPool3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.AdaptiveAvgPool3d</span></code></a></p></td>
<td><p>Applies a 3D adaptive average pooling over an input signal composed of several input planes.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="padding-layers">
<h2><a class="toc-backref" href="#id1">Padding Layers</a><a class="headerlink" href="#padding-layers" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.ReflectionPad1d.html#torch.nn.ReflectionPad1d" title="torch.nn.ReflectionPad1d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.ReflectionPad1d</span></code></a></p></td>
<td><p>Pads the input tensor using the reflection of the input boundary.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.ReflectionPad2d.html#torch.nn.ReflectionPad2d" title="torch.nn.ReflectionPad2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.ReflectionPad2d</span></code></a></p></td>
<td><p>Pads the input tensor using the reflection of the input boundary.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.ReplicationPad1d.html#torch.nn.ReplicationPad1d" title="torch.nn.ReplicationPad1d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.ReplicationPad1d</span></code></a></p></td>
<td><p>Pads the input tensor using replication of the input boundary.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.ReplicationPad2d.html#torch.nn.ReplicationPad2d" title="torch.nn.ReplicationPad2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.ReplicationPad2d</span></code></a></p></td>
<td><p>Pads the input tensor using replication of the input boundary.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.ReplicationPad3d.html#torch.nn.ReplicationPad3d" title="torch.nn.ReplicationPad3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.ReplicationPad3d</span></code></a></p></td>
<td><p>Pads the input tensor using replication of the input boundary.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.ZeroPad2d.html#torch.nn.ZeroPad2d" title="torch.nn.ZeroPad2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.ZeroPad2d</span></code></a></p></td>
<td><p>Pads the input tensor boundaries with zero.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.ConstantPad1d.html#torch.nn.ConstantPad1d" title="torch.nn.ConstantPad1d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.ConstantPad1d</span></code></a></p></td>
<td><p>Pads the input tensor boundaries with a constant value.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.ConstantPad2d.html#torch.nn.ConstantPad2d" title="torch.nn.ConstantPad2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.ConstantPad2d</span></code></a></p></td>
<td><p>Pads the input tensor boundaries with a constant value.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.ConstantPad3d.html#torch.nn.ConstantPad3d" title="torch.nn.ConstantPad3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.ConstantPad3d</span></code></a></p></td>
<td><p>Pads the input tensor boundaries with a constant value.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="non-linear-activations-weighted-sum-nonlinearity">
<h2><a class="toc-backref" href="#id1">Non-linear Activations (weighted sum, nonlinearity)</a><a class="headerlink" href="#non-linear-activations-weighted-sum-nonlinearity" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.ELU.html#torch.nn.ELU" title="torch.nn.ELU"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.ELU</span></code></a></p></td>
<td><p>Applies the element-wise function:</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.Hardshrink.html#torch.nn.Hardshrink" title="torch.nn.Hardshrink"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Hardshrink</span></code></a></p></td>
<td><p>Applies the hard shrinkage function element-wise:</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.Hardsigmoid.html#torch.nn.Hardsigmoid" title="torch.nn.Hardsigmoid"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Hardsigmoid</span></code></a></p></td>
<td><p>Applies the element-wise function:</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.Hardtanh.html#torch.nn.Hardtanh" title="torch.nn.Hardtanh"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Hardtanh</span></code></a></p></td>
<td><p>Applies the HardTanh function element-wise</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.Hardswish.html#torch.nn.Hardswish" title="torch.nn.Hardswish"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Hardswish</span></code></a></p></td>
<td><p>Applies the hardswish function, element-wise, as described in the paper:</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.LeakyReLU.html#torch.nn.LeakyReLU" title="torch.nn.LeakyReLU"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.LeakyReLU</span></code></a></p></td>
<td><p>Applies the element-wise function:</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.LogSigmoid.html#torch.nn.LogSigmoid" title="torch.nn.LogSigmoid"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.LogSigmoid</span></code></a></p></td>
<td><p>Applies the element-wise function:</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.MultiheadAttention.html#torch.nn.MultiheadAttention" title="torch.nn.MultiheadAttention"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.MultiheadAttention</span></code></a></p></td>
<td><p>Allows the model to jointly attend to information from different representation subspaces.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.PReLU.html#torch.nn.PReLU" title="torch.nn.PReLU"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.PReLU</span></code></a></p></td>
<td><p>Applies the element-wise function:</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.ReLU.html#torch.nn.ReLU" title="torch.nn.ReLU"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.ReLU</span></code></a></p></td>
