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<title>Generative Adversarial Networks (GAN)</title>
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<a class="parent" href="index.html">gan</a>
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<a href="https://github.com/lab-ml/labml_nn/tree/master/labml_nn/gan/__init__.py">
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<div class='section' id='section-0'>
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<a href='#section-0'>#</a>
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<h1>Generative Adversarial Networks (GAN)</h1>
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<p>This is an implementation of
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<a href="https://arxiv.org/abs/1406.2661">Generative Adversarial Networks</a>.</p>
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<p>The generator, $G(\pmb{z}; \theta_g)$ generates samples that match the
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distribution of data, while the discriminator, $D(\pmb{x}; \theta_g)$
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gives the probability that $\pmb{x}$ came from data rather than $G$.</p>
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<p>We train $D$ and $G$ simultaneously on a two-player min-max game with value
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function $V(G, D)$.</p>
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<p>
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<script type="math/tex; mode=display">\min_G \max_D V(D, G) =
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\mathop{\mathbb{E}}_{\pmb{x} \sim p_{data}(\pmb{x})}
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\big[\log D(\pmb{x})\big] +
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\mathop{\mathbb{E}}_{\pmb{z} \sim p_{\pmb{z}}(\pmb{z})}
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\big[\log (1 - D(G(\pmb{z}))\big]
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</script>
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</p>
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<p>$p_{data}(\pmb{x})$ is the probability distribution over data,
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whilst $p_{\pmb{z}}(\pmb{z})$ probability distribution of $\pmb{z}$, which is set to
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gaussian noise.</p>
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<p>This file defines the loss functions. <a href="simple_mnist_experiment.html">Here</a> is an MNIST example
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with two multilayer perceptron for the generator and discriminator.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">34</span><span></span><span class="kn">import</span> <span class="nn">torch</span>
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<span class="lineno">35</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">36</span><span class="kn">import</span> <span class="nn">torch.utils.data</span>
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<span class="lineno">37</span><span class="kn">import</span> <span class="nn">torch.utils.data</span>
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<span class="lineno">38</span>
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<span class="lineno">39</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>Discriminator Loss</h2>
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<p>Discriminator should <strong>ascend</strong> on the gradient,</p>
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<p>
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<script type="math/tex; mode=display">\nabla_{\theta_d} \frac{1}{m} \sum_{i=1}^m \Bigg[
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\log D\Big(\pmb{x}^{(i)}\Big) +
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\log \Big(1 - D\Big(G\Big(\pmb{z}^{(i)}\Big)\Big)\Big)
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\Bigg]</script>
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</p>
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<p>$m$ is the mini-batch size and $(i)$ is used to index samples in the mini-batch.
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$\pmb{x}$ are samples from $p_{data}$ and $\pmb{z}$ are samples from $p_z$.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">42</span><span class="k">class</span> <span class="nc">DiscriminatorLogitsLoss</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">57</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">smoothing</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.2</span><span class="p">):</span>
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<span class="lineno">58</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</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-3'>
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<div class='docs'>
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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>We use PyTorch Binary Cross Entropy Loss, which is
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$-\sum\Big[y \log(\hat{y}) + (1 - y) \log(1 - \hat{y})\Big]$,
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where $y$ are the labels and $\hat{y}$ are the predictions.
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<em>Note the negative sign</em>.
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We use labels equal to $1$ for $\pmb{x}$ from $p_{data}$
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and labels equal to $0$ for $\pmb{x}$ from $p_{G}.$
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Then descending on the sum of these is same as ascending on
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the above gradient.</p>
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<p><code>BCEWithLogitsLoss</code> combines softmax and binary cross entropy loss.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">69</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss_true</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">BCEWithLogitsLoss</span><span class="p">()</span>
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<span class="lineno">70</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss_false</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">BCEWithLogitsLoss</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>We use label smoothing because it seems to work better in some cases</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">73</span> <span class="bp">self</span><span class="o">.</span><span class="n">smoothing</span> <span class="o">=</span> <span class="n">smoothing</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>Labels are registered as buffered and persistence is set to <code>False</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">76</span> <span class="bp">self</span><span class="o">.</span><span class="n">register_buffer</span><span class="p">(</span><span class="s1">'labels_true'</span><span class="p">,</span> <span class="n">_create_labels</span><span class="p">(</span><span class="mi">256</span><span class="p">,</span> <span class="mf">1.0</span> <span class="o">-</span> <span class="n">smoothing</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">),</span> <span class="kc">False</span><span class="p">)</span>
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<span class="lineno">77</span> <span class="bp">self</span><span class="o">.</span><span class="n">register_buffer</span><span class="p">(</span><span class="s1">'labels_false'</span><span class="p">,</span> <span class="n">_create_labels</span><span class="p">(</span><span class="mi">256</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="n">smoothing</span><span class="p">),</span> <span class="kc">False</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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<p><code>logits_true</code> are logits from $D(\pmb{x}^{(i)})$ and
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<code>logits_false</code> are logits from $D(G(\pmb{z}^{(i)}))$</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">79</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">logits_true</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">logits_false</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-7'>
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<div class='docs'>
