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<a href='#section-0'>#</a>
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<h1>Long Short-Term Memory (LSTM)</h1>
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<p>This is a <a href="https://pytorch.org">PyTorch</a> implementation of Long Short-Term Memory.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">12</span><span></span><span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Optional</span><span class="p">,</span> <span class="n">Tuple</span>
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<span class="lineno">13</span>
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<span class="lineno">14</span><span class="kn">import</span> <span class="nn">torch</span>
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<span class="lineno">15</span><span class="kn">from</span> <span class="nn">torch</span> <span class="kn">import</span> <span class="n">nn</span>
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<span class="lineno">16</span>
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<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></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>Long Short-Term Memory Cell</h2>
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<p>LSTM Cell computes $c$, and $h$. $c$ is like the long-term memory,
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and $h$ is like the short term memory.
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We use the input $x$ and $h$ to update the long term memory.
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In the update, some features of $c$ are cleared with a forget gate $f$,
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and some features $i$ are added through a gate $g$.</p>
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<p>The new short term memory is the $\tanh$ of the long-term memory
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multiplied by the output gate $o$.</p>
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<p>Note that the cell doesn’t look at long term memory $c$ when doing the update. It only modifies it.
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Also $c$ never goes through a linear transformation.
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This is what solves vanishing and exploding gradients.</p>
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<p>Here’s the update rule.</p>
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<p>
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<script type="math/tex; mode=display">\begin{align}
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c_t &= \sigma(f_t) \odot c_{t-1} + \sigma(i_t) \odot \tanh(g_t) \\
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h_t &= \sigma(o_t) \odot \tanh(c_t)
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\end{align}</script>
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</p>
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<p>$\odot$ stands for element-wise multiplication.</p>
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<p>Intermediate values and gates are computed as linear transformations of the hidden
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state and input.</p>
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<p>
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<script type="math/tex; mode=display">\begin{align}
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i_t &= lin_x^i(x_t) + lin_h^i(h_{t-1}) \\
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f_t &= lin_x^f(x_t) + lin_h^f(h_{t-1}) \\
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g_t &= lin_x^g(x_t) + lin_h^g(h_{t-1}) \\
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o_t &= lin_x^o(x_t) + lin_h^o(h_{t-1})
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\end{align}</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">20</span><span class="k">class</span> <span class="nc">LSTMCell</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">58</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">input_size</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">hidden_size</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">layer_norm</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">):</span>
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<span class="lineno">59</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>These are the linear layer to transform the <code>input</code> and <code>hidden</code> vectors.
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One of them doesn’t need a bias since we add the transformations.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre></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>This combines $lin_x^i$, $lin_x^f$, $lin_x^g$, and $lin_x^o$ transformations.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">65</span> <span class="bp">self</span><span class="o">.</span><span class="n">hidden_lin</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="n">hidden_size</span><span class="p">,</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">hidden_size</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-5'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-5'>#</a>
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</div>
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<p>This combines $lin_h^i$, $lin_h^f$, $lin_h^g$, and $lin_h^o$ transformations.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">67</span> <span class="bp">self</span><span class="o">.</span><span class="n">input_lin</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="n">input_size</span><span class="p">,</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">hidden_size</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>
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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'>
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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>Whether to apply layer normalizations.</p>
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<p>Applying layer normalization gives better results.