<td><p>Applies the rectified linear unit function element-wise:</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.ReLU6.html#torch.nn.ReLU6" title="torch.nn.ReLU6"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.ReLU6</span></code></a></p></td>
<td><p>Applies the element-wise function:</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.RReLU.html#torch.nn.RReLU" title="torch.nn.RReLU"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.RReLU</span></code></a></p></td>
<td><p>Applies the randomized leaky rectified liner unit function, element-wise, as described in the paper:</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.SELU.html#torch.nn.SELU" title="torch.nn.SELU"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.SELU</span></code></a></p></td>
<td><p>Applied element-wise, as:</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.CELU.html#torch.nn.CELU" title="torch.nn.CELU"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.CELU</span></code></a></p></td>
<td><p>Applies the element-wise function:</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.GELU.html#torch.nn.GELU" title="torch.nn.GELU"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.GELU</span></code></a></p></td>
<td><p>Applies the Gaussian Error Linear Units function:</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.Sigmoid.html#torch.nn.Sigmoid" title="torch.nn.Sigmoid"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Sigmoid</span></code></a></p></td>
<td><p>Applies the element-wise function:</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.SiLU.html#torch.nn.SiLU" title="torch.nn.SiLU"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.SiLU</span></code></a></p></td>
<td><p>Applies the silu function, element-wise.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.Softplus.html#torch.nn.Softplus" title="torch.nn.Softplus"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Softplus</span></code></a></p></td>
<td><p>Applies the element-wise function:</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.Softshrink.html#torch.nn.Softshrink" title="torch.nn.Softshrink"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Softshrink</span></code></a></p></td>
<td><p>Applies the soft shrinkage function elementwise:</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.Softsign.html#torch.nn.Softsign" title="torch.nn.Softsign"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Softsign</span></code></a></p></td>
<td><p>Applies the element-wise function:</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.Tanh.html#torch.nn.Tanh" title="torch.nn.Tanh"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Tanh</span></code></a></p></td>
<td><p>Applies the element-wise function:</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.Tanhshrink.html#torch.nn.Tanhshrink" title="torch.nn.Tanhshrink"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Tanhshrink</span></code></a></p></td>
<td><p>Applies the element-wise function:</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.Threshold.html#torch.nn.Threshold" title="torch.nn.Threshold"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Threshold</span></code></a></p></td>
<td><p>Thresholds each element of the input Tensor.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="non-linear-activations-other">
<h2><a class="toc-backref" href="#id1">Non-linear Activations (other)</a><a class="headerlink" href="#non-linear-activations-other" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.Softmin.html#torch.nn.Softmin" title="torch.nn.Softmin"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Softmin</span></code></a></p></td>
<td><p>Applies the Softmin function to an n-dimensional input Tensor rescaling them so that the elements of the n-dimensional output Tensor lie in the range <cite>[0, 1]</cite> and sum to 1.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.Softmax.html#torch.nn.Softmax" title="torch.nn.Softmax"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Softmax</span></code></a></p></td>
<td><p>Applies the Softmax function to an n-dimensional input Tensor rescaling them so that the elements of the n-dimensional output Tensor lie in the range [0,1] and sum to 1.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.Softmax2d.html#torch.nn.Softmax2d" title="torch.nn.Softmax2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Softmax2d</span></code></a></p></td>
<td><p>Applies SoftMax over features to each spatial location.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.LogSoftmax.html#torch.nn.LogSoftmax" title="torch.nn.LogSoftmax"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.LogSoftmax</span></code></a></p></td>
<td><p>Applies the <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>log</mi><mo></mo><mo stretchy="false">(</mo><mtext>Softmax</mtext><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\log(\text{Softmax}(x))</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mopen">(</span><span class="mord text"><span class="mord">Softmax</span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mclose">)</span></span></span></span>
</span> function to an n-dimensional input Tensor.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.AdaptiveLogSoftmaxWithLoss.html#torch.nn.AdaptiveLogSoftmaxWithLoss" title="torch.nn.AdaptiveLogSoftmaxWithLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.AdaptiveLogSoftmaxWithLoss</span></code></a></p></td>
<td><p>Efficient softmax approximation as described in <a class="reference external" href="https://arxiv.org/abs/1609.04309">Efficient softmax approximation for GPUs by Edouard Grave, Armand Joulin, Moustapha Cissé, David Grangier, and Hervé Jégou</a>.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="normalization-layers">
