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<h1>Capsule Networks</h1>
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<p>This is a <a href="https://pytorch.org">PyTorch</a> implementation/tutorial of
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<a href="https://papers.labml.ai/paper/1710.09829">Dynamic Routing Between Capsules</a>.</p>
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<p>Capsule network is a neural network architecture that embeds features
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as capsules and routes them with a voting mechanism to next layer of capsules.</p>
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<p>Unlike in other implementations of models, we’ve included a sample, because
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it is difficult to understand some concepts with just the modules.
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<a href="mnist.html">This is the annotated code for a model that uses capsules to classify MNIST dataset</a></p>
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<p>This file holds the implementations of the core modules of Capsule Networks.</p>
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<p>I used <a href="https://github.com/jindongwang/Pytorch-CapsuleNet">jindongwang/Pytorch-CapsuleNet</a> to clarify some
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confusions I had with the paper.</p>
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<p>Here’s a notebook for training a Capsule Network on MNIST dataset.</p>
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<p><a href="https://colab.research.google.com/github/labmlai/annotated_deep_learning_paper_implementations/blob/master/labml_nn/capsule_networks/mnist.ipynb"><img alt="Open In Colab" src="https://colab.research.google.com/assets/colab-badge.svg" /></a>
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<a href="https://app.labml.ai/run/e7c08e08586711ebb3e30242ac1c0002"><img alt="View Run" src="https://img.shields.io/badge/labml-experiment-brightgreen" /></a></p>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">33</span><span></span><span class="kn">import</span> <span class="nn">torch.nn</span> <span class="k">as</span> <span class="nn">nn</span>
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<span class="lineno">34</span><span class="kn">import</span> <span class="nn">torch.nn.functional</span> <span class="k">as</span> <span class="nn">F</span>
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<span class="lineno">35</span><span class="kn">import</span> <span class="nn">torch.utils.data</span>
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<span class="lineno">36</span>
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<span class="lineno">37</span><span class="kn">from</span> <span class="nn">labml_helpers.module</span> <span class="kn">import</span> <span class="n">Module</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-1'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-1'>#</a>
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</div>
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<h2>Squash</h2>
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<p>This is <strong>squashing</strong> function from paper, given by equation $(1)$.</p>
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<p>
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<script type="math/tex; mode=display">\mathbf{v}_j = \frac{{\lVert \mathbf{s}_j \rVert}^2}{1 + {\lVert \mathbf{s}_j \rVert}^2}
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\frac{\mathbf{s}_j}{\lVert \mathbf{s}_j \rVert}</script>
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</p>
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<p>$\frac{\mathbf{s}_j}{\lVert \mathbf{s}_j \rVert}$
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normalizes the length of all the capsules, whilst
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$\frac{{\lVert \mathbf{s}_j \rVert}^2}{1 + {\lVert \mathbf{s}_j \rVert}^2}$
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shrinks the capsules that have a length smaller than one .</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">40</span><span class="k">class</span> <span class="nc">Squash</span><span class="p">(</span><span class="n">Module</span><span class="p">):</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-2'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-2'>#</a>
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</div>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">55</span> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">epsilon</span><span class="o">=</span><span class="mf">1e-8</span><span class="p">):</span>
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<span class="lineno">56</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
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<span class="lineno">57</span> <span class="bp">self</span><span class="o">.</span><span class="n">epsilon</span> <span class="o">=</span> <span class="n">epsilon</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-3'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-3'>#</a>
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</div>
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<p>The shape of <code>s</code> is <code>[batch_size, n_capsules, n_features]</code></p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">59</span> <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">s</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">):</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-4'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-4'>#</a>
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</div>
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<p>${\lVert \mathbf{s}_j \rVert}^2$</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">65</span> <span class="n">s2</span> <span class="o">=</span> <span class="p">(</span><span class="n">s</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">dim</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-5'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-5'>#</a>
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</div>
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<p>We add an epsilon when calculating $\lVert \mathbf{s}_j \rVert$ to make sure it doesn’t become zero.
