📚 batch norm

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Varuna Jayasiri
2021-02-01 14:43:11 +05:30
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<div class="highlight"><pre><span class="lineno">1</span><span></span><span class="kn">import</span> <span class="nn">torch</span>
<span class="lineno">2</span><span class="kn">from</span> <span class="nn">torch</span> <span class="kn">import</span> <span class="n">nn</span>
<span class="lineno">3</span>
<span class="lineno">4</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 class="highlight"><pre><span class="lineno">7</span><span class="k">class</span> <span class="nc">BatchNorm</span><span class="p">(</span><span class="n">Module</span><span class="p">):</span></pre></div>
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<div class="highlight"><pre><span class="lineno">8</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">channels</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span>
<span class="lineno">9</span> <span class="n">eps</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">1e-5</span><span class="p">,</span> <span class="n">momentum</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">10</span> <span class="n">affine</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">,</span> <span class="n">track_running_stats</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">):</span>
<span class="lineno">11</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">12</span>
<span class="lineno">13</span> <span class="bp">self</span><span class="o">.</span><span class="n">channels</span> <span class="o">=</span> <span class="n">channels</span>
<span class="lineno">14</span>
<span class="lineno">15</span> <span class="bp">self</span><span class="o">.</span><span class="n">eps</span> <span class="o">=</span> <span class="n">eps</span>
<span class="lineno">16</span> <span class="bp">self</span><span class="o">.</span><span class="n">momentum</span> <span class="o">=</span> <span class="n">momentum</span>
<span class="lineno">17</span> <span class="bp">self</span><span class="o">.</span><span class="n">affine</span> <span class="o">=</span> <span class="n">affine</span>
<span class="lineno">18</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_running_stats</span> <span class="o">=</span> <span class="n">track_running_stats</span>
<span class="lineno">19</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">affine</span><span class="p">:</span>
<span class="lineno">20</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">ones</span><span class="p">(</span><span class="n">channels</span><span class="p">))</span>
<span class="lineno">21</span> <span class="bp">self</span><span class="o">.</span><span class="n">bias</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">zeros</span><span class="p">(</span><span class="n">channels</span><span class="p">))</span>
<span class="lineno">22</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_running_stats</span><span class="p">:</span>
<span class="lineno">23</span> <span class="bp">self</span><span class="o">.</span><span class="n">register_buffer</span><span class="p">(</span><span class="s1">&#39;running_mean&#39;</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">channels</span><span class="p">))</span>
<span class="lineno">24</span> <span class="bp">self</span><span class="o">.</span><span class="n">register_buffer</span><span class="p">(</span><span class="s1">&#39;running_var&#39;</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">channels</span><span class="p">))</span></pre></div>
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<div class="highlight"><pre><span class="lineno">26</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">x</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="lineno">27</span> <span class="n">x_shape</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span>
<span class="lineno">28</span> <span class="n">batch_size</span> <span class="o">=</span> <span class="n">x_shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
<span class="lineno">29</span>
<span class="lineno">30</span> <span class="n">x</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">batch_size</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">channels</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="lineno">31</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">training</span> <span class="ow">or</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_running_stats</span><span class="p">:</span>
<span class="lineno">32</span> <span class="n">mean</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">dim</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="lineno">33</span> <span class="n">mean_x2</span> <span class="o">=</span> <span class="p">(</span><span class="n">x</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">dim</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="lineno">34</span> <span class="n">var</span> <span class="o">=</span> <span class="n">mean_x2</span> <span class="o">-</span> <span class="n">mean</span> <span class="o">**</span> <span class="mi">2</span>
<span class="lineno">35</span>
<span class="lineno">36</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">training</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_running_stats</span><span class="p">:</span>
<span class="lineno">37</span> <span class="bp">self</span><span class="o">.</span><span class="n">running_mean</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">momentum</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">running_mean</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">momentum</span> <span class="o">*</span> <span class="n">mean</span>
<span class="lineno">38</span> <span class="bp">self</span><span class="o">.</span><span class="n">running_var</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">momentum</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">running_var</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">momentum</span> <span class="o">*</span> <span class="n">var</span>
<span class="lineno">39</span> <span class="k">else</span><span class="p">:</span>
<span class="lineno">40</span> <span class="n">mean</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">running_mean</span>
<span class="lineno">41</span> <span class="n">var</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">running_var</span>
<span class="lineno">42</span>
<span class="lineno">43</span> <span class="n">x_norm</span> <span class="o">=</span> <span class="p">(</span><span class="n">x</span> <span class="o">-</span> <span class="n">mean</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</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">var</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="lineno">44</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">affine</span><span class="p">:</span>
<span class="lineno">45</span> <span class="n">x_norm</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">weight</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">x_norm</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">bias</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="lineno">46</span>
<span class="lineno">47</span> <span class="k">return</span> <span class="n">x_norm</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">x_shape</span><span class="p">)</span></pre></div>
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<h1>Batch Normalization</h1>
<p>This is a <a href="https://pytorch.org">PyTorch</a> implementation of Batch Normalization from paper
<a href="https://arxiv.org/abs/1502.03167">Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift</a>.</p>
<h3>Internal Covariate Shift</h3>
<p>The paper defines <em>Internal Covariate Shift</em> as the change in the
distribution of network activations due to the change in
network parameters during training.
