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<a class="parent" href="index.html">hypernetworks</a>
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<div class='section' id='section-0'>
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<div class='docs doc-strings'>
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<a href='#section-0'>#</a>
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</div>
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<h1>HyperNetworks - HyperLSTM</h1>
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<p>We have implemented HyperLSTM introduced in paper
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<a href="https://arxiv.org/abs/1609.09106">HyperNetworks</a>, with annotations
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using <a href="https://pytorch.org">PyTorch</a>.
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<a href="https://blog.otoro.net/2016/09/28/hyper-networks/">This blog post</a>
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by David Ha gives a good explanation of HyperNetworks.</p>
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<p>We have an experiment that trains a HyperLSTM to predict text on Shakespeare dataset.
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Here’s the link to code: <a href="experiment.html"><code>experiment.py</code></a></p>
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<p><a href="https://colab.research.google.com/github/lab-ml/nn/blob/master/labml_nn/hypernetworks/experiment.ipynb"><img alt="Open In Colab" src="https://colab.research.google.com/assets/colab-badge.svg" /></a>
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<a href="https://web.lab-ml.com/run?uuid=9e7f39e047e811ebbaff2b26e3148b3d"><img alt="View Run" src="https://img.shields.io/badge/labml-experiment-brightgreen" /></a></p>
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<p>HyperNetworks use a smaller network to generate weights of a larger network.
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There are two variants: static hyper-networks and dynamic hyper-networks.
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Static HyperNetworks have smaller networks that generate weights (kernels)
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of a convolutional network. Dynamic HyperNetworks generate parameters of a
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recurrent neural network
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for each step. This is an implementation of the latter.</p>
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<h2>Dynamic HyperNetworks</h2>
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<p>In a RNN the parameters stay constant for each step.
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Dynamic HyperNetworks generate different parameters for each step.
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HyperLSTM has the structure of a LSTM but the parameters of
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each step are changed by a smaller LSTM network.</p>
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<p>In the basic form, a Dynamic HyperNetwork has a smaller recurrent network that generates
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a feature vector corresponding to each parameter tensor of the larger recurrent network.
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Let’s say the larger network has some parameter $\color{cyan}{W_h}$ the smaller network generates a feature
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vector $z_h$ and we dynamically compute $\color{cyan}{W_h}$ as a linear transformation of $z_h$.
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For instance $\color{cyan}{W_h} = \langle W_{hz}, z_h \rangle$ where
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$W_{hz}$ is a 3-d tensor parameter and $\langle . \rangle$ is a tensor-vector multiplication.
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$z_h$ is usually a linear transformation of the output of the smaller recurrent network.</p>
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<h3>Weight scaling instead of computing</h3>
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<p>Large recurrent networks have large dynamically computed parameters.
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These are calculated using linear transformation of feature vector $z$.
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And this transformation requires an even larger weight tensor.
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That is, when $\color{cyan}{W_h}$ has shape $N_h \times N_h$,
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$W_{hz}$ will be $N_h \times N_h \times N_z$.</p>
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<p>To overcome this, we compute the weight parameters of the recurrent network by
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dynamically scaling each row of a matrix of same size.
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<script type="math/tex; mode=display">\begin{align}
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d(z) = W_{hz} z_h \\
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\\
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\color{cyan}{W_h} =
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\begin{pmatrix}
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d_0(z) W_{hd_0} \\
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d_1(z) W_{hd_1} \\
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... \\
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d_{N_h}(z) W_{hd_{N_h}} \\
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\end{pmatrix}
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\end{align}</script>
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where $W_{hd}$ is a $N_h \times N_h$ parameter matrix.</p>
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<p>We can further optimize this when we compute $\color{cyan}{W_h} h$,
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as
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<script type="math/tex; mode=display">\color{lightgreen}{d(z) \odot (W_{hd} h)}</script>
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where $\odot$ stands for element-wise multiplication.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">71</span><span></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">72</span>
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<span class="lineno">73</span><span class="kn">import</span> <span class="nn">torch</span>
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<span class="lineno">74</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">75</span>
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<span class="lineno">76</span><span class="kn">from</span> <span class="nn">labml_helpers.module</span> <span class="kn">import</span> <span class="n">Module</span>
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<span class="lineno">77</span><span class="kn">from</span> <span class="nn">labml_nn.lstm</span> <span class="kn">import</span> <span class="n">LSTMCell</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>HyperLSTM Cell</h2>
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<p>For HyperLSTM the smaller network and the larger network both have the LSTM structure.