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$i$, $f$, $g$ and $o$ embeddings are normalized and $c_t$ is normalized in
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$h_t = o_t \odot \tanh(\mathop{LN}(c_t))$</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">74</span> <span class="k">if</span> <span class="n">layer_norm</span><span class="p">:</span>
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<span class="lineno">75</span> <span class="bp">self</span><span class="o">.</span><span class="n">layer_norm</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">ModuleList</span><span class="p">([</span><span class="n">nn</span><span class="o">.</span><span class="n">LayerNorm</span><span class="p">(</span><span class="n">hidden_size</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">)])</span>
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<span class="lineno">76</span> <span class="bp">self</span><span class="o">.</span><span class="n">layer_norm_c</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">LayerNorm</span><span class="p">(</span><span class="n">hidden_size</span><span class="p">)</span>
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<span class="lineno">77</span> <span class="k">else</span><span class="p">:</span>
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<span class="lineno">78</span> <span class="bp">self</span><span class="o">.</span><span class="n">layer_norm</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">ModuleList</span><span class="p">([</span><span class="n">nn</span><span class="o">.</span><span class="n">Identity</span><span class="p">()</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">)])</span>
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<span class="lineno">79</span> <span class="bp">self</span><span class="o">.</span><span class="n">layer_norm_c</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Identity</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">81</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="n">h</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">c</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-8'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-8'>#</a>
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</div>
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<p>We compute the linear transformations for $i_t$, $f_t$, $g_t$ and $o_t$
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using the same linear layers.</p>
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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="n">ifgo</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hidden_lin</span><span class="p">(</span><span class="n">h</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">input_lin</span><span class="p">(</span><span class="n">x</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-9'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-9'>#</a>
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</div>
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<p>Each layer produces an output of 4 times the <code>hidden_size</code> and we split them</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">86</span> <span class="n">ifgo</span> <span class="o">=</span> <span class="n">ifgo</span><span class="o">.</span><span class="n">chunk</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="n">dim</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span></pre></div>
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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>Apply layer normalization (not in original paper, but gives better results)</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">89</span> <span class="n">ifgo</span> <span class="o">=</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">layer_norm</span><span class="p">[</span><span class="n">i</span><span class="p">](</span><span class="n">ifgo</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">)]</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-11'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-11'>#</a>
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</div>
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<p>
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<script type="math/tex; mode=display">i_t, f_t, g_t, o_t</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">92</span> <span class="n">i</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">,</span> <span class="n">o</span> <span class="o">=</span> <span class="n">ifgo</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-12'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-12'>#</a>
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</div>
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<p>
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<script type="math/tex; mode=display">c_t = \sigma(f_t) \odot c_{t-1} + \sigma(i_t) \odot \tanh(g_t) </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="n">c_next</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">sigmoid</span><span class="p">(</span><span class="n">f</span><span class="p">)</span> <span class="o">*</span> <span class="n">c</span> <span class="o">+</span> <span class="n">torch</span><span class="o">.</span><span class="n">sigmoid</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="o">*</span> <span class="n">torch</span><span class="o">.</span><span class="n">tanh</span><span class="p">(</span><span class="n">g</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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<p>
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<script type="math/tex; mode=display">h_t = \sigma(o_t) \odot \tanh(c_t)</script>
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Optionally, apply layer norm to $c_t$</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">99</span> <span class="n">h_next</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">sigmoid</span><span class="p">(</span><span class="n">o</span><span class="p">)</span> <span class="o">*</span> <span class="n">torch</span><span class="o">.</span><span class="n">tanh</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">layer_norm_c</span><span class="p">(</span><span class="n">c_next</span><span class="p">))</span>
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<span class="lineno">100</span>
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<span class="lineno">101</span> <span class="k">return</span> <span class="n">h_next</span><span class="p">,</span> <span class="n">c_next</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-14'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-14'>#</a>
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</div>
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<h2>Multilayer LSTM</h2>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">104</span><span class="k">class</span> <span class="nc">LSTM</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-15'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-15'>#</a>
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</div>
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<p>Create a network of <code>n_layers</code> of LSTM.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">109</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">input_size</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">hidden_size</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">n_layers</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-16'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-16'>#</a>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">114</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">115</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_layers</span> <span class="o">=</span> <span class="n">n_layers</span>
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<span class="lineno">116</span> <span class="bp">self</span><span class="o">.</span><span class="n">hidden_size</span> <span class="o">=</span> <span class="n">hidden_size</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-17'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-17'>#</a>
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</div>
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<p>Create cells for each layer. Note that only the first layer gets the input directly.