For example, let&rsquo;s say there are two layers $l_1$ and $l_2$.
During the beginning of the training $l_1$ outputs (inputs to $l_2$)
could be in distribution $\mathcal{N}(0.5, 1)$.
Then, after some training steps it could move to $\mathcal{N}(0.5, 1)$.
This is <em>internal covariate shift</em>.</p>
<p>Internal covriate shift will adversely affect training speed because the later layers
($l_2$ in the above example) has to adapt to this shifted distribution.</p>
<p>By stabilizing the distribution batch normalization minimizes the internal covariate shift.</p>
<h2>Normalization</h2>
<p>It is known that whitening improves training speed and convergence.
<em>Whitening</em> is linearly transforming inputs to have zero mean, unit variance
and be uncorrelated.</p>
<h3>Normalizing outside gradient computation doesn&rsquo;t work</h3>
<p>Normalizing outside the gradient computation using pre-computed (detached)
means and variances doesn&rsquo;t work. For instance. (ignoring variance), let
<script type="math/tex; mode=display">\hat{x} = x - \mathbb{E}[x]</script>
where $x = u + b$ and $b$ is a trained bias.
and $\mathbb{E}[x]$ is outside gradient computation (pre-computed constant).</p>
<p>Note that $\hat{x}$ has no effect of $b$.
Therefore,
$b$ will increase or decrease based
$\frac{\partial{\mathcal{L}}}{\partial x}$,
and keep on growing indefinitely in each training update.
Paper notes that similar explosions happen with variances.</p>
<h3>Batch Normalization</h3>
<p>Whitening is computationally expensive because you need to de-correlate and
the gradients must flow through the full whitening calculation.</p>
<p>The paper introduces simplified version which they call <em>Batch Normalization</em>.
First simplification is that it normalizes each feature independently to have
zero mean and unit variance:
<script type="math/tex; mode=display">\hat{x}^{(k)} = \frac{x^{(k)} - \mathbb{E}[x^{(k)}]}{\sqrt{Var[x^{(k)}]}}</script>
where $x = (x^{(1)} &hellip; x^{(d)})$ is the $d$-dimensional input.</p>
<p>The second simplification is to use estimates of mean $\mathbb{E}[x^{(k)}]$
and variance $Var[x^{(k)}]$ from the mini-batch
for normalization; instead of calculating the mean and variance across whole dataset.</p>
<p>Normalizing each feature to zero mean and unit variance could effect what the layer
can represent.
As an example paper illustrates that, if the inputs to a sigmoid are normalized
most of it will be within $[-1, 1]$ range where the sigmoid is linear.
To overcome this each feature is scaled and shifted by two trained parameters
$\gamma^{(k)}$ and $\beta^{(k)}$.
<script type="math/tex; mode=display">y^{(k)} =\gamma^{(k)} \hat{x}^{(k)} + \beta^{(k)}</script>
where $y^{(k)}$ is the output of of the batch normalization layer.</p>
<p>Note that when applying batch normalization after a linear transform
like $Wu + b$ the bias parameter $b$ gets cancelled due to normalization.
So you can and should omit bias parameter in linear transforms right before the
batch normalization.</p>
<h2>Inference</h2>
<p>We need to know $\mathbb{E}[x^{(k)}]$ and $Var[x^{(k)}]$ in order to
perform the normalization.
So during inference, you either need to go through the whole (or part of) dataset
and find the mean and variance, or you can use an estimate calculated during training.