<h2><a class="toc-backref" href="#id1">Normalization Layers</a><a class="headerlink" href="#normalization-layers" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.BatchNorm1d.html#torch.nn.BatchNorm1d" title="torch.nn.BatchNorm1d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.BatchNorm1d</span></code></a></p></td>
<td><p>Applies Batch Normalization over a 2D or 3D input (a mini-batch of 1D inputs with optional additional channel dimension) as described in the paper <a class="reference external" href="https://arxiv.org/abs/1502.03167">Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift</a> .</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.BatchNorm2d.html#torch.nn.BatchNorm2d" title="torch.nn.BatchNorm2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.BatchNorm2d</span></code></a></p></td>
<td><p>Applies Batch Normalization over a 4D input (a mini-batch of 2D inputs with additional channel dimension) as described in the paper <a class="reference external" href="https://arxiv.org/abs/1502.03167">Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift</a> .</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.BatchNorm3d.html#torch.nn.BatchNorm3d" title="torch.nn.BatchNorm3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.BatchNorm3d</span></code></a></p></td>
<td><p>Applies Batch Normalization over a 5D input (a mini-batch of 3D inputs with additional channel dimension) as described in the paper <a class="reference external" href="https://arxiv.org/abs/1502.03167">Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift</a> .</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.GroupNorm.html#torch.nn.GroupNorm" title="torch.nn.GroupNorm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.GroupNorm</span></code></a></p></td>
<td><p>Applies Group Normalization over a mini-batch of inputs as described in the paper <a class="reference external" href="https://arxiv.org/abs/1803.08494">Group Normalization</a></p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.SyncBatchNorm.html#torch.nn.SyncBatchNorm" title="torch.nn.SyncBatchNorm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.SyncBatchNorm</span></code></a></p></td>
<td><p>Applies Batch Normalization over a N-Dimensional input (a mini-batch of [N-2]D inputs with additional channel dimension) as described in the paper <a class="reference external" href="https://arxiv.org/abs/1502.03167">Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift</a> .</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.InstanceNorm1d.html#torch.nn.InstanceNorm1d" title="torch.nn.InstanceNorm1d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.InstanceNorm1d</span></code></a></p></td>
<td><p>Applies Instance Normalization over a 3D input (a mini-batch of 1D inputs with optional additional channel dimension) as described in the paper <a class="reference external" href="https://arxiv.org/abs/1607.08022">Instance Normalization: The Missing Ingredient for Fast Stylization</a>.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.InstanceNorm2d.html#torch.nn.InstanceNorm2d" title="torch.nn.InstanceNorm2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.InstanceNorm2d</span></code></a></p></td>
<td><p>Applies Instance Normalization over a 4D input (a mini-batch of 2D inputs with additional channel dimension) as described in the paper <a class="reference external" href="https://arxiv.org/abs/1607.08022">Instance Normalization: The Missing Ingredient for Fast Stylization</a>.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.InstanceNorm3d.html#torch.nn.InstanceNorm3d" title="torch.nn.InstanceNorm3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.InstanceNorm3d</span></code></a></p></td>
<td><p>Applies Instance Normalization over a 5D input (a mini-batch of 3D inputs with additional channel dimension) as described in the paper <a class="reference external" href="https://arxiv.org/abs/1607.08022">Instance Normalization: The Missing Ingredient for Fast Stylization</a>.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.LayerNorm.html#torch.nn.LayerNorm" title="torch.nn.LayerNorm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.LayerNorm</span></code></a></p></td>
<td><p>Applies Layer Normalization over a mini-batch of inputs as described in the paper <a class="reference external" href="https://arxiv.org/abs/1607.06450">Layer Normalization</a></p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.LocalResponseNorm.html#torch.nn.LocalResponseNorm" title="torch.nn.LocalResponseNorm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.LocalResponseNorm</span></code></a></p></td>
<td><p>Applies local response normalization over an input signal composed of several input planes, where channels occupy the second dimension.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="recurrent-layers">
<h2><a class="toc-backref" href="#id1">Recurrent Layers</a><a class="headerlink" href="#recurrent-layers" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.RNNBase.html#torch.nn.RNNBase" title="torch.nn.RNNBase"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.RNNBase</span></code></a></p></td>
<td><p></p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.RNN.html#torch.nn.RNN" title="torch.nn.RNN"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.RNN</span></code></a></p></td>
<td><p>Applies a multi-layer Elman RNN with <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>tanh</mi><mo></mo></mrow><annotation encoding="application/x-tex">\tanh</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mop">tanh</span></span></span></span>
</span> or <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>ReLU</mtext></mrow><annotation encoding="application/x-tex">\text{ReLU}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord text"><span class="mord">ReLU</span></span></span></span></span>
