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<title>FNet Experiment</title>
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<p>
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<a class="parent" href="../index.html">transformers</a>
<a class="parent" href="index.html">fnet</a>
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<p>
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<a href="https://github.com/labmlai/annotated_deep_learning_paper_implementations/tree/master/labml_nn/transformers/fnet/experiment.py" target="_blank">
View code on Github</a>
</p>
</div>
</div>
<div class='section' id='section-0'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-0'>#</a>
</div>
<h1><a href="index.html">FNet</a> Experiment</h1>
<p>This is an annotated PyTorch experiment to train a <a href="index.html">FNet model</a>.</p>
<p>This is based on <a href="../../experiments/nlp_classification.html">general training loop and configurations for AG News classification task</a>.</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">15</span><span></span><span class="kn">import</span> <span class="nn">torch</span>
<span class="lineno">16</span><span class="kn">from</span> <span class="nn">torch</span> <span class="kn">import</span> <span class="n">nn</span>
<span class="lineno">17</span>
<span class="lineno">18</span><span class="kn">from</span> <span class="nn">labml</span> <span class="kn">import</span> <span class="n">experiment</span>
<span class="lineno">19</span><span class="kn">from</span> <span class="nn">labml.configs</span> <span class="kn">import</span> <span class="n">option</span>
<span class="lineno">20</span><span class="kn">from</span> <span class="nn">labml_nn.experiments.nlp_classification</span> <span class="kn">import</span> <span class="n">NLPClassificationConfigs</span>
<span class="lineno">21</span><span class="kn">from</span> <span class="nn">labml_nn.transformers</span> <span class="kn">import</span> <span class="n">Encoder</span>
<span class="lineno">22</span><span class="kn">from</span> <span class="nn">labml_nn.transformers</span> <span class="kn">import</span> <span class="n">TransformerConfigs</span></pre></div>
</div>
</div>
<div class='section' id='section-1'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-1'>#</a>
</div>
<h1>Transformer based classifier model</h1>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">25</span><span class="k">class</span> <span class="nc">TransformerClassifier</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">Module</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-2'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-2'>#</a>
</div>
<ul><li><code class="highlight"><span></span><span class="n">encoder</span></code>
is the transformer <a href="../models.html#Encoder">Encoder</a> </li>
<li><code class="highlight"><span></span><span class="n">src_embed</span></code>
is the token <a href="../models.html#EmbeddingsWithLearnedPositionalEncoding">embedding module (with positional encodings)</a> </li>
<li><code class="highlight"><span></span><span class="n">generator</span></code>
is the <a href="../models.html#Generator">final fully connected layer</a> that gives the logits.</li></ul>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">29</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">encoder</span><span class="p">:</span> <span class="n">Encoder</span><span class="p">,</span> <span class="n">src_embed</span><span class="p">:</span> <span class="n">nn</span><span class="o">.</span><span class="n">Module</span><span class="p">,</span> <span class="n">generator</span><span class="p">:</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-3'>
<div class='docs'>
<div class='section-link'>
<a href='#section-3'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">36</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
<span class="lineno">37</span> <span class="bp">self</span><span class="o">.</span><span class="n">src_embed</span> <span class="o">=</span> <span class="n">src_embed</span>
<span class="lineno">38</span> <span class="bp">self</span><span class="o">.</span><span class="n">encoder</span> <span class="o">=</span> <span class="n">encoder</span>
<span class="lineno">39</span> <span class="bp">self</span><span class="o">.</span><span class="n">generator</span> <span class="o">=</span> <span class="n">generator</span></pre></div>
</div>
</div>
<div class='section' id='section-4'>
<div class='docs'>
<div class='section-link'>
<a href='#section-4'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">41</span> <span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">:</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-5'>
<div class='docs'>
<div class='section-link'>
<a href='#section-5'>#</a>
</div>
<p>Get the token embeddings with positional encodings </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">43</span> <span class="n">x</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">src_embed</span><span class="p">(</span><span class="n">x</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-6'>