The usual practice is to calculate an exponential moving average of
mean and variance during training phase and use that for inference.</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">89</span><span></span><span class="kn">import</span> <span class="nn">torch</span>
<span class="lineno">90</span><span class="kn">from</span> <span class="nn">torch</span> <span class="kn">import</span> <span class="n">nn</span>
<span class="lineno">91</span>
<span class="lineno">92</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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<h2>Batch Normalization Layer</h2>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">95</span><span class="k">class</span> <span class="nc">BatchNorm</span><span class="p">(</span><span class="n">Module</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-2'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-2'>#</a>
</div>
<ul>
<li><code>channels</code> is the number of features in the input</li>
<li><code>eps</code> is $\epsilon$, used in $\sqrt{Var[x^{(k)}] + \epsilon}$ for numerical stability</li>
<li><code>momentum</code> is the momentum in taking the exponential moving average</li>
<li><code>affine</code> is whether to scale and shift the normalized value</li>
<li><code>track_running_stats</code> is whether to calculate the moving averages or mean and variance</li>
</ul>
<p>We&rsquo;ve tried to use the same names for arguments as PyTorch <code>BatchNorm</code> implementation.</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">99</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">channels</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="o">*</span><span class="p">,</span>
<span class="lineno">100</span> <span class="n">eps</span><span class="p">:</span> <span class="nb">float</span> <span class="o">=</span> <span class="mf">1e-5</span><span class="p">,</span> <span class="n">momentum</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">101</span> <span class="n">affine</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">,</span> <span class="n">track_running_stats</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">True</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-3'>
<div class='docs'>
<div class='section-link'>
<a href='#section-3'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">111</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">112</span>
<span class="lineno">113</span> <span class="bp">self</span><span class="o">.</span><span class="n">channels</span> <span class="o">=</span> <span class="n">channels</span>
<span class="lineno">114</span>
<span class="lineno">115</span> <span class="bp">self</span><span class="o">.</span><span class="n">eps</span> <span class="o">=</span> <span class="n">eps</span>
<span class="lineno">116</span> <span class="bp">self</span><span class="o">.</span><span class="n">momentum</span> <span class="o">=</span> <span class="n">momentum</span>
<span class="lineno">117</span> <span class="bp">self</span><span class="o">.</span><span class="n">affine</span> <span class="o">=</span> <span class="n">affine</span>
<span class="lineno">118</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_running_stats</span> <span class="o">=</span> <span class="n">track_running_stats</span></pre></div>
</div>
</div>
<div class='section' id='section-4'>
<div class='docs'>
<div class='section-link'>
<a href='#section-4'>#</a>
</div>
<p>Create parameters for $\gamma$ and $\beta$ for scale and shift</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">120</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">affine</span><span class="p">:</span>
<span class="lineno">121</span> <span class="bp">self</span><span class="o">.</span><span class="n">scale</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">ones</span><span class="p">(</span><span class="n">channels</span><span class="p">))</span>
<span class="lineno">122</span> <span class="bp">self</span><span class="o">.</span><span class="n">shift</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">zeros</span><span class="p">(</span><span class="n">channels</span><span class="p">))</span></pre></div>
</div>
</div>
<div class='section' id='section-5'>
<div class='docs'>
<div class='section-link'>
<a href='#section-5'>#</a>
</div>
<p>Create buffers to store exponential moving averages of
mean $\mathbb{E}[x^{(k)}]$ and variance $Var[x^{(k)}]$</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">125</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_running_stats</span><span class="p">:</span>
<span class="lineno">126</span> <span class="bp">self</span><span class="o">.</span><span class="n">register_buffer</span><span class="p">(</span><span class="s1">&#39;exp_mean&#39;</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">channels</span><span class="p">))</span>
<span class="lineno">127</span> <span class="bp">self</span><span class="o">.</span><span class="n">register_buffer</span><span class="p">(</span><span class="s1">&#39;exp_var&#39;</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">channels</span><span class="p">))</span></pre></div>
</div>
</div>
<div class='section' id='section-6'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-6'>#</a>
</div>
<p><code>x</code> is a tensor of shape <code>[batch_size, channels, *]</code>.
<code>*</code> could be any (even *) dimensions.
For example, in an image (2D) convolution this will be
<code>[batch_size, channels, height, width]</code></p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">129</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">x</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>
</div>
<div class='section' id='section-7'>
<div class='docs'>
<div class='section-link'>
<a href='#section-7'>#</a>
</div>
<p>Keep the original shape</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">137</span> <span class="n">x_shape</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span></pre></div>
</div>
</div>
<div class='section' id='section-8'>
<div class='docs'>
<div class='section-link'>
<a href='#section-8'>#</a>
</div>
<p>Get the batch size</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">139</span> <span class="n">batch_size</span> <span class="o">=</span> <span class="n">x_shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span></pre></div>
</div>
</div>
<div class='section' id='section-9'>
<div class='docs'>
<div class='section-link'>
<a href='#section-9'>#</a>
</div>
<p>Sanity check to make sure the number of features is same</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">141</span> <span class="k">assert</span> <span class="bp">self</span><span class="o">.</span><span class="n">channels</span> <span class="o">==</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span></pre></div>
</div>
</div>
<div class='section' id='section-10'>
<div class='docs'>
<div class='section-link'>
<a href='#section-10'>#</a>
</div>
<p>Reshape into <code>[batch_size, channels, n]</code></p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">144</span> <span class="n">x</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">batch_size</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">channels</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-11'>
<div class='docs'>
<div class='section-link'>
<a href='#section-11'>#</a>
</div>
<p>We will calculate the mini-batch mean and variance
if we are in training mode or if we have not tracked exponential moving averages</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">148</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">training</span> <span class="ow">or</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_running_stats</span><span class="p">:</span></pre></div>