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This is defined in Appendix A.2.2 in the paper.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">80</span><span class="k">class</span> <span class="nc">HyperLSTMCell</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 doc-strings'>
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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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<p><code>input_size</code> is the size of the input $x_t$,
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<code>hidden_size</code> is the size of the LSTM, and
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<code>hyper_size</code> is the size of the smaller LSTM that alters the weights of the larger outer LSTM.
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<code>n_z</code> is the size of the feature vectors used to alter the LSTM weights.</p>
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<p>We use the output of the smaller LSTM to compute $z_h^{i,f,g,o}$, $z_x^{i,f,g,o}$ and
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$z_b^{i,f,g,o}$ using linear transformations.
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We calculate $d_h^{i,f,g,o}(z_h^{i,f,g,o})$, $d_x^{i,f,g,o}(z_x^{i,f,g,o})$, and
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$d_b^{i,f,g,o}(z_b^{i,f,g,o})$ from these, using linear transformations again.
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These are then used to scale the rows of weight and bias tensors of the main LSTM.</p>
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<p>📝 Since the computation of $z$ and $d$ are two sequential linear transformations
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these can be combined into a single linear transformation.
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However we’ve implemented this separately so that it matches with the description
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in the paper.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">88</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">hyper_size</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">n_z</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-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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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">106</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span></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>The input to the hyperLSTM is
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<script type="math/tex; mode=display">
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\hat{x}_t = \begin{pmatrix}
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h_{t-1} \\
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x_t
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\end{pmatrix}
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</script>
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where $x_t$ is the input and $h_{t-1}$ is the output of the outer LSTM at previous step.
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So the input size is <code>hidden_size + input_size</code>.</p>
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<p>The output of hyperLSTM is $\hat{h}_t$ and $\hat{c}_t$.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">119</span> <span class="bp">self</span><span class="o">.</span><span class="n">hyper</span> <span class="o">=</span> <span class="n">LSTMCell</span><span class="p">(</span><span class="n">hidden_size</span> <span class="o">+</span> <span class="n">input_size</span><span class="p">,</span> <span class="n">hyper_size</span><span class="p">,</span> <span class="n">layer_norm</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-5'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-5'>#</a>
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</div>
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<p>
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<script type="math/tex; mode=display">z_h^{i,f,g,o} = lin_{h}^{i,f,g,o}(\hat{h}_t)</script>
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🤔 In the paper it was specified as
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<script type="math/tex; mode=display">z_h^{i,f,g,o} = lin_{h}^{i,f,g,o}(\hat{h}_{\color{red}{t-1}})</script>
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I feel that it’s a typo.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">125</span> <span class="bp">self</span><span class="o">.</span><span class="n">z_h</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">hyper_size</span><span class="p">,</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">n_z</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>
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<script type="math/tex; mode=display">z_x^{i,f,g,o} = lin_x^{i,f,g,o}(\hat{h}_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">127</span> <span class="bp">self</span><span class="o">.</span><span class="n">z_x</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">hyper_size</span><span class="p">,</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">n_z</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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<p>
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<script type="math/tex; mode=display">z_b^{i,f,g,o} = lin_b^{i,f,g,o}(\hat{h}_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">129</span> <span class="bp">self</span><span class="o">.</span><span class="n">z_b</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">hyper_size</span><span class="p">,</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">n_z</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-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>
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<script type="math/tex; mode=display">d_h^{i,f,g,o}(z_h^{i,f,g,o}) = lin_{dh}^{i,f,g,o}(z_h^{i,f,g,o})</script>
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</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">132</span> <span class="n">d_h</span> <span class="o">=</span> <span class="p">[</span><span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="n">n_z</span><span class="p">,</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> <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">133</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_h</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">d_h</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>
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<script type="math/tex; mode=display">d_x^{i,f,g,o}(z_x^{i,f,g,o}) = lin_{dx}^{i,f,g,o}(z_x^{i,f,g,o})</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">135</span> <span class="n">d_x</span> <span class="o">=</span> <span class="p">[</span><span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="n">n_z</span><span class="p">,</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> <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">136</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_x</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">d_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-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>