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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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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">84</span> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">logits_true</span><span class="p">)</span> <span class="o">></span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">labels_true</span><span class="p">):</span>
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<span class="lineno">85</span> <span class="bp">self</span><span class="o">.</span><span class="n">register_buffer</span><span class="p">(</span><span class="s2">"labels_true"</span><span class="p">,</span>
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<span class="lineno">86</span> <span class="n">_create_labels</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">logits_true</span><span class="p">),</span> <span class="mf">1.0</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">smoothing</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="n">logits_true</span><span class="o">.</span><span class="n">device</span><span class="p">),</span> <span class="kc">False</span><span class="p">)</span>
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<span class="lineno">87</span> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">logits_false</span><span class="p">)</span> <span class="o">></span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">labels_false</span><span class="p">):</span>
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<span class="lineno">88</span> <span class="bp">self</span><span class="o">.</span><span class="n">register_buffer</span><span class="p">(</span><span class="s2">"labels_false"</span><span class="p">,</span>
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<span class="lineno">89</span> <span class="n">_create_labels</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">logits_false</span><span class="p">),</span> <span class="mf">0.0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">smoothing</span><span class="p">,</span> <span class="n">logits_false</span><span class="o">.</span><span class="n">device</span><span class="p">),</span> <span class="kc">False</span><span class="p">)</span>
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<span class="lineno">90</span>
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<span class="lineno">91</span> <span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">loss_true</span><span class="p">(</span><span class="n">logits_true</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">labels_true</span><span class="p">[:</span><span class="nb">len</span><span class="p">(</span><span class="n">logits_true</span><span class="p">)]),</span>
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<span class="lineno">92</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss_false</span><span class="p">(</span><span class="n">logits_false</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">labels_false</span><span class="p">[:</span><span class="nb">len</span><span class="p">(</span><span class="n">logits_false</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 doc-strings'>
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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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<h2>Generator Loss</h2>
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<p>Generator should <strong>descend</strong> on the gradient,</p>
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<p>
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<script type="math/tex; mode=display">\nabla_{\theta_g} \frac{1}{m} \sum_{i=1}^m \Bigg[
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\log \Big(1 - D\Big(G\Big(\pmb{z}^{(i)}\Big)\Big)\Big)
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\Bigg]</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">95</span><span class="k">class</span> <span class="nc">GeneratorLogitsLoss</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-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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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">105</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">smoothing</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">0.2</span><span class="p">):</span>
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<span class="lineno">106</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">107</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss_true</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">BCEWithLogitsLoss</span><span class="p">()</span>
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<span class="lineno">108</span> <span class="bp">self</span><span class="o">.</span><span class="n">smoothing</span> <span class="o">=</span> <span class="n">smoothing</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'>
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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>We use labels equal to $1$ for $\pmb{x}$ from $p_{G}.$
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Then descending on this loss is same as descending on
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the above gradient.</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="bp">self</span><span class="o">.</span><span class="n">register_buffer</span><span class="p">(</span><span class="s1">'fake_labels'</span><span class="p">,</span> <span class="n">_create_labels</span><span class="p">(</span><span class="mi">256</span><span class="p">,</span> <span class="mf">1.0</span> <span class="o">-</span> <span class="n">smoothing</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">),</span> <span class="kc">False</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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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">114</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">logits</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">):</span>
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<span class="lineno">115</span> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">logits</span><span class="p">)</span> <span class="o">></span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fake_labels</span><span class="p">):</span>
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<span class="lineno">116</span> <span class="bp">self</span><span class="o">.</span><span class="n">register_buffer</span><span class="p">(</span><span class="s2">"fake_labels"</span><span class="p">,</span>
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<span class="lineno">117</span> <span class="n">_create_labels</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">logits</span><span class="p">),</span> <span class="mf">1.0</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">smoothing</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="n">logits</span><span class="o">.</span><span class="n">device</span><span class="p">),</span> <span class="kc">False</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="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss_true</span><span class="p">(</span><span class="n">logits</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">fake_labels</span><span class="p">[:</span><span class="nb">len</span><span class="p">(</span><span class="n">logits</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 doc-strings'>
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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>Create smoothed labels</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">def</span> <span class="nf">_create_labels</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">r1</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span> <span class="n">r2</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span> <span class="n">device</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">device</span> <span class="o">=</span> <span class="kc">None</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-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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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">126</span> <span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">requires_grad</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">device</span><span class="o">=</span><span class="n">device</span><span class="p">)</span><span class="o">.</span><span class="n">uniform_</span><span class="p">(</span><span class="n">r1</span><span class="p">,</span> <span class="n">r2</span><span class="p">)</span></pre></div>
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