</div>
</div>
<div class='section' id='section-12'>
<div class='docs'>
<div class='section-link'>
<a href='#section-12'>#</a>
</div>
<p>Calculate the mean across first and last dimension;
i.e. the means for each feature $\mathbb{E}[x^{(k)}]$</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">151</span> <span class="n">mean</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">dim</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span></pre></div>
</div>
</div>
<div class='section' id='section-13'>
<div class='docs'>
<div class='section-link'>
<a href='#section-13'>#</a>
</div>
<p>Calculate the squared mean across first and last dimension;
i.e. the means for each feature $\mathbb{E}[(x^{(k)})^2]$</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">154</span> <span class="n">mean_x2</span> <span class="o">=</span> <span class="p">(</span><span class="n">x</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">dim</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span></pre></div>
</div>
</div>
<div class='section' id='section-14'>
<div class='docs'>
<div class='section-link'>
<a href='#section-14'>#</a>
</div>
<p>Variance for each feature $Var[x^{(k)}] = \mathbb{E}[(x^{(k)})^2] - \mathbb{E}[x^{(k)}]^2$</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">156</span> <span class="n">var</span> <span class="o">=</span> <span class="n">mean_x2</span> <span class="o">-</span> <span class="n">mean</span> <span class="o">**</span> <span class="mi">2</span></pre></div>
</div>
</div>
<div class='section' id='section-15'>
<div class='docs'>
<div class='section-link'>
<a href='#section-15'>#</a>
</div>
<p>Update exponential moving averages</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">159</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">training</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_running_stats</span><span class="p">:</span>
<span class="lineno">160</span> <span class="bp">self</span><span class="o">.</span><span class="n">exp_mean</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">momentum</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">exp_mean</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">momentum</span> <span class="o">*</span> <span class="n">mean</span>
<span class="lineno">161</span> <span class="bp">self</span><span class="o">.</span><span class="n">exp_var</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">momentum</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">exp_var</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">momentum</span> <span class="o">*</span> <span class="n">var</span></pre></div>
</div>
</div>
<div class='section' id='section-16'>
<div class='docs'>
<div class='section-link'>
<a href='#section-16'>#</a>
</div>
<p>Use exponential moving averages as estimates</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">163</span> <span class="k">else</span><span class="p">:</span>
<span class="lineno">164</span> <span class="n">mean</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">exp_mean</span>
<span class="lineno">165</span> <span class="n">var</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">exp_var</span></pre></div>
</div>
</div>
<div class='section' id='section-17'>
<div class='docs'>
<div class='section-link'>
<a href='#section-17'>#</a>
</div>
<p>Normalize <script type="math/tex; mode=display">\hat{x}^{(k)} = \frac{x^{(k)} - \mathbb{E}[x^{(k)}]}{\sqrt{Var[x^{(k)}] + \epsilon}}</script>
</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">168</span> <span class="n">x_norm</span> <span class="o">=</span> <span class="p">(</span><span class="n">x</span> <span class="o">-</span> <span class="n">mean</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</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">var</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-18'>
<div class='docs'>
<div class='section-link'>
<a href='#section-18'>#</a>
</div>
<p>Scale and shift <script type="math/tex; mode=display">y^{(k)} =\gamma^{(k)} \hat{x}^{(k)} + \beta^{(k)}</script>
</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">170</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">affine</span><span class="p">:</span>
<span class="lineno">171</span> <span class="n">x_norm</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">scale</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">x_norm</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">shift</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-19'>
<div class='docs'>
<div class='section-link'>
<a href='#section-19'>#</a>
</div>
<p>Reshape to original and return</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">174</span> <span class="k">return</span> <span class="n">x_norm</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="n">x_shape</span><span class="p">)</span></pre></div>
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<h1>MNIST Experiment for Batch Normalization</h1>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">11</span><span></span><span class="kn">import</span> <span class="nn">torch.nn</span> <span class="k">as</span> <span class="nn">nn</span>
<span class="lineno">12</span><span class="kn">import</span> <span class="nn">torch.nn.functional</span> <span class="k">as</span> <span class="nn">F</span>
<span class="lineno">13</span><span class="kn">import</span> <span class="nn">torch.utils.data</span>
<span class="lineno">14</span>
<span class="lineno">15</span><span class="kn">from</span> <span class="nn">labml</span> <span class="kn">import</span> <span class="n">experiment</span>
<span class="lineno">16</span><span class="kn">from</span> <span class="nn">labml.configs</span> <span class="kn">import</span> <span class="n">option</span>
<span class="lineno">17</span><span class="kn">from</span> <span class="nn">labml_helpers.module</span> <span class="kn">import</span> <span class="n">Module</span>
<span class="lineno">18</span><span class="kn">from</span> <span class="nn">labml_nn.experiments.mnist</span> <span class="kn">import</span> <span class="n">MNISTConfigs</span>
<span class="lineno">19</span><span class="kn">from</span> <span class="nn">labml_nn.normalization.batch_norm</span> <span class="kn">import</span> <span class="n">BatchNorm</span></pre></div>
</div>
</div>
<div class='section' id='section-1'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-1'>#</a>
</div>
<h3>Model definition</h3>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">22</span><span class="k">class</span> <span class="nc">Model</span><span class="p">(</span><span class="n">Module</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-2'>
<div class='docs'>
<div class='section-link'>
<a href='#section-2'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">27</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="lineno">28</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>
</div>
</div>
<div class='section' id='section-3'>
<div class='docs'>
<div class='section-link'>
<a href='#section-3'>#</a>
</div>
<p>Note that we omit the bias parameter</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">30</span> <span class="bp">self</span><span class="o">.</span><span class="n">conv1</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Conv2d</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">bias</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-4'>
<div class='docs'>
<div class='section-link'>
<a href='#section-4'>#</a>
</div>
<p>Batch normalization with 20 channels (output of convolution layer).