<div class='docs'>
<div class='section-link'>
<a href='#section-6'>#</a>
</div>
<p>Transformer encoder </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">45</span> <span class="n">x</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">encoder</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span></pre></div>
</div>
</div>
<div class='section' id='section-7'>
<div class='docs'>
<div class='section-link'>
<a href='#section-7'>#</a>
</div>
<p>Get logits for classification.</p>
<p>We set the <code class="highlight"><span></span><span class="p">[</span><span class="n">CLS</span><span class="p">]</span></code>
token at the last position of the sequence. This is extracted by <code class="highlight"><span></span><span class="n">x</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span></code>
, where <code class="highlight"><span></span><span class="n">x</span></code>
is of shape <code class="highlight"><span></span><span class="p">[</span><span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">d_model</span><span class="p">]</span></code>
</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">51</span> <span class="n">x</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">generator</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span></pre></div>
</div>
</div>
<div class='section' id='section-8'>
<div class='docs'>
<div class='section-link'>
<a href='#section-8'>#</a>
</div>
<p>Return results (second value is for state, since our trainer is used with RNNs also) </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">55</span> <span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="kc">None</span></pre></div>
</div>
</div>
<div class='section' id='section-9'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-9'>#</a>
</div>
<h2>Configurations</h2>
<p>This inherits from <a href="../../experiments/nlp_classification.html"><code class="highlight"><span></span><span class="n">NLPClassificationConfigs</span></code>
</a></p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">58</span><span class="k">class</span> <span class="nc">Configs</span><span class="p">(</span><span class="n">NLPClassificationConfigs</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-10'>
<div class='docs'>
<div class='section-link'>
<a href='#section-10'>#</a>
</div>
<p>Classification model </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">67</span> <span class="n">model</span><span class="p">:</span> <span class="n">TransformerClassifier</span></pre></div>
</div>
</div>
<div class='section' id='section-11'>
<div class='docs'>
<div class='section-link'>
<a href='#section-11'>#</a>
</div>
<p>Transformer </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">69</span> <span class="n">transformer</span><span class="p">:</span> <span class="n">TransformerConfigs</span></pre></div>
</div>
</div>
<div class='section' id='section-12'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-12'>#</a>
</div>
<h3>Transformer configurations</h3>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">72</span><span class="nd">@option</span><span class="p">(</span><span class="n">Configs</span><span class="o">.</span><span class="n">transformer</span><span class="p">)</span>
<span class="lineno">73</span><span class="k">def</span> <span class="nf">_transformer_configs</span><span class="p">(</span><span class="n">c</span><span class="p">:</span> <span class="n">Configs</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-13'>
<div class='docs'>
<div class='section-link'>
<a href='#section-13'>#</a>
</div>
<p>We use our <a href="../configs.html#TransformerConfigs">configurable transformer implementation</a> </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">80</span> <span class="n">conf</span> <span class="o">=</span> <span class="n">TransformerConfigs</span><span class="p">()</span></pre></div>
</div>
</div>
<div class='section' id='section-14'>
<div class='docs'>
<div class='section-link'>
<a href='#section-14'>#</a>
</div>
<p>Set the vocabulary sizes for embeddings and generating logits </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">82</span> <span class="n">conf</span><span class="o">.</span><span class="n">n_src_vocab</span> <span class="o">=</span> <span class="n">c</span><span class="o">.</span><span class="n">n_tokens</span>
<span class="lineno">83</span> <span class="n">conf</span><span class="o">.</span><span class="n">n_tgt_vocab</span> <span class="o">=</span> <span class="n">c</span><span class="o">.</span><span class="n">n_tokens</span></pre></div>
</div>
</div>
<div class='section' id='section-15'>
<div class='docs'>
<div class='section-link'>
<a href='#section-15'>#</a>
</div>
<p> </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">86</span> <span class="k">return</span> <span class="n">conf</span></pre></div>
</div>
</div>
<div class='section' id='section-16'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-16'>#</a>
</div>
<p> Create <code class="highlight"><span></span><span class="n">FNetMix</span></code>