</span> non-linearity to an input sequence.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.LSTM.html#torch.nn.LSTM" title="torch.nn.LSTM"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.LSTM</span></code></a></p></td>
<td><p>Applies a multi-layer long short-term memory (LSTM) RNN to an input sequence.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.GRU.html#torch.nn.GRU" title="torch.nn.GRU"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.GRU</span></code></a></p></td>
<td><p>Applies a multi-layer gated recurrent unit (GRU) RNN to an input sequence.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.RNNCell.html#torch.nn.RNNCell" title="torch.nn.RNNCell"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.RNNCell</span></code></a></p></td>
<td><p>An Elman RNN cell with tanh or ReLU non-linearity.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.LSTMCell.html#torch.nn.LSTMCell" title="torch.nn.LSTMCell"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.LSTMCell</span></code></a></p></td>
<td><p>A long short-term memory (LSTM) cell.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.GRUCell.html#torch.nn.GRUCell" title="torch.nn.GRUCell"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.GRUCell</span></code></a></p></td>
<td><p>A gated recurrent unit (GRU) cell</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="transformer-layers">
<h2><a class="toc-backref" href="#id1">Transformer Layers</a><a class="headerlink" href="#transformer-layers" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.Transformer.html#torch.nn.Transformer" title="torch.nn.Transformer"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Transformer</span></code></a></p></td>
<td><p>A transformer model.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.TransformerEncoder.html#torch.nn.TransformerEncoder" title="torch.nn.TransformerEncoder"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.TransformerEncoder</span></code></a></p></td>
<td><p>TransformerEncoder is a stack of N encoder layers</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.TransformerDecoder.html#torch.nn.TransformerDecoder" title="torch.nn.TransformerDecoder"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.TransformerDecoder</span></code></a></p></td>
<td><p>TransformerDecoder is a stack of N decoder layers</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.TransformerEncoderLayer.html#torch.nn.TransformerEncoderLayer" title="torch.nn.TransformerEncoderLayer"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.TransformerEncoderLayer</span></code></a></p></td>
<td><p>TransformerEncoderLayer is made up of self-attn and feedforward network.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.TransformerDecoderLayer.html#torch.nn.TransformerDecoderLayer" title="torch.nn.TransformerDecoderLayer"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.TransformerDecoderLayer</span></code></a></p></td>
<td><p>TransformerDecoderLayer is made up of self-attn, multi-head-attn and feedforward network.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="linear-layers">
<h2><a class="toc-backref" href="#id1">Linear Layers</a><a class="headerlink" href="#linear-layers" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.Identity.html#torch.nn.Identity" title="torch.nn.Identity"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Identity</span></code></a></p></td>
<td><p>A placeholder identity operator that is argument-insensitive.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.Linear.html#torch.nn.Linear" title="torch.nn.Linear"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Linear</span></code></a></p></td>
<td><p>Applies a linear transformation to the incoming data: <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi><mo>=</mo><mi>x</mi><msup><mi>A</mi><mi>T</mi></msup><mo>+</mo><mi>b</mi></mrow><annotation encoding="application/x-tex">y = xA^T + b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.924661em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">x</span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal">b</span></span></span></span>
</span></p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.Bilinear.html#torch.nn.Bilinear" title="torch.nn.Bilinear"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Bilinear</span></code></a></p></td>
<td><p>Applies a bilinear transformation to the incoming data: <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi><mo>=</mo><msubsup><mi>x</mi><mn>1</mn><mi>T</mi></msubsup><mi>A</mi><msub><mi>x</mi><mn>2</mn></msub><mo>+</mo><mi>b</mi></mrow><annotation encoding="application/x-tex">y = x_1^T A x_2 + b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.0894389999999998em;vertical-align:-0.24810799999999997em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8413309999999999em;"><span style="top:-2.4518920000000004em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.24810799999999997em;"><span></span></span></span></span></span></span><span class="mord mathnormal">A</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal">b</span></span></span></span>
</span></p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.LazyLinear.html#torch.nn.LazyLinear" title="torch.nn.LazyLinear"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.LazyLinear</span></code></a></p></td>
<td><p>A <a class="reference internal" href="generated/torch.nn.Linear.html#torch.nn.Linear" title="torch.nn.Linear"><code class="xref py py-class docutils literal notranslate"><span class="pre">torch.nn.Linear</span></code></a> module with lazy initialization.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="dropout-layers">