The input to this layer will have shape <code>[batch_size, 20, height(24), width(24)]</code></p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">33</span> <span class="bp">self</span><span class="o">.</span><span class="n">bn1</span> <span class="o">=</span> <span class="n">BatchNorm</span><span class="p">(</span><span class="mi">20</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-5'>
<div class='docs'>
<div class='section-link'>
<a href='#section-5'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">35</span> <span class="bp">self</span><span class="o">.</span><span class="n">conv2</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Conv2d</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">bias</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-6'>
<div class='docs'>
<div class='section-link'>
<a href='#section-6'>#</a>
</div>
<p>Batch normalization with 50 channels.
The input to this layer will have shape <code>[batch_size, 50, height(8), width(8)]</code></p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">38</span> <span class="bp">self</span><span class="o">.</span><span class="n">bn2</span> <span class="o">=</span> <span class="n">BatchNorm</span><span class="p">(</span><span class="mi">50</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-7'>
<div class='docs'>
<div class='section-link'>
<a href='#section-7'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">40</span> <span class="bp">self</span><span class="o">.</span><span class="n">fc1</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="mi">4</span> <span class="o">*</span> <span class="mi">50</span><span class="p">,</span> <span class="mi">500</span><span class="p">,</span> <span class="n">bias</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-8'>
<div class='docs'>
<div class='section-link'>
<a href='#section-8'>#</a>
</div>
<p>Batch normalization with 500 channels (output of fully connected layer).
The input to this layer will have shape <code>[batch_size, 500]</code></p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">43</span> <span class="bp">self</span><span class="o">.</span><span class="n">bn3</span> <span class="o">=</span> <span class="n">BatchNorm</span><span class="p">(</span><span class="mi">500</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-9'>
<div class='docs'>
<div class='section-link'>
<a href='#section-9'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">45</span> <span class="bp">self</span><span class="o">.</span><span class="n">fc2</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">500</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-10'>
<div class='docs'>
<div class='section-link'>
<a href='#section-10'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">47</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">x</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="lineno">48</span> <span class="n">x</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">bn1</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">conv1</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span>
<span class="lineno">49</span> <span class="n">x</span> <span class="o">=</span> <span class="n">F</span><span class="o">.</span><span class="n">max_pool2d</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="lineno">50</span> <span class="n">x</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">bn2</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">conv2</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span>
<span class="lineno">51</span> <span class="n">x</span> <span class="o">=</span> <span class="n">F</span><span class="o">.</span><span class="n">max_pool2d</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="lineno">52</span> <span class="n">x</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span> <span class="o">*</span> <span class="mi">4</span> <span class="o">*</span> <span class="mi">50</span><span class="p">)</span>
<span class="lineno">53</span> <span class="n">x</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">bn3</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fc1</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span>
<span class="lineno">54</span> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">fc2</span><span class="p">(</span><span class="n">x</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-11'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-11'>#</a>
</div>
<h3>Create model</h3>
<p>We use <a href="../../experiments/mnist.html#MNISTConfigs"><code>MNISTConfigs</code></a> configurations
and set a new function to calculate the model.</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">57</span><span class="nd">@option</span><span class="p">(</span><span class="n">MNISTConfigs</span><span class="o">.</span><span class="n">model</span><span class="p">)</span>
<span class="lineno">58</span><span class="k">def</span> <span class="nf">model</span><span class="p">(</span><span class="n">c</span><span class="p">:</span> <span class="n">MNISTConfigs</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-12'>
<div class='docs'>
<div class='section-link'>
<a href='#section-12'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">65</span> <span class="k">return</span> <span class="n">Model</span><span class="p">()</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">c</span><span class="o">.</span><span class="n">device</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-13'>
<div class='docs'>
<div class='section-link'>
<a href='#section-13'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">68</span><span class="k">def</span> <span class="nf">main</span><span class="p">():</span></pre></div>
</div>
</div>
<div class='section' id='section-14'>
<div class='docs'>
<div class='section-link'>
<a href='#section-14'>#</a>
</div>
<p>Create experiment</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">70</span> <span class="n">experiment</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">name</span><span class="o">=</span><span class="s1">&#39;mnist_batch_norm&#39;</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-15'>
<div class='docs'>
<div class='section-link'>
<a href='#section-15'>#</a>
</div>