module that can replace the self-attention in <a href="../models.html#TransformerLayer">transformer encoder layer</a> .</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">89</span><span class="nd">@option</span><span class="p">(</span><span class="n">TransformerConfigs</span><span class="o">.</span><span class="n">encoder_attn</span><span class="p">)</span>
<span class="lineno">90</span><span class="k">def</span> <span class="nf">fnet_mix</span><span class="p">():</span></pre></div>
</div>
</div>
<div class='section' id='section-17'>
<div class='docs'>
<div class='section-link'>
<a href='#section-17'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">96</span> <span class="kn">from</span> <span class="nn">labml_nn.transformers.fnet</span> <span class="kn">import</span> <span class="n">FNetMix</span>
<span class="lineno">97</span> <span class="k">return</span> <span class="n">FNetMix</span><span class="p">()</span></pre></div>
</div>
</div>
<div class='section' id='section-18'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-18'>#</a>
</div>
<p> Create classification model</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">100</span><span class="nd">@option</span><span class="p">(</span><span class="n">Configs</span><span class="o">.</span><span class="n">model</span><span class="p">)</span>
<span class="lineno">101</span><span class="k">def</span> <span class="nf">_model</span><span class="p">(</span><span class="n">c</span><span class="p">:</span> <span class="n">Configs</span><span class="p">):</span></pre></div>
</div>
</div>
<div class='section' id='section-19'>
<div class='docs'>
<div class='section-link'>
<a href='#section-19'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">105</span> <span class="n">m</span> <span class="o">=</span> <span class="n">TransformerClassifier</span><span class="p">(</span><span class="n">c</span><span class="o">.</span><span class="n">transformer</span><span class="o">.</span><span class="n">encoder</span><span class="p">,</span>
<span class="lineno">106</span> <span class="n">c</span><span class="o">.</span><span class="n">transformer</span><span class="o">.</span><span class="n">src_embed</span><span class="p">,</span>
<span class="lineno">107</span> <span class="n">nn</span><span class="o">.</span><span class="n">Linear</span><span class="p">(</span><span class="n">c</span><span class="o">.</span><span class="n">d_model</span><span class="p">,</span> <span class="n">c</span><span class="o">.</span><span class="n">n_classes</span><span class="p">))</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">c</span><span class="o">.</span><span class="n">device</span><span class="p">)</span>
<span class="lineno">108</span>
<span class="lineno">109</span> <span class="k">return</span> <span class="n">m</span></pre></div>
</div>
</div>
<div class='section' id='section-20'>
<div class='docs'>
<div class='section-link'>
<a href='#section-20'>#</a>
</div>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">112</span><span class="k">def</span> <span class="nf">main</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>Create experiment </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">114</span> <span class="n">experiment</span><span class="o">.</span><span class="n">create</span><span class="p">(</span><span class="n">name</span><span class="o">=</span><span class="s2">&quot;fnet&quot;</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>Create configs </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">116</span> <span class="n">conf</span> <span class="o">=</span> <span class="n">Configs</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>Override configurations </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">118</span> <span class="n">experiment</span><span class="o">.</span><span class="n">configs</span><span class="p">(</span><span class="n">conf</span><span class="p">,</span> <span class="p">{</span></pre></div>
</div>
</div>
<div class='section' id='section-24'>
<div class='docs'>
<div class='section-link'>
<a href='#section-24'>#</a>
</div>
<p>Use world level tokenizer </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">120</span> <span class="s1">&#39;tokenizer&#39;</span><span class="p">:</span> <span class="s1">&#39;basic_english&#39;</span><span class="p">,</span></pre></div>
</div>
</div>
<div class='section' id='section-25'>
<div class='docs'>
<div class='section-link'>
<a href='#section-25'>#</a>
</div>
<p>Train for <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">32</span></span></span></span></span> epochs </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">123</span> <span class="s1">&#39;epochs&#39;</span><span class="p">:</span> <span class="mi">32</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>Switch between training and validation for <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">10</span></span></span></span></span> times per epoch </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">126</span> <span class="s1">&#39;inner_iterations&#39;</span><span class="p">:</span> <span class="mi">10</span><span class="p">,</span></pre></div>