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If this becomes zero it starts giving out <code>nan</code> values and training fails.
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<script type="math/tex; mode=display">\mathbf{v}_j = \frac{{\lVert \mathbf{s}_j \rVert}^2}{1 + {\lVert \mathbf{s}_j \rVert}^2}
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\frac{\mathbf{s}_j}{\sqrt{{\lVert \mathbf{s}_j \rVert}^2 + \epsilon}}</script>
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</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">71</span> <span class="k">return</span> <span class="p">(</span><span class="n">s2</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">s2</span><span class="p">))</span> <span class="o">*</span> <span class="p">(</span><span class="n">s</span> <span class="o">/</span> <span class="n">torch</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">s2</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">epsilon</span><span class="p">))</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-6'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-6'>#</a>
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</div>
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<h2>Routing Algorithm</h2>
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<p>This is the routing mechanism described in the paper.
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You can use multiple routing layers in your models.</p>
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<p>This combines calculating $\mathbf{s}_j$ for this layer and
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the routing algorithm described in <em>Procedure 1</em>.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">74</span><span class="k">class</span> <span class="nc">Router</span><span class="p">(</span><span class="n">Module</span><span class="p">):</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-7'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-7'>#</a>
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</div>
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<p><code>in_caps</code> is the number of capsules, and <code>in_d</code> is the number of features per capsule from the layer below.
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<code>out_caps</code> and <code>out_d</code> are the same for this layer.</p>
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<p><code>iterations</code> is the number of routing iterations, symbolized by $r$ in the paper.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">85</span> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">in_caps</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">out_caps</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">in_d</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">out_d</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">iterations</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-8'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-8'>#</a>
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</div>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">92</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
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<span class="lineno">93</span> <span class="bp">self</span><span class="o">.</span><span class="n">in_caps</span> <span class="o">=</span> <span class="n">in_caps</span>
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<span class="lineno">94</span> <span class="bp">self</span><span class="o">.</span><span class="n">out_caps</span> <span class="o">=</span> <span class="n">out_caps</span>
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<span class="lineno">95</span> <span class="bp">self</span><span class="o">.</span><span class="n">iterations</span> <span class="o">=</span> <span class="n">iterations</span>
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<span class="lineno">96</span> <span class="bp">self</span><span class="o">.</span><span class="n">softmax</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Softmax</span><span class="p">(</span><span class="n">dim</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
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<span class="lineno">97</span> <span class="bp">self</span><span class="o">.</span><span class="n">squash</span> <span class="o">=</span> <span class="n">Squash</span><span class="p">()</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-9'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-9'>#</a>
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</div>
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<p>This is the weight matrix $\mathbf{W}_{ij}$. It maps each capsule in the
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lower layer to each capsule in this layer</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">101</span> <span class="bp">self</span><span class="o">.</span><span class="n">weight</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Parameter</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">in_caps</span><span class="p">,</span> <span class="n">out_caps</span><span class="p">,</span> <span class="n">in_d</span><span class="p">,</span> <span class="n">out_d</span><span class="p">),</span> <span class="n">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-10'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-10'>#</a>
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</div>
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<p>The shape of <code>u</code> is <code>[batch_size, n_capsules, n_features]</code>.
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These are the capsules from the lower layer.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">103</span> <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">u</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">):</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-11'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-11'>#</a>
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</div>
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<p>
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<script type="math/tex; mode=display">\hat{\mathbf{u}}_{j|i} = \mathbf{W}_{ij} \mathbf{u}_i</script>
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Here $j$ is used to index capsules in this layer, whilst $i$ is
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used to index capsules in the layer below (previous).</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">112</span> <span class="n">u_hat</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="s1">'ijnm,bin->bijm'</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">weight</span><span class="p">,</span> <span class="n">u</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-12'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-12'>#</a>
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</div>
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<p>Initial logits $b_{ij}$ are the log prior probabilities that capsule $i$
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should be coupled with $j$.