<h2><a class="toc-backref" href="#id1">Dropout Layers</a><a class="headerlink" href="#dropout-layers" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.Dropout.html#torch.nn.Dropout" title="torch.nn.Dropout"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Dropout</span></code></a></p></td>
<td><p>During training, randomly zeroes some of the elements of the input tensor with probability <code class="xref py py-attr docutils literal notranslate"><span class="pre">p</span></code> using samples from a Bernoulli distribution.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.Dropout2d.html#torch.nn.Dropout2d" title="torch.nn.Dropout2d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Dropout2d</span></code></a></p></td>
<td><p>Randomly zero out entire channels (a channel is a 2D feature map, e.g., the <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span></span></span></span>
</span>-th channel of the <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span></span></span></span>
</span>-th sample in the batched input is a 2D tensor <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>input</mtext><mo stretchy="false">[</mo><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">\text{input}[i, j]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord text"><span class="mord">input</span></span><span class="mopen">[</span><span class="mord mathnormal">i</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span><span class="mclose">]</span></span></span></span>
</span>).</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.Dropout3d.html#torch.nn.Dropout3d" title="torch.nn.Dropout3d"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Dropout3d</span></code></a></p></td>
<td><p>Randomly zero out entire channels (a channel is a 3D feature map, e.g., the <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span></span></span></span>
</span>-th channel of the <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span></span></span></span>
</span>-th sample in the batched input is a 3D tensor <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>input</mtext><mo stretchy="false">[</mo><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">\text{input}[i, j]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord text"><span class="mord">input</span></span><span class="mopen">[</span><span class="mord mathnormal">i</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span><span class="mclose">]</span></span></span></span>
</span>).</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.AlphaDropout.html#torch.nn.AlphaDropout" title="torch.nn.AlphaDropout"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.AlphaDropout</span></code></a></p></td>
<td><p>Applies Alpha Dropout over the input.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="sparse-layers">
<h2><a class="toc-backref" href="#id1">Sparse Layers</a><a class="headerlink" href="#sparse-layers" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.Embedding.html#torch.nn.Embedding" title="torch.nn.Embedding"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.Embedding</span></code></a></p></td>
<td><p>A simple lookup table that stores embeddings of a fixed dictionary and size.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.EmbeddingBag.html#torch.nn.EmbeddingBag" title="torch.nn.EmbeddingBag"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.EmbeddingBag</span></code></a></p></td>
<td><p>Computes sums or means of ‘bags’ of embeddings, without instantiating the intermediate embeddings.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="distance-functions">
<h2><a class="toc-backref" href="#id1">Distance Functions</a><a class="headerlink" href="#distance-functions" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.CosineSimilarity.html#torch.nn.CosineSimilarity" title="torch.nn.CosineSimilarity"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.CosineSimilarity</span></code></a></p></td>
<td><p>Returns cosine similarity between <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">x_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>
</span> and <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">x_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>
</span>, computed along dim.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.PairwiseDistance.html#torch.nn.PairwiseDistance" title="torch.nn.PairwiseDistance"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.PairwiseDistance</span></code></a></p></td>
<td><p>Computes the batchwise pairwise distance between vectors <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>v</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">v_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>
</span>, <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>v</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">v_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>
</span> using the p-norm:</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="loss-functions">
<h2><a class="toc-backref" href="#id1">Loss Functions</a><a class="headerlink" href="#loss-functions" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.L1Loss.html#torch.nn.L1Loss" title="torch.nn.L1Loss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.L1Loss</span></code></a></p></td>
<td><p>Creates a criterion that measures the mean absolute error (MAE) between each element in the input <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span>
</span> and target <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span>
</span>.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.MSELoss.html#torch.nn.MSELoss" title="torch.nn.MSELoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.MSELoss</span></code></a></p></td>
<td><p>Creates a criterion that measures the mean squared error (squared L2 norm) between each element in the input <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span>