<p>Create configurations</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">72</span> <span class="n">conf</span> <span class="o">=</span> <span class="n">MNISTConfigs</span><span class="p">()</span></pre></div>
</div>
</div>
<div class='section' id='section-16'>
<div class='docs'>
<div class='section-link'>
<a href='#section-16'>#</a>
</div>
<p>Load configurations</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">74</span> <span class="n">experiment</span><span class="o">.</span><span class="n">configs</span><span class="p">(</span><span class="n">conf</span><span class="p">,</span> <span class="p">{</span><span class="s1">&#39;optimizer.optimizer&#39;</span><span class="p">:</span> <span class="s1">&#39;Adam&#39;</span><span class="p">})</span></pre></div>
</div>
</div>
<div class='section' id='section-17'>
<div class='docs'>
<div class='section-link'>
<a href='#section-17'>#</a>
</div>
<p>Start the experiment and run the training loop</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">76</span> <span class="k">with</span> <span class="n">experiment</span><span class="o">.</span><span class="n">start</span><span class="p">():</span>
<span class="lineno">77</span> <span class="n">conf</span><span class="o">.</span><span class="n">run</span><span class="p">()</span></pre></div>
</div>
</div>
<div class='section' id='section-18'>
<div class='docs'>
<div class='section-link'>
<a href='#section-18'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">81</span><span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">&#39;__main__&#39;</span><span class="p">:</span>
<span class="lineno">82</span> <span class="n">main</span><span class="p">()</span></pre></div>
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<div class="highlight"><pre><span class="lineno">1</span><span></span><span class="kn">import</span> <span class="nn">torch.nn</span> <span class="k">as</span> <span class="nn">nn</span>
<span class="lineno">2</span><span class="kn">import</span> <span class="nn">torch.nn.functional</span> <span class="k">as</span> <span class="nn">F</span>
<span class="lineno">3</span><span class="kn">import</span> <span class="nn">torch.utils.data</span>
<span class="lineno">4</span>
<span class="lineno">5</span><span class="kn">from</span> <span class="nn">labml</span> <span class="kn">import</span> <span class="n">experiment</span><span class="p">,</span> <span class="n">tracker</span>
<span class="lineno">6</span><span class="kn">from</span> <span class="nn">labml.configs</span> <span class="kn">import</span> <span class="n">option</span>
<span class="lineno">7</span><span class="kn">from</span> <span class="nn">labml_helpers.datasets.mnist</span> <span class="kn">import</span> <span class="n">MNISTConfigs</span>
<span class="lineno">8</span><span class="kn">from</span> <span class="nn">labml_helpers.device</span> <span class="kn">import</span> <span class="n">DeviceConfigs</span>
<span class="lineno">9</span><span class="kn">from</span> <span class="nn">labml_helpers.metrics.accuracy</span> <span class="kn">import</span> <span class="n">Accuracy</span>
<span class="lineno">10</span><span class="kn">from</span> <span class="nn">labml_helpers.module</span> <span class="kn">import</span> <span class="n">Module</span>
<span class="lineno">11</span><span class="kn">from</span> <span class="nn">labml_helpers.seed</span> <span class="kn">import</span> <span class="n">SeedConfigs</span>
<span class="lineno">12</span><span class="kn">from</span> <span class="nn">labml_helpers.train_valid</span> <span class="kn">import</span> <span class="n">TrainValidConfigs</span><span class="p">,</span> <span class="n">BatchIndex</span><span class="p">,</span> <span class="n">hook_model_outputs</span>
<span class="lineno">13</span><span class="kn">from</span> <span class="nn">labml_nn.normalization.batch_norm</span> <span class="kn">import</span> <span class="n">BatchNorm</span></pre></div>
</div>
</div>
<div class='section' id='section-1'>
<div class='docs'>
<div class='section-link'>
<a href='#section-1'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">16</span><span class="k">class</span> <span class="nc">Net</span><span class="p">(</span><span class="n">Module</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-2'>
<div class='docs'>
<div class='section-link'>
<a href='#section-2'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">17</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="lineno">18</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">19</span> <span class="bp">self</span><span class="o">.</span><span class="n">conv1</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Conv2d</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="lineno">20</span> <span class="bp">self</span><span class="o">.</span><span class="n">bn1</span> <span class="o">=</span> <span class="n">BatchNorm</span><span class="p">(</span><span class="mi">20</span><span class="p">)</span>
<span class="lineno">21</span> <span class="bp">self</span><span class="o">.</span><span class="n">conv2</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Conv2d</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="lineno">22</span> <span class="bp">self</span><span class="o">.</span><span class="n">bn2</span> <span class="o">=</span> <span class="n">BatchNorm</span><span class="p">(</span><span class="mi">50</span><span class="p">)</span>
<span class="lineno">23</span> <span class="bp">self</span><span class="o">.</span><span class="n">fc1</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="mi">4</span> <span class="o">*</span> <span class="mi">50</span><span class="p">,</span> <span class="mi">500</span><span class="p">)</span>
<span class="lineno">24</span> <span class="bp">self</span><span class="o">.</span><span class="n">bn3</span> <span class="o">=</span> <span class="n">BatchNorm</span><span class="p">(</span><span class="mi">500</span><span class="p">)</span>
<span class="lineno">25</span> <span class="bp">self</span><span class="o">.</span><span class="n">fc2</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="mi">500</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-3'>
<div class='docs'>
<div class='section-link'>