</div>
</div>
<div class='section' id='section-27'>
<div class='docs'>
<div class='section-link'>
<a href='#section-27'>#</a>
</div>
<p>Transformer configurations (same as defaults) </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">129</span> <span class="s1">&#39;transformer.d_model&#39;</span><span class="p">:</span> <span class="mi">512</span><span class="p">,</span>
<span class="lineno">130</span> <span class="s1">&#39;transformer.ffn.d_ff&#39;</span><span class="p">:</span> <span class="mi">2048</span><span class="p">,</span>
<span class="lineno">131</span> <span class="s1">&#39;transformer.n_heads&#39;</span><span class="p">:</span> <span class="mi">8</span><span class="p">,</span>
<span class="lineno">132</span> <span class="s1">&#39;transformer.n_layers&#39;</span><span class="p">:</span> <span class="mi">6</span><span class="p">,</span></pre></div>
</div>
</div>
<div class='section' id='section-28'>
<div class='docs'>
<div class='section-link'>
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<p>Use <a href="index.html">FNet</a> instead of self-a ttention </p>
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<div class='code'>
<div class="highlight"><pre><span class="lineno">136</span> <span class="s1">&#39;transformer.encoder_attn&#39;</span><span class="p">:</span> <span class="s1">&#39;fnet_mix&#39;</span><span class="p">,</span></pre></div>
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<p>Use <a href="../../optimizers/noam.html">Noam optimizer</a> </p>
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<div class="highlight"><pre><span class="lineno">139</span> <span class="s1">&#39;optimizer.optimizer&#39;</span><span class="p">:</span> <span class="s1">&#39;Noam&#39;</span><span class="p">,</span>
<span class="lineno">140</span> <span class="s1">&#39;optimizer.learning_rate&#39;</span><span class="p">:</span> <span class="mf">1.</span><span class="p">,</span>
<span class="lineno">141</span> <span class="p">})</span></pre></div>
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<p>Set models for saving and loading </p>
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<div class="highlight"><pre><span class="lineno">144</span> <span class="n">experiment</span><span class="o">.</span><span class="n">add_pytorch_models</span><span class="p">({</span><span class="s1">&#39;model&#39;</span><span class="p">:</span> <span class="n">conf</span><span class="o">.</span><span class="n">model</span><span class="p">})</span></pre></div>
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<p>Start the experiment </p>
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<div class="highlight"><pre><span class="lineno">147</span> <span class="k">with</span> <span class="n">experiment</span><span class="o">.</span><span class="n">start</span><span class="p">():</span></pre></div>
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<p>Run training </p>
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<div class="highlight"><pre><span class="lineno">149</span> <span class="n">conf</span><span class="o">.</span><span class="n">run</span><span class="p">()</span></pre></div>
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<p> </p>
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<div class="highlight"><pre><span class="lineno">153</span><span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">&#39;__main__&#39;</span><span class="p">:</span>
<span class="lineno">154</span> <span class="n">main</span><span class="p">()</span></pre></div>
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<h1>FNet: Mixing Tokens with Fourier Transforms</h1>
<p>This is a <a href="https://pytorch.org">PyTorch</a> implementation of the paper <a href="https://arxiv.org/abs/2105.03824">FNet: Mixing Tokens with Fourier Transforms</a>.</p>
<p>This paper replaces the <a href="../mha.html">self-attention layer</a> with two <a href="https://en.wikipedia.org/wiki/Discrete_Fourier_transform">Fourier transforms</a> to <em>mix</em> tokens. This is a <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">7</span><span class="mord">×</span></span></span></span></span> more efficient than self-attention. The accuracy loss of using this over self-attention is about 92% for <a href="https://paperswithcode.com/method/bert">BERT</a> on <a href="https://paperswithcode.com/dataset/glue">GLUE benchmark</a>.</p>
<h2>Mixing tokens with two Fourier transforms</h2>
<p>We apply Fourier transform along the hidden dimension (embedding dimension) and then along the sequence dimension.</p>