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<script type="math/tex; mode=display">d_b^{i,f,g,o}(z_b^{i,f,g,o}) = lin_{db}^{i,f,g,o}(z_b^{i,f,g,o})</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">138</span> <span class="n">d_b</span> <span class="o">=</span> <span class="p">[</span><span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="n">n_z</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">139</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_b</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">d_b</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-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>The weight matrices $W_h^{i,f,g,o}$</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">142</span> <span class="bp">self</span><span class="o">.</span><span class="n">w_h</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">ParameterList</span><span class="p">([</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">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="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-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>The weight matrices $W_x^{i,f,g,o}$</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">144</span> <span class="bp">self</span><span class="o">.</span><span class="n">w_x</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">ParameterList</span><span class="p">([</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">hidden_size</span><span class="p">,</span> <span class="n">input_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></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>Layer normalization</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="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">148</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></pre></div>
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</div>
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</div>
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<div class='section' id='section-14'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-14'>#</a>
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</div>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">150</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>
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<span class="lineno">151</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>
|
|
<span class="lineno">152</span> <span class="n">h_hat</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_hat</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-15'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-15'>#</a>
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</div>
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<p>
|
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<script type="math/tex; mode=display">
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|
\hat{x}_t = \begin{pmatrix}
|
|
h_{t-1} \\
|
|
x_t
|
|
\end{pmatrix}
|
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</script>
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</p>
|
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</div>
|
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<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">159</span> <span class="n">x_hat</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">cat</span><span class="p">((</span><span class="n">h</span><span class="p">,</span> <span class="n">x</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>
|
|
<div class='section' id='section-16'>
|
|
<div class='docs'>
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|
<div class='section-link'>
|
|
<a href='#section-16'>#</a>
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|
</div>
|
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<p>
|
|
<script type="math/tex; mode=display">\hat{h}_t, \hat{c}_t = lstm(\hat{x}_t, \hat{h}_{t-1}, \hat{c}_{t-1})</script>
|
|
</p>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">161</span> <span class="n">h_hat</span><span class="p">,</span> <span class="n">c_hat</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hyper</span><span class="p">(</span><span class="n">x_hat</span><span class="p">,</span> <span class="n">h_hat</span><span class="p">,</span> <span class="n">c_hat</span><span class="p">)</span></pre></div>
|
|
</div>
|
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</div>
|
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<div class='section' id='section-17'>
|
|
<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-17'>#</a>
|
|
</div>
|
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<p>
|
|
<script type="math/tex; mode=display">z_h^{i,f,g,o} = lin_{h}^{i,f,g,o}(\hat{h}_t)</script>
|
|
</p>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">164</span> <span class="n">z_h</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">z_h</span><span class="p">(</span><span class="n">h_hat</span><span class="p">)</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>
|
|
</div>
|
|
</div>
|
|
<div class='section' id='section-18'>
|
|
<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-18'>#</a>
|
|
</div>
|
|
<p>
|
|
<script type="math/tex; mode=display">z_x^{i,f,g,o} = lin_x^{i,f,g,o}(\hat{h}_t)</script>
|
|
</p>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">166</span> <span class="n">z_x</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">z_x</span><span class="p">(</span><span class="n">h_hat</span><span class="p">)</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>
|
|
</div>
|
|
</div>
|
|
<div class='section' id='section-19'>
|
|
<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-19'>#</a>
|
|
</div>
|
|
<p>
|
|
<script type="math/tex; mode=display">z_b^{i,f,g,o} = lin_b^{i,f,g,o}(\hat{h}_t)</script>
|
|
</p>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">168</span> <span class="n">z_b</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">z_b</span><span class="p">(</span><span class="n">h_hat</span><span class="p">)</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>
|
|
</div>
|
|
</div>
|
|
<div class='section' id='section-20'>
|
|
<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-20'>#</a>
|
|
</div>
|
|
<p>We calculate $i$, $f$, $g$ and $o$ in a loop</p>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">171</span> <span class="n">ifgo</span> <span class="o">=</span> <span class="p">[]</span>
|
|
<span class="lineno">172</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>
|
|
</div>
|
|
</div>
|
|
<div class='section' id='section-21'>
|
|
<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-21'>#</a>
|
|
</div>
|
|
<p>
|
|
<script type="math/tex; mode=display">d_h^{i,f,g,o}(z_h^{i,f,g,o}) = lin_{dh}^{i,f,g,o}(z_h^{i,f,g,o})</script>
|
|