<a href='#section-3'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">27</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">x</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="lineno">28</span> <span class="n">x</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">bn1</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">conv1</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span>
<span class="lineno">29</span> <span class="n">x</span> <span class="o">=</span> <span class="n">F</span><span class="o">.</span><span class="n">max_pool2d</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="lineno">30</span> <span class="n">x</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">bn2</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">conv2</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span>
<span class="lineno">31</span> <span class="n">x</span> <span class="o">=</span> <span class="n">F</span><span class="o">.</span><span class="n">max_pool2d</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="lineno">32</span> <span class="n">x</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span> <span class="o">*</span> <span class="mi">4</span> <span class="o">*</span> <span class="mi">50</span><span class="p">)</span>
<span class="lineno">33</span> <span class="n">x</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">bn3</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fc1</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span>
<span class="lineno">34</span> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">fc2</span><span class="p">(</span><span class="n">x</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-4'>
<div class='docs'>
<div class='section-link'>
<a href='#section-4'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">37</span><span class="k">class</span> <span class="nc">Configs</span><span class="p">(</span><span class="n">MNISTConfigs</span><span class="p">,</span> <span class="n">TrainValidConfigs</span><span class="p">):</span>
<span class="lineno">38</span> <span class="n">optimizer</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">optim</span><span class="o">.</span><span class="n">Adam</span>
<span class="lineno">39</span> <span class="n">model</span><span class="p">:</span> <span class="n">nn</span><span class="o">.</span><span class="n">Module</span>
<span class="lineno">40</span> <span class="n">set_seed</span> <span class="o">=</span> <span class="n">SeedConfigs</span><span class="p">()</span>
<span class="lineno">41</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="n">DeviceConfigs</span><span class="p">()</span>
<span class="lineno">42</span> <span class="n">epochs</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">10</span>
<span class="lineno">43</span>
<span class="lineno">44</span> <span class="n">is_save_models</span> <span class="o">=</span> <span class="kc">True</span>
<span class="lineno">45</span> <span class="n">model</span><span class="p">:</span> <span class="n">nn</span><span class="o">.</span><span class="n">Module</span>
<span class="lineno">46</span> <span class="n">inner_iterations</span> <span class="o">=</span> <span class="mi">10</span>
<span class="lineno">47</span>
<span class="lineno">48</span> <span class="n">accuracy_func</span> <span class="o">=</span> <span class="n">Accuracy</span><span class="p">()</span>
<span class="lineno">49</span> <span class="n">loss_func</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">CrossEntropyLoss</span><span class="p">()</span></pre></div>
</div>
</div>
<div class='section' id='section-5'>
<div class='docs'>
<div class='section-link'>
<a href='#section-5'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">51</span> <span class="k">def</span> <span class="nf">init</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="lineno">52</span> <span class="n">tracker</span><span class="o">.</span><span class="n">set_queue</span><span class="p">(</span><span class="s2">&quot;loss.*&quot;</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span>
<span class="lineno">53</span> <span class="n">tracker</span><span class="o">.</span><span class="n">set_scalar</span><span class="p">(</span><span class="s2">&quot;accuracy.*&quot;</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span>
<span class="lineno">54</span> <span class="n">hook_model_outputs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mode</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">model</span><span class="p">,</span> <span class="s1">&#39;model&#39;</span><span class="p">)</span>
<span class="lineno">55</span> <span class="bp">self</span><span class="o">.</span><span class="n">state_modules</span> <span class="o">=</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">accuracy_func</span><span class="p">]</span></pre></div>
</div>
</div>
<div class='section' id='section-6'>
<div class='docs'>
<div class='section-link'>
<a href='#section-6'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">57</span> <span class="k">def</span> <span class="nf">step</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">batch</span><span class="p">:</span> <span class="nb">any</span><span class="p">,</span> <span class="n">batch_idx</span><span class="p">:</span> <span class="n">BatchIndex</span><span class="p">):</span>
<span class="lineno">58</span> <span class="n">data</span><span class="p">,</span> <span class="n">target</span> <span class="o">=</span> <span class="n">batch</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">device</span><span class="p">),</span> <span class="n">batch</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">device</span><span class="p">)</span>
<span class="lineno">59</span>
<span class="lineno">60</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">mode</span><span class="o">.</span><span class="n">is_train</span><span class="p">:</span>
<span class="lineno">61</span> <span class="n">tracker</span><span class="o">.</span><span class="n">add_global_step</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">))</span>
<span class="lineno">62</span>
<span class="lineno">63</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">mode</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">is_log_activations</span><span class="o">=</span><span class="n">batch_idx</span><span class="o">.</span><span class="n">is_last</span><span class="p">):</span>