<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.20001em;vertical-align:-0.35001em;"></span><span class="mord coloredeq eqa" style=""><span class="mord" style=""><span class="mord coloredeq eqb" style=""><span class="mord mathcal coloredeq eqi" style="">R</span></span><span class="mord coloredeq eqb" style=""><span class="delimsizing size1" style=""><span style="">(</span></span></span><span class="mord coloredeq eqb" style=""><span class="mord coloredeq eqc" style=""><span class="mord" style=""><span class="mord mathcal coloredeq eqh" style="margin-right:0.09931em">F</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord text mtight" style=""><span class="mord mtight" style="">seq</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mord coloredeq eqc" style=""><span class="delimsizing size1" style=""><span style="">(</span></span></span><span class="mord coloredeq eqc" style=""><span class="mord coloredeq eqe" style=""><span class="mord" style=""><span class="mord mathcal coloredeq eqh" style="margin-right:0.09931em">F</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord text mtight" style=""><span class="mord mtight" style="">hidden</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqe" style="">(</span><span class="mord coloredeq eqe" style=""><span class="mord mathnormal coloredeq eql" style="">x</span></span><span class="mclose coloredeq eqe" style="">)</span></span><span class="mord coloredeq eqc" style=""><span class="delimsizing size1" style=""><span style="">)</span></span></span></span><span class="mord coloredeq eqb" style=""><span class="delimsizing size1" style=""><span style="">)</span></span></span></span></span></span></span></span></span></span></p>
<p>where <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eql" style=""><span class="mord mathnormal" style="">x</span></span></span></span></span></span> is the embedding input, <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqh" style=""><span class="mord mathcal" style="margin-right:0.09931em">F</span></span></span></span></span></span> stands for the fourier transform and <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord coloredeq eqi" style=""><span class="mord mathcal" style="">R</span></span></span></span></span></span> stands for the real component in complex numbers.</p>
<p>This is very simple to implement on PyTorch - just 1 line of code. The paper suggests using a precomputed DFT matrix and doing matrix multiplication to get the Fourier transformation.</p>
<p>Here is <a href="experiment.html">the training code</a> for using a FNet based model for classifying <a href="https://paperswithcode.com/dataset/ag-news">AG News</a>.</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">41</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="lineno">42</span>
<span class="lineno">43</span><span class="kn">import</span> <span class="nn">torch</span>
<span class="lineno">44</span><span class="kn">from</span> <span class="nn">torch</span> <span class="kn">import</span> <span class="n">nn</span></pre></div>
</div>
</div>
<div class='section' id='section-1'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-1'>#</a>
</div>
<h2>FNet - Mix tokens</h2>
<p>This module simply implements <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.20001em;vertical-align:-0.35001em;"></span><span class="mord coloredeq eqa" style=""><span class="mord" style=""><span class="mord coloredeq eqb" style=""><span class="mord mathcal coloredeq eqi" style="">R</span></span><span class="mord coloredeq eqb" style=""><span class="delimsizing size1" style=""><span style="">(</span></span></span><span class="mord coloredeq eqb" style=""><span class="mord coloredeq eqc" style=""><span class="mord" style=""><span class="mord mathcal coloredeq eqh" style="margin-right:0.09931em">F</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord text mtight" style=""><span class="mord mtight" style="">seq</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mord coloredeq eqc" style=""><span class="delimsizing size1" style=""><span style="">(</span></span></span><span class="mord coloredeq eqc" style=""><span class="mord coloredeq eqe" style=""><span class="mord" style=""><span class="mord mathcal coloredeq eqh" style="margin-right:0.09931em">F</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord text mtight" style=""><span class="mord mtight" style="">hidden</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqe" style="">(</span><span class="mord coloredeq eqe" style=""><span class="mord mathnormal coloredeq eql" style="">x</span></span><span class="mclose coloredeq eqe" style="">)</span></span><span class="mord coloredeq eqc" style=""><span class="delimsizing size1" style=""><span style="">)</span></span></span></span><span class="mord coloredeq eqb" style=""><span class="delimsizing size1" style=""><span style="">)</span></span></span></span></span></span></span></span></span></span></p>
<p>The structure of this module is made similar to a <a href="../mha.html">standard attention module</a> so that we can simply replace it.</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">47</span><span class="k">class</span> <span class="nc">FNetMix</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">Module</span><span class="p">):</span></pre></div>
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<div class='section' id='section-2'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-2'>#</a>