</span> and target <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span>
</span>.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.CrossEntropyLoss.html#torch.nn.CrossEntropyLoss" title="torch.nn.CrossEntropyLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.CrossEntropyLoss</span></code></a></p></td>
<td><p>This criterion combines <a class="reference internal" href="generated/torch.nn.LogSoftmax.html#torch.nn.LogSoftmax" title="torch.nn.LogSoftmax"><code class="xref py py-class docutils literal notranslate"><span class="pre">LogSoftmax</span></code></a> and <a class="reference internal" href="generated/torch.nn.NLLLoss.html#torch.nn.NLLLoss" title="torch.nn.NLLLoss"><code class="xref py py-class docutils literal notranslate"><span class="pre">NLLLoss</span></code></a> in one single class.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.CTCLoss.html#torch.nn.CTCLoss" title="torch.nn.CTCLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.CTCLoss</span></code></a></p></td>
<td><p>The Connectionist Temporal Classification loss.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.NLLLoss.html#torch.nn.NLLLoss" title="torch.nn.NLLLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.NLLLoss</span></code></a></p></td>
<td><p>The negative log likelihood loss.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.PoissonNLLLoss.html#torch.nn.PoissonNLLLoss" title="torch.nn.PoissonNLLLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.PoissonNLLLoss</span></code></a></p></td>
<td><p>Negative log likelihood loss with Poisson distribution of target.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.GaussianNLLLoss.html#torch.nn.GaussianNLLLoss" title="torch.nn.GaussianNLLLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.GaussianNLLLoss</span></code></a></p></td>
<td><p>Gaussian negative log likelihood loss.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.KLDivLoss.html#torch.nn.KLDivLoss" title="torch.nn.KLDivLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.KLDivLoss</span></code></a></p></td>
<td><p>The Kullback-Leibler divergence loss measure</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.BCELoss.html#torch.nn.BCELoss" title="torch.nn.BCELoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.BCELoss</span></code></a></p></td>
<td><p>Creates a criterion that measures the Binary Cross Entropy between the target and the output:</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.BCEWithLogitsLoss.html#torch.nn.BCEWithLogitsLoss" title="torch.nn.BCEWithLogitsLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.BCEWithLogitsLoss</span></code></a></p></td>
<td><p>This loss combines a <cite>Sigmoid</cite> layer and the <cite>BCELoss</cite> in one single class.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.MarginRankingLoss.html#torch.nn.MarginRankingLoss" title="torch.nn.MarginRankingLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.MarginRankingLoss</span></code></a></p></td>
<td><p>Creates a criterion that measures the loss given inputs <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mn>1</mn></mrow><annotation encoding="application/x-tex">x1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord mathnormal">x</span><span class="mord">1</span></span></span></span>
</span>, <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mn>2</mn></mrow><annotation encoding="application/x-tex">x2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord mathnormal">x</span><span class="mord">2</span></span></span></span>
</span>, two 1D mini-batch <cite>Tensors</cite>, and a label 1D mini-batch tensor <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span>
</span> (containing 1 or -1).</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.HingeEmbeddingLoss.html#torch.nn.HingeEmbeddingLoss" title="torch.nn.HingeEmbeddingLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.HingeEmbeddingLoss</span></code></a></p></td>
<td><p>Measures the loss given an input tensor <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span>
</span> and a labels tensor <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span>
</span> (containing 1 or -1).</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.MultiLabelMarginLoss.html#torch.nn.MultiLabelMarginLoss" title="torch.nn.MultiLabelMarginLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.MultiLabelMarginLoss</span></code></a></p></td>
<td><p>Creates a criterion that optimizes a multi-class multi-classification hinge loss (margin-based loss) between input <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span>
</span> (a 2D mini-batch <cite>Tensor</cite>) and output <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span>
</span> (which is a 2D <cite>Tensor</cite> of target class indices).</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.SmoothL1Loss.html#torch.nn.SmoothL1Loss" title="torch.nn.SmoothL1Loss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.SmoothL1Loss</span></code></a></p></td>
<td><p>Creates a criterion that uses a squared term if the absolute element-wise error falls below beta and an L1 term otherwise.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.SoftMarginLoss.html#torch.nn.SoftMarginLoss" title="torch.nn.SoftMarginLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.SoftMarginLoss</span></code></a></p></td>
<td><p>Creates a criterion that optimizes a two-class classification logistic loss between input tensor <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span>
</span> and target tensor <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span>
</span> (containing 1 or -1).</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.MultiLabelSoftMarginLoss.html#torch.nn.MultiLabelSoftMarginLoss" title="torch.nn.MultiLabelSoftMarginLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.MultiLabelSoftMarginLoss</span></code></a></p></td>