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We initialize these at zero</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">117</span> <span class="n">b</span> <span class="o">=</span> <span class="n">u</span><span class="o">.</span><span class="n">new_zeros</span><span class="p">(</span><span class="n">u</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">in_caps</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">out_caps</span><span class="p">)</span>
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<span class="lineno">118</span>
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<span class="lineno">119</span> <span class="n">v</span> <span class="o">=</span> <span class="kc">None</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-13'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-13'>#</a>
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</div>
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<p>Iterate</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">122</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">iterations</span><span class="p">):</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-14'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-14'>#</a>
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</div>
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<p>routing softmax <script type="math/tex; mode=display">c_{ij} = \frac{\exp({b_{ij}})}{\sum_k\exp({b_{ik}})}</script>
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</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">124</span> <span class="n">c</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">softmax</span><span class="p">(</span><span class="n">b</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-15'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-15'>#</a>
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</div>
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<p>
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<script type="math/tex; mode=display">\mathbf{s}_j = \sum_i{c_{ij} \hat{\mathbf{u}}_{j|i}}</script>
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</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">126</span> <span class="n">s</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="s1">'bij,bijm->bjm'</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">u_hat</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-16'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-16'>#</a>
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</div>
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<p>
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<script type="math/tex; mode=display">\mathbf{v}_j = squash(\mathbf{s}_j)</script>
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</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">128</span> <span class="n">v</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">squash</span><span class="p">(</span><span class="n">s</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-17'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-17'>#</a>
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</div>
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<p>
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<script type="math/tex; mode=display">a_{ij} = \mathbf{v}_j \cdot \hat{\mathbf{u}}_{j|i}</script>
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</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">130</span> <span class="n">a</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="s1">'bjm,bijm->bij'</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">u_hat</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-18'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-18'>#</a>
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</div>
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<p>
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<script type="math/tex; mode=display">b_{ij} \gets b_{ij} + \mathbf{v}_j \cdot \hat{\mathbf{u}}_{j|i}</script>
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</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">132</span> <span class="n">b</span> <span class="o">=</span> <span class="n">b</span> <span class="o">+</span> <span class="n">a</span>
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<span class="lineno">133</span>
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<span class="lineno">134</span> <span class="k">return</span> <span class="n">v</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-19'>
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<div class='docs doc-strings'>
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<div class='section-link'>
|
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<a href='#section-19'>#</a>
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</div>
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<h2>Margin loss for class existence</h2>
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<p>A separate margin loss is used for each output capsule and the total loss is the sum of them.
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The length of each output capsule is the probability that class is present in the input.</p>
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<p>Loss for each output capsule or class $k$ is,
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<script type="math/tex; mode=display">\mathcal{L}_k = T_k \max(0, m^{+} - \lVert\mathbf{v}_k\rVert)^2 +
|
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\lambda (1 - T_k) \max(0, \lVert\mathbf{v}_k\rVert - m^{-})^2</script>
|
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</p>
|
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<p>$T_k$ is $1$ if the class $k$ is present and $0$ otherwise.
|
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The first component of the loss is $0$ when the class is not present,
|
|
and the second component is $0$ if the class is present.
|
|
The $\max(0, x)$ is used to avoid predictions going to extremes.
|
|
$m^{+}$ is set to be $0.9$ and $m^{-}$ to be $0.1$ in the paper.</p>
|
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<p>The $\lambda$ down-weighting is used to stop the length of all capsules from
|
|
falling during the initial phase of training.</p>
|
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</div>
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<div class='code'>
|
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<div class="highlight"><pre><span class="lineno">137</span><span class="k">class</span> <span class="nc">MarginLoss</span><span class="p">(</span><span class="n">Module</span><span class="p">):</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-20'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-20'>#</a>
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</div>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">157</span> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span> <span class="n">n_labels</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">lambda_</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.5</span><span class="p">,</span> <span class="n">m_positive</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.9</span><span class="p">,</span> <span class="n">m_negative</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.1</span><span class="p">):</span>
|
|
<span class="lineno">158</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
|
|
<span class="lineno">159</span>
|
|
<span class="lineno">160</span> <span class="bp">self</span><span class="o">.</span><span class="n">m_negative</span> <span class="o">=</span> <span class="n">m_negative</span>
|
|
<span class="lineno">161</span> <span class="bp">self</span><span class="o">.</span><span class="n">m_positive</span> <span class="o">=</span> <span class="n">m_positive</span>
|
|
<span class="lineno">162</span> <span class="bp">self</span><span class="o">.</span><span class="n">lambda_</span> <span class="o">=</span> <span class="n">lambda_</span>
|
|
<span class="lineno">163</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_labels</span> <span class="o">=</span> <span class="n">n_labels</span></pre></div>
|
|
</div>
|
|
</div>
|
|
<div class='section' id='section-21'>
|
|
<div class='docs doc-strings'>
|
|
<div class='section-link'>
|
|
<a href='#section-21'>#</a>
|
|
</div>
|
|
<p><code>v</code>, $\mathbf{v}_j$ are the squashed output capsules.