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<p> The <a href="../mha.html">normal attention module</a> can be fed with different token embeddings for <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqf" style=""><span class="mord text" style=""><span class="mord" style="">query</span></span></span></span></span></span></span>,<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqj" style=""><span class="mord text" style=""><span class="mord" style="">key</span></span></span></span></span></span></span>, and <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord coloredeq eqg" style=""><span class="mord text" style=""><span class="mord" style="">value</span></span></span></span></span></span></span> and a mask.</p>
<p>We follow the same function signature so that we can replace it directly.</p>
<p>For FNet mixing, <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eql" style=""><span class="mord mathnormal" style="">x</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqf" style=""><span class="mord text" style=""><span class="mord" style="">query</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqj" style=""><span class="mord text" style=""><span class="mord" style="">key</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord coloredeq eqg" style=""><span class="mord text" style=""><span class="mord" style="">value</span></span></span></span></span></span></span></span> and masking is not possible. Shape of <code class="highlight"><span></span><span class="n">query</span></code>
(and <code class="highlight"><span></span><span class="n">key</span></code>
and <code class="highlight"><span></span><span class="n">value</span></code>
) is <code class="highlight"><span></span><span class="p">[</span><span class="n">seq_len</span><span class="p">,</span> <span class="n">batch_size</span><span class="p">,</span> <span class="n">d_model</span><span class="p">]</span></code>
.</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">60</span> <span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">query</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">key</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">value</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">mask</span><span class="p">:</span> <span class="n">Optional</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>
</div>
</div>
<div class='section' id='section-3'>
<div class='docs'>
<div class='section-link'>
<a href='#section-3'>#</a>
</div>
<p><span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqf" style=""><span class="mord text" style=""><span class="mord" style="">query</span></span></span></span></span></span></span>,<span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord coloredeq eqj" style=""><span class="mord text" style=""><span class="mord" style="">key</span></span></span></span></span></span></span>, and <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord coloredeq eqg" style=""><span class="mord text" style=""><span class="mord" style="">value</span></span></span></span></span></span></span> all should be equal to <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord coloredeq eql" style=""><span class="mord mathnormal" style="">x</span></span></span></span></span></span> for token mixing </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">72</span> <span class="k">assert</span> <span class="n">query</span> <span class="ow">is</span> <span class="n">key</span> <span class="ow">and</span> <span class="n">key</span> <span class="ow">is</span> <span class="n">value</span></pre></div>
</div>
</div>
<div class='section' id='section-4'>
<div class='docs'>
<div class='section-link'>
<a href='#section-4'>#</a>
</div>
<p>Token mixing doesn&#x27;t support masking. i.e. all tokens will see all other token embeddings. </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">74</span> <span class="k">assert</span> <span class="n">mask</span> <span class="ow">is</span> <span class="kc">None</span></pre></div>
</div>
</div>
<div class='section' id='section-5'>
<div class='docs'>
<div class='section-link'>
<a href='#section-5'>#</a>
</div>
<p>Assign to <code class="highlight"><span></span><span class="n">x</span></code>
for clarity </p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">77</span> <span class="n">x</span> <span class="o">=</span> <span class="n">query</span></pre></div>
</div>
</div>
<div class='section' id='section-6'>
<div class='docs'>
<div class='section-link'>
<a href='#section-6'>#</a>
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<p>Apply the Fourier transform along the hidden (embedding) dimension <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord coloredeq eqe" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathcal coloredeq eqh" style="margin-right:0.09931em">F</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord text mtight" style=""><span class="mord mtight" style="">hidden</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal coloredeq eql" style="">x</span></span><span class="mclose" style="">)</span></span></span></span></span></span></span></p>