</p>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">174</span> <span class="n">d_h</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_h</span><span class="p">[</span><span class="n">i</span><span class="p">](</span><span class="n">z_h</span><span class="p">[</span><span class="n">i</span><span class="p">])</span></pre></div>
|
|
</div>
|
|
</div>
|
|
<div class='section' id='section-22'>
|
|
<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-22'>#</a>
|
|
</div>
|
|
<p>
|
|
<script type="math/tex; mode=display">d_x^{i,f,g,o}(z_x^{i,f,g,o}) = lin_{dx}^{i,f,g,o}(z_x^{i,f,g,o})</script>
|
|
</p>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">176</span> <span class="n">d_x</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_x</span><span class="p">[</span><span class="n">i</span><span class="p">](</span><span class="n">z_x</span><span class="p">[</span><span class="n">i</span><span class="p">])</span></pre></div>
|
|
</div>
|
|
</div>
|
|
<div class='section' id='section-23'>
|
|
<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-23'>#</a>
|
|
</div>
|
|
<p>
|
|
<script type="math/tex; mode=display">\begin{align}
|
|
{i,f,g,o} = LN(&\color{lightgreen}{d_h^{i,f,g,o}(z_h) \odot (W_h^{i,f,g,o} h_{t-1})} \\
|
|
+ &\color{lightgreen}{d_x^{i,f,g,o}(z_x) \odot (W_h^{i,f,g,o} x_t)} \\
|
|
+ &d_b^{i,f,g,o}(z_b))
|
|
\end{align}</script>
|
|
</p>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">183</span> <span class="n">y</span> <span class="o">=</span> <span class="n">d_h</span> <span class="o">*</span> <span class="n">torch</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="s1">'ij,bj->bi'</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">w_h</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">h</span><span class="p">)</span> <span class="o">+</span> \
|
|
<span class="lineno">184</span> <span class="n">d_x</span> <span class="o">*</span> <span class="n">torch</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="s1">'ij,bj->bi'</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">w_x</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">x</span><span class="p">)</span> <span class="o">+</span> \
|
|
<span class="lineno">185</span> <span class="bp">self</span><span class="o">.</span><span class="n">d_b</span><span class="p">[</span><span class="n">i</span><span class="p">](</span><span class="n">z_b</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
|
|
<span class="lineno">186</span>
|
|
<span class="lineno">187</span> <span class="n">ifgo</span><span class="o">.</span><span class="n">append</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">y</span><span class="p">))</span></pre></div>
|
|
</div>
|
|
</div>
|
|
<div class='section' id='section-24'>
|
|
<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-24'>#</a>
|
|
</div>
|
|
<p>
|
|
<script type="math/tex; mode=display">i_t, f_t, g_t, o_t</script>
|
|
</p>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">190</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>
|
|
</div>
|
|
</div>
|
|
<div class='section' id='section-25'>
|
|
<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-25'>#</a>
|
|
</div>
|
|
<p>
|
|
<script type="math/tex; mode=display">c_t = \sigma(f_t) \odot c_{t-1} + \sigma(i_t) \odot \tanh(g_t) </script>
|
|
</p>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">193</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>
|
|
</div>
|
|
</div>
|
|
<div class='section' id='section-26'>
|
|
<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-26'>#</a>
|
|
</div>
|
|
<p>
|
|
<script type="math/tex; mode=display">h_t = \sigma(o_t) \odot \tanh(LN(c_t))</script>
|
|
</p>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">196</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>
|
|
<span class="lineno">197</span>
|
|
<span class="lineno">198</span> <span class="k">return</span> <span class="n">h_next</span><span class="p">,</span> <span class="n">c_next</span><span class="p">,</span> <span class="n">h_hat</span><span class="p">,</span> <span class="n">c_hat</span></pre></div>
|
|
</div>
|
|
</div>
|
|
<div class='section' id='section-27'>
|
|
<div class='docs doc-strings'>
|
|
<div class='section-link'>
|
|
<a href='#section-27'>#</a>
|
|
</div>
|
|
<h1>HyperLSTM module</h1>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">201</span><span class="k">class</span> <span class="nc">HyperLSTM</span><span class="p">(</span><span class="n">Module</span><span class="p">):</span></pre></div>
|
|
</div>
|
|
</div>
|
|
<div class='section' id='section-28'>
|
|
<div class='docs doc-strings'>
|
|
<div class='section-link'>
|
|
<a href='#section-28'>#</a>
|
|
</div>
|
|
<p>Create a network of <code>n_layers</code> of HyperLSTM.</p>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">205</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">hyper_size</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">n_z</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>
|
|
</div>
|
|
</div>
|
|
<div class='section' id='section-29'>
|
|
<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-29'>#</a>
|
|
</div>
|
|
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">210</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-30'>
|
|
<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-30'>#</a>
|
|
</div>
|
|
<p>Store sizes to initialize state</p>
|
|
</div>
|
|
<div class='code'>
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<div class="highlight"><pre><span class="lineno">213</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">214</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>
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<span class="lineno">215</span> <span class="bp">self</span><span class="o">.</span><span class="n">hyper_size</span> <span class="o">=</span> <span class="n">hyper_size</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-31'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-31'>#</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">219</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">HyperLSTMCell</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="n">hyper_size</span><span class="p">,</span> <span class="n">n_z</span><span class="p">)]</span> <span class="o">+</span>
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<span class="lineno">220</span> <span class="p">[</span><span class="n">HyperLSTMCell</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="n">hyper_size</span><span class="p">,</span> <span class="n">n_z</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span>
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<span class="lineno">221</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-32'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-32'>#</a>
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</div>
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<ul>
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<li><code>x</code> has shape <code>[n_steps, batch_size, input_size]</code> and</li>
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<li><code>state</code> is a tuple of $h, c, \hat{h}, \hat{c}$.