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Rest of the layers get the input from the layer below</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">119</span> <span class="bp">self</span><span class="o">.</span><span class="n">cells</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">ModuleList</span><span class="p">([</span><span class="n">LSTMCell</span><span class="p">(</span><span class="n">input_size</span><span class="p">,</span> <span class="n">hidden_size</span><span class="p">)]</span> <span class="o">+</span>
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<span class="lineno">120</span> <span class="p">[</span><span class="n">LSTMCell</span><span class="p">(</span><span class="n">hidden_size</span><span class="p">,</span> <span class="n">hidden_size</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_layers</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)])</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-18'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-18'>#</a>
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</div>
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<p><code>x</code> has shape <code>[n_steps, batch_size, input_size]</code> and
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<code>state</code> is a tuple of $h$ and $c$, each with a shape of <code>[batch_size, hidden_size]</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">122</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="n">state</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">Tuple</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">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">]]</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-19'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-19'>#</a>
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</div>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">127</span> <span class="n">n_steps</span><span class="p">,</span> <span class="n">batch_size</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">2</span><span class="p">]</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-20'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-20'>#</a>
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</div>
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<p>Initialize the state if <code>None</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">130</span> <span class="k">if</span> <span class="n">state</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
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<span class="lineno">131</span> <span class="n">h</span> <span class="o">=</span> <span class="p">[</span><span class="n">x</span><span class="o">.</span><span class="n">new_zeros</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">hidden_size</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_layers</span><span class="p">)]</span>
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<span class="lineno">132</span> <span class="n">c</span> <span class="o">=</span> <span class="p">[</span><span class="n">x</span><span class="o">.</span><span class="n">new_zeros</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">hidden_size</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_layers</span><span class="p">)]</span>
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<span class="lineno">133</span> <span class="k">else</span><span class="p">:</span>
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<span class="lineno">134</span> <span class="p">(</span><span class="n">h</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span> <span class="o">=</span> <span class="n">state</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-21'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-21'>#</a>
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</div>
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<p>Reverse stack the tensors to get the states of each layer <br />
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📝 You can just work with the tensor itself but this is easier to debug</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">137</span> <span class="n">h</span><span class="p">,</span> <span class="n">c</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">unbind</span><span class="p">(</span><span class="n">h</span><span class="p">)),</span> <span class="nb">list</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">unbind</span><span class="p">(</span><span class="n">c</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-22'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-22'>#</a>
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</div>
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<p>Array to collect the outputs of the final layer at each time step.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">140</span> <span class="n">out</span> <span class="o">=</span> <span class="p">[]</span>
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<span class="lineno">141</span> <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_steps</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-23'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-23'>#</a>
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</div>
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<p>Input to the first layer is the input itself</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">143</span> <span class="n">inp</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="n">t</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-24'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-24'>#</a>
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</div>
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<p>Loop through the layers</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">145</span> <span class="k">for</span> <span class="n">layer</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_layers</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-25'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-25'>#</a>
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</div>
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<p>Get the state of the layer</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">147</span> <span class="n">h</span><span class="p">[</span><span class="n">layer</span><span class="p">],</span> <span class="n">c</span><span class="p">[</span><span class="n">layer</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cells</span><span class="p">[</span><span class="n">layer</span><span class="p">](</span><span class="n">inp</span><span class="p">,</span> <span class="n">h</span><span class="p">[</span><span class="n">layer</span><span class="p">],</span> <span class="n">c</span><span class="p">[</span><span class="n">layer</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-26'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-26'>#</a>
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</div>
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<p>Input to the next layer is the state of this layer</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">149</span> <span class="n">inp</span> <span class="o">=</span> <span class="n">h</span><span class="p">[</span><span class="n">layer</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-27'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-27'>#</a>
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</div>
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<p>Collect the output $h$ of the final layer</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">151</span> <span class="n">out</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">h</span><span class="p">[</span><span class="o">-</span><span class="mi">1</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-28'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-28'>#</a>
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</div>
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<p>Stack the outputs and states</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">154</span> <span class="n">out</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">stack</span><span class="p">(</span><span class="n">out</span><span class="p">)</span>
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<span class="lineno">155</span> <span class="n">h</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">stack</span><span class="p">(</span><span class="n">h</span><span class="p">)</span>
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<span class="lineno">156</span> <span class="n">c</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">stack</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
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<span class="lineno">157</span>
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<span class="lineno">158</span> <span class="k">return</span> <span class="n">out</span><span class="p">,</span> <span class="p">(</span><span class="n">h</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span></pre></div>
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