<span class="lineno">64</span> <span class="n">output</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">model</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="lineno">65</span>
<span class="lineno">66</span> <span class="n">loss</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss_func</span><span class="p">(</span><span class="n">output</span><span class="p">,</span> <span class="n">target</span><span class="p">)</span>
<span class="lineno">67</span> <span class="bp">self</span><span class="o">.</span><span class="n">accuracy_func</span><span class="p">(</span><span class="n">output</span><span class="p">,</span> <span class="n">target</span><span class="p">)</span>
<span class="lineno">68</span> <span class="n">tracker</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="s2">&quot;loss.&quot;</span><span class="p">,</span> <span class="n">loss</span><span class="p">)</span>
<span class="lineno">69</span>
<span class="lineno">70</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">mode</span><span class="o">.</span><span class="n">is_train</span><span class="p">:</span>
<span class="lineno">71</span> <span class="n">loss</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
<span class="lineno">72</span>
<span class="lineno">73</span> <span class="bp">self</span><span class="o">.</span><span class="n">optimizer</span><span class="o">.</span><span class="n">step</span><span class="p">()</span>
<span class="lineno">74</span> <span class="k">if</span> <span class="n">batch_idx</span><span class="o">.</span><span class="n">is_last</span><span class="p">:</span>
<span class="lineno">75</span> <span class="n">tracker</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="s1">&#39;model&#39;</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">model</span><span class="p">)</span>
<span class="lineno">76</span> <span class="bp">self</span><span class="o">.</span><span class="n">optimizer</span><span class="o">.</span><span class="n">zero_grad</span><span class="p">()</span>
<span class="lineno">77</span>
<span class="lineno">78</span> <span class="n">tracker</span><span class="o">.</span><span class="n">save</span><span class="p">()</span></pre></div>
</div>
</div>
<div class='section' id='section-7'>
<div class='docs'>
<div class='section-link'>
<a href='#section-7'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">81</span><span class="nd">@option</span><span class="p">(</span><span class="n">Configs</span><span class="o">.</span><span class="n">model</span><span class="p">)</span>
<span class="lineno">82</span><span class="k">def</span> <span class="nf">model</span><span class="p">(</span><span class="n">c</span><span class="p">:</span> <span class="n">Configs</span><span class="p">):</span>
<span class="lineno">83</span> <span class="k">return</span> <span class="n">Net</span><span class="p">()</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">c</span><span class="o">.</span><span class="n">device</span><span class="p">)</span>
<span class="lineno">84</span>
<span class="lineno">85</span>
<span class="lineno">86</span><span class="nd">@option</span><span class="p">(</span><span class="n">Configs</span><span class="o">.</span><span class="n">optimizer</span><span class="p">)</span>
<span class="lineno">87</span><span class="k">def</span> <span class="nf">_optimizer</span><span class="p">(</span><span class="n">c</span><span class="p">:</span> <span class="n">Configs</span><span class="p">):</span>
<span class="lineno">88</span> <span class="kn">from</span> <span class="nn">labml_helpers.optimizer</span> <span class="kn">import</span> <span class="n">OptimizerConfigs</span>
<span class="lineno">89</span> <span class="n">opt_conf</span> <span class="o">=</span> <span class="n">OptimizerConfigs</span><span class="p">()</span>
<span class="lineno">90</span> <span class="n">opt_conf</span><span class="o">.</span><span class="n">parameters</span> <span class="o">=</span> <span class="n">c</span><span class="o">.</span><span class="n">model</span><span class="o">.</span><span class="n">parameters</span><span class="p">()</span>
<span class="lineno">91</span> <span class="k">return</span> <span class="n">opt_conf</span>
<span class="lineno">92</span>
<span class="lineno">93</span>
<span class="lineno">94</span><span class="k">def</span> <span class="nf">main</span><span class="p">():</span>
<span class="lineno">95</span> <span class="n">conf</span> <span class="o">=</span> <span class="n">Configs</span><span class="p">()</span>
<span class="lineno">96</span> <span class="n">experiment</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">name</span><span class="o">=</span><span class="s1">&#39;mnist_labml_helpers&#39;</span><span class="p">)</span>
<span class="lineno">97</span> <span class="n">experiment</span><span class="o">.</span><span class="n">configs</span><span class="p">(</span><span class="n">conf</span><span class="p">,</span> <span class="p">{</span><span class="s1">&#39;optimizer.optimizer&#39;</span><span class="p">:</span> <span class="s1">&#39;Adam&#39;</span><span class="p">})</span>
<span class="lineno">98</span> <span class="n">conf</span><span class="o">.</span><span class="n">set_seed</span><span class="o">.</span><span class="n">set</span><span class="p">()</span>
<span class="lineno">99</span> <span class="n">experiment</span><span class="o">.</span><span class="n">add_pytorch_models</span><span class="p">(</span><span class="nb">dict</span><span class="p">(</span><span class="n">model</span><span class="o">=</span><span class="n">conf</span><span class="o">.</span><span class="n">model</span><span class="p">))</span>
<span class="lineno">100</span> <span class="k">with</span> <span class="n">experiment</span><span class="o">.</span><span class="n">start</span><span class="p">():</span>
<span class="lineno">101</span> <span class="n">conf</span><span class="o">.</span><span class="n">run</span><span class="p">()</span>
<span class="lineno">102</span>
<span class="lineno">103</span>
<span class="lineno">104</span><span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">&#39;__main__&#39;</span><span class="p">:</span>
<span class="lineno">105</span> <span class="n">main</span><span class="p">()</span></pre></div>
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