<p>The output of the Fourier transform is a tensor of <a href="https://pytorch.org/docs/stable/complex_numbers.html">complex numbers</a>. </p>
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<div class="highlight"><pre><span class="lineno">84</span> <span class="n">fft_hidden</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fft</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">2</span><span class="p">)</span></pre></div>
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<p>Apply the Fourier transform along the sequence dimension <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.20001em;vertical-align:-0.35001em;"></span><span class="mord coloredeq eqc" style=""><span class="mord" style=""><span class="mord" style=""><span class="mord mathcal coloredeq eqh" style="margin-right:0.09931em">F</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord text mtight" style=""><span class="mord mtight" style="">seq</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mord" style=""><span class="delimsizing size1" style=""><span style="">(</span></span></span><span class="mord" style=""><span class="mord coloredeq eqe" style=""><span class="mord" style=""><span class="mord mathcal coloredeq eqh" style="margin-right:0.09931em">F</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord text mtight" style=""><span class="mord mtight" style="">hidden</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqe" style="">(</span><span class="mord coloredeq eqe" style=""><span class="mord mathnormal coloredeq eql" style="">x</span></span><span class="mclose coloredeq eqe" style="">)</span></span><span class="mord" style=""><span class="delimsizing size1" style=""><span style="">)</span></span></span></span></span></span></span></span></span> </p>
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<div class="highlight"><pre><span class="lineno">87</span> <span class="n">fft_seq</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fft</span><span class="p">(</span><span class="n">fft_hidden</span><span class="p">,</span> <span class="n">dim</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span></pre></div>
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<p>Get the real component <span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:1.20001em;vertical-align:-0.35001em;"></span><span class="mord coloredeq eqb" style=""><span class="mord" style=""><span class="mord mathcal coloredeq eqi" style="">R</span></span><span class="mord" style=""><span class="delimsizing size1" style=""><span style="">(</span></span></span><span class="mord" style=""><span class="mord coloredeq eqc" style=""><span class="mord" style=""><span class="mord mathcal coloredeq eqh" style="margin-right:0.09931em">F</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.15139200000000003em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord text mtight" style=""><span class="mord mtight" style="">seq</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mord coloredeq eqc" style=""><span class="delimsizing size1" style=""><span style="">(</span></span></span><span class="mord coloredeq eqc" style=""><span class="mord coloredeq eqe" style=""><span class="mord" style=""><span class="mord mathcal coloredeq eqh" style="margin-right:0.09931em">F</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord text mtight" style=""><span class="mord mtight" style="">hidden</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen coloredeq eqe" style="">(</span><span class="mord coloredeq eqe" style=""><span class="mord mathnormal coloredeq eql" style="">x</span></span><span class="mclose coloredeq eqe" style="">)</span></span><span class="mord coloredeq eqc" style=""><span class="delimsizing size1" style=""><span style="">)</span></span></span></span><span class="mord" style=""><span class="delimsizing size1" style=""><span style="">)</span></span></span></span></span></span></span></span></span> </p>
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<div class="highlight"><pre><span class="lineno">91</span> <span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">real</span><span class="p">(</span><span class="n">fft_seq</span><span class="p">)</span></pre></div>
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<h1><a href="https://nn.labml.ai/transformers/fnet/index.html">FNet: Mixing Tokens with Fourier Transforms</a></h1>
<p>This is a <a href="https://pytorch.org">PyTorch</a> implementation of the paper <a href="https://arxiv.org/abs/2105.03824">FNet: Mixing Tokens with Fourier Transforms</a>.</p>
<p>This paper replaces the <a href="https://nn.labml.ai/transformers//mha.html">self-attention layer</a> with two <a href="https://en.wikipedia.org/wiki/Discrete_Fourier_transform">Fourier transforms</a> to <em>mix</em> tokens. This is a 7X more efficient than self-attention. The accuracy loss of using this over self-attention is about 92% for <a href="https://paperswithcode.com/method/bert">BERT</a> on <a href="https://paperswithcode.com/dataset/glue">GLUE benchmark</a>. </p>
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