|
|
This has shape <code>[batch_size, n_labels, n_features]</code>; that is, there is a capsule for each label.</p>
|
|
<p><code>labels</code> are the labels, and has shape <code>[batch_size]</code>.</p>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">165</span> <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">v</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span> <span class="n">labels</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">):</span></pre></div>
|
|
</div>
|
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</div>
|
|
<div class='section' id='section-22'>
|
|
<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-22'>#</a>
|
|
</div>
|
|
<p>
|
|
<script type="math/tex; mode=display">\lVert \mathbf{v}_j \rVert</script>
|
|
</p>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">173</span> <span class="n">v_norm</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">sqrt</span><span class="p">((</span><span class="n">v</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">dim</span><span class="o">=-</span><span class="mi">1</span><span class="p">))</span></pre></div>
|
|
</div>
|
|
</div>
|
|
<div class='section' id='section-23'>
|
|
<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-23'>#</a>
|
|
</div>
|
|
<p>
|
|
<script type="math/tex; mode=display">\mathcal{L}</script>
|
|
<code>labels</code> is one-hot encoded labels of shape <code>[batch_size, n_labels]</code></p>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">177</span> <span class="n">labels</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_labels</span><span class="p">,</span> <span class="n">device</span><span class="o">=</span><span class="n">labels</span><span class="o">.</span><span class="n">device</span><span class="p">)[</span><span class="n">labels</span><span class="p">]</span></pre></div>
|
|
</div>
|
|
</div>
|
|
<div class='section' id='section-24'>
|
|
<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-24'>#</a>
|
|
</div>
|
|
<p>
|
|
<script type="math/tex; mode=display">\mathcal{L}_k = T_k \max(0, m^{+} - \lVert\mathbf{v}_k\rVert)^2 +
|
|
\lambda (1 - T_k) \max(0, \lVert\mathbf{v}_k\rVert - m^{-})^2</script>
|
|
<code>loss</code> has shape <code>[batch_size, n_labels]</code>. We have parallelized the computation
|
|
of $\mathcal{L}_k$ for for all $k$.</p>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">183</span> <span class="n">loss</span> <span class="o">=</span> <span class="n">labels</span> <span class="o">*</span> <span class="n">F</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">m_positive</span> <span class="o">-</span> <span class="n">v_norm</span><span class="p">)</span> <span class="o">+</span> \
|
|
<span class="lineno">184</span> <span class="bp">self</span><span class="o">.</span><span class="n">lambda_</span> <span class="o">*</span> <span class="p">(</span><span class="mf">1.0</span> <span class="o">-</span> <span class="n">labels</span><span class="p">)</span> <span class="o">*</span> <span class="n">F</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span><span class="n">v_norm</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">m_negative</span><span class="p">)</span></pre></div>
|
|
</div>
|
|
</div>
|
|
<div class='section' id='section-25'>
|
|
<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-25'>#</a>
|
|
</div>
|
|
<p>
|
|
<script type="math/tex; mode=display">\sum_k \mathcal{L}_k</script>
|
|
</p>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">187</span> <span class="k">return</span> <span class="n">loss</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">dim</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span></pre></div>
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