<td><p>Creates a criterion that optimizes a multi-label one-versus-all loss based on max-entropy, between input <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span>
</span> and target <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span>
</span> of size <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>N</mi><mo separator="true">,</mo><mi>C</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(N, C)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mclose">)</span></span></span></span>
</span>.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.CosineEmbeddingLoss.html#torch.nn.CosineEmbeddingLoss" title="torch.nn.CosineEmbeddingLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.CosineEmbeddingLoss</span></code></a></p></td>
<td><p>Creates a criterion that measures the loss given input tensors <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">x_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>
</span>, <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">x_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>
</span> and a <cite>Tensor</cite> label <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span>
</span> with values 1 or -1.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.MultiMarginLoss.html#torch.nn.MultiMarginLoss" title="torch.nn.MultiMarginLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.MultiMarginLoss</span></code></a></p></td>
<td><p>Creates a criterion that optimizes a multi-class classification hinge loss (margin-based loss) between input <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span>
</span> (a 2D mini-batch <cite>Tensor</cite>) and output <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span>
</span> (which is a 1D tensor of target class indices, <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn><mo>≤</mo><mi>y</mi><mo>≤</mo><mtext>x.size</mtext><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">0 \leq y \leq \text{x.size}(1)-1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.78041em;vertical-align:-0.13597em;"></span><span class="mord">0</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.8304100000000001em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord text"><span class="mord">x.size</span></span><span class="mopen">(</span><span class="mord">1</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span>
</span>):</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.TripletMarginLoss.html#torch.nn.TripletMarginLoss" title="torch.nn.TripletMarginLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.TripletMarginLoss</span></code></a></p></td>
<td><p>Creates a criterion that measures the triplet loss given an input tensors <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mn>1</mn></mrow><annotation encoding="application/x-tex">x1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord mathnormal">x</span><span class="mord">1</span></span></span></span>
</span>, <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mn>2</mn></mrow><annotation encoding="application/x-tex">x2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord mathnormal">x</span><span class="mord">2</span></span></span></span>
</span>, <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mn>3</mn></mrow><annotation encoding="application/x-tex">x3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord mathnormal">x</span><span class="mord">3</span></span></span></span>
</span> and a margin with a value greater than <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span></span></span></span>
</span>.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/torch.nn.TripletMarginWithDistanceLoss.html#torch.nn.TripletMarginWithDistanceLoss" title="torch.nn.TripletMarginWithDistanceLoss"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.TripletMarginWithDistanceLoss</span></code></a></p></td>
<td><p>Creates a criterion that measures the triplet loss given input tensors <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi></mrow><annotation encoding="application/x-tex">a</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">a</span></span></span></span>
</span>, <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi></mrow><annotation encoding="application/x-tex">p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal">p</span></span></span></span>
</span>, and <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span>
</span> (representing anchor, positive, and negative examples, respectively), and a nonnegative, real-valued function (“distance function”) used to compute the relationship between the anchor and positive example (“positive distance”) and the anchor and negative example (“negative distance”).</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="vision-layers">
<h2><a class="toc-backref" href="#id1">Vision Layers</a><a class="headerlink" href="#vision-layers" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils colwidths-auto align-default">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/torch.nn.PixelShuffle.html#torch.nn.PixelShuffle" title="torch.nn.PixelShuffle"><code class="xref py py-obj docutils literal notranslate"><span class="pre">nn.PixelShuffle</span></code></a></p></td>
<td><p>Rearranges elements in a tensor of shape <span class="math"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mo>∗</mo><mo separator="true">,</mo><mi>C</mi><mo>×</mo><msup><mi>r</mi><mn>2</mn></msup><mo separator="true">,</mo><mi>H</mi><mo separator="true">,</mo><mi>W</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(*, C \times r^2, H, W)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">∗</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mclose">)</span></span></span></span>