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$h, c$ have shape <code>[batch_size, hidden_size]</code> and
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$\hat{h}, \hat{c}$ have shape <code>[batch_size, hyper_size]</code>.</li>
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</ul>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">223</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>
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<span class="lineno">224</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="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-33'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-33'>#</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">231</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-34'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-34'>#</a>
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</div>
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<p>Initialize the state with zeros 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">234</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">235</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">236</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">237</span> <span class="n">h_hat</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">hyper_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">238</span> <span class="n">c_hat</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">hyper_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></pre></div>
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</div>
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</div>
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<div class='section' id='section-35'>
|
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-35'>#</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">240</span> <span class="k">else</span><span class="p">:</span>
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<span class="lineno">241</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="n">h_hat</span><span class="p">,</span> <span class="n">c_hat</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-36'>
|
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<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-36'>#</a>
|
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</div>
|
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<p>Reverse stack the tensors to get the states of each layer</p>
|
|
<p>📝 You can just work with the tensor itself but this is easier to debug</p>
|
|
</div>
|
|
<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">245</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>
|
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<span class="lineno">246</span> <span class="n">h_hat</span><span class="p">,</span> <span class="n">c_hat</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_hat</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_hat</span><span class="p">))</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-37'>
|
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<div class='docs'>
|
|
<div class='section-link'>
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<a href='#section-37'>#</a>
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</div>
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<p>Collect the outputs of the final layer at each step</p>
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|
</div>
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<div class='code'>
|
|
<div class="highlight"><pre><span class="lineno">249</span> <span class="n">out</span> <span class="o">=</span> <span class="p">[]</span>
|
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<span class="lineno">250</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-38'>
|
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<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-38'>#</a>
|
|
</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">252</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-39'>
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<div class='docs'>
|
|
<div class='section-link'>
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<a href='#section-39'>#</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">254</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>
|
|
<div class='section' id='section-40'>
|
|
<div class='docs'>
|
|
<div class='section-link'>
|
|
<a href='#section-40'>#</a>
|
|
</div>
|
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<p>Get the state of the layer</p>
|
|
</div>
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<div class='code'>
|
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<div class="highlight"><pre><span class="lineno">256</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="n">h_hat</span><span class="p">[</span><span class="n">layer</span><span class="p">],</span> <span class="n">c_hat</span><span class="p">[</span><span class="n">layer</span><span class="p">]</span> <span class="o">=</span> \
|
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<span class="lineno">257</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> <span class="n">h_hat</span><span class="p">[</span><span class="n">layer</span><span class="p">],</span> <span class="n">c_hat</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>
|
|
<div class='section' id='section-41'>
|
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<div class='docs'>
|
|
<div class='section-link'>
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<a href='#section-41'>#</a>
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</div>
|
|
<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">259</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-42'>
|
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<div class='docs'>
|
|
<div class='section-link'>
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<a href='#section-42'>#</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">261</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-43'>
|
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<div class='docs'>
|
|
<div class='section-link'>
|
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<a href='#section-43'>#</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">264</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">265</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">266</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">267</span> <span class="n">h_hat</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_hat</span><span class="p">)</span>
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<span class="lineno">268</span> <span class="n">c_hat</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_hat</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-44'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-44'>#</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">271</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> <span class="n">h_hat</span><span class="p">,</span> <span class="n">c_hat</span><span class="p">)</span></pre></div>
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