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<title>FNet 实验</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>
</p>
<p>
<a href="https://github.com/labmlai/annotated_deep_learning_paper_implementations" target="_blank">
<img alt="Github"
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<p>
<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> 实验</h1>
<p>这是一个带注释的 PyTorch 实验，用于训练 <a href="index.html">FNet 模型</a>。</p>
<p>这是基于 <a href="../../experiments/nlp_classification.html">AG News 分类任务的一般训练循环和配置</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_helpers.module</span> <span class="kn">import</span> <span class="n">Module</span>
<span class="lineno">21</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">22</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">23</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>基于变压器的分类器模型</h1>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">26</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>
是变压器<a href="../models.html#Encoder">编码器</a></li>
<li><code class="highlight"><span></span><span class="n">src_embed</span></code>
是令牌<a href="../models.html#EmbeddingsWithLearnedPositionalEncoding">嵌入模块（带有位置编码）</a></li>
<li><code class="highlight"><span></span><span class="n">generator</span></code>
是给<a href="../models.html#Generator">出 logit 的最后一个完全连接的层</a>。</li></ul>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">30</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">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">37</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">38</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">39</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">40</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">42</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>使用位置编码获取令牌嵌入</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">44</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>变压器编码</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">46</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>获取分类日志。</p>
<p>我们将令<code class="highlight"><span></span><span class="p">[</span><span class="n">CLS</span><span class="p">]</span></code>
牌设置在序列的最后一个位置。这是由，wher<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>
e<code class="highlight"><span></span><span class="n">x</span></code>
是形状提取</p>的<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>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">52</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>返回结果（第二个值用于状态，因为我们的训练器也与 RNN 一起使用）</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">56</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>配置</h2>
<p>这继承自 <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">59</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>分类模型</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">68</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>变压器</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">70</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>变压器配置</h3>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">73</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">74</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>我们使用我们的<a href="../configs.html#TransformerConfigs">可配置变压器实现</a></p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">81</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>设置嵌入和生成 logit 的词汇量大小</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">83</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">84</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">87</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>创建可以取代<a href="../models.html#TransformerLayer">变压器编码器层</a>中的自我注意力的<code class="highlight"><span></span><span class="n">FNetMix</span></code>
模块。</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">90</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">91</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">97</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">98</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>创建分类模型</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">101</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">102</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">106</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">107</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">108</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">109</span>
<span class="lineno">110</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">113</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>创建实验</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">115</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>创建配置</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">117</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>覆盖配置</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">119</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>使用世界级分词器</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">121</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>为<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>时代而训练</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">124</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>在训练和验证之间切换每个纪元的<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>次数</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">127</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>变压器配置（与默认值相同）</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">130</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">131</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">132</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">133</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>
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</div>
<div class='section' id='section-28'>
<div class='docs'>
<div class='section-link'>
<a href='#section-28'>#</a>
</div>
<p>使用 <a href="index.html">FNet</a> 而不是自我关注</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">137</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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</div>
<div class='section' id='section-29'>
<div class='docs'>
<div class='section-link'>
<a href='#section-29'>#</a>
</div>
<p>使用 <a href="../../optimizers/noam.html">Noam 优化器</a></p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">140</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">141</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">142</span> <span class="p">})</span></pre></div>
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<div class='section' id='section-30'>
<div class='docs'>
<div class='section-link'>
<a href='#section-30'>#</a>
</div>
<p>设置用于保存和加载的模型</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">145</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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<div class='section' id='section-31'>
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<div class='section-link'>
<a href='#section-31'>#</a>
</div>
<p>开始实验</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">148</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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<div class='section-link'>
<a href='#section-32'>#</a>
</div>
<p>跑步训练</p>
</div>
<div class='code'>
<div class="highlight"><pre><span class="lineno">150</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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<a href='#section-33'>#</a>
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<p></p>
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<div class="highlight"><pre><span class="lineno">154</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">155</span> <span class="n">main</span><span class="p">()</span></pre></div>
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<h1>FNet：将令牌与傅里叶变换混合</h1>
<p>这是论文《<a href="https://arxiv.org/abs/2105.03824">FNet：将代币与傅里叶变换混合》的 PyTor</a> <a href="https://pytorch.org">ch</a> 实现。</p>
<p>本文用两个<a href="https://en.wikipedia.org/wiki/Discrete_Fourier_transform">傅里叶变</a>换取代了<a href="../mha.html">自我注意力层</a>，以<em>混合</em>令牌。这比自我注意力<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>更有效。在 GLUE <a href="https://paperswithcode.com/dataset/glue">基准测试</a>中，<a href="https://paperswithcode.com/method/bert">BERT</a> 使用它而不是自我注意力的准确性损失约为92％。</p>
<h2>将令牌与两个傅里叶变换混合</h2>
<p>我们沿隐藏维度（嵌入维度）应用傅里叶变换，然后沿序列维度应用傅里叶变换。</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>其中<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>是嵌入输入，<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>代表傅里叶变换，<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>代表复数中的实分量。</p>
<p>这在 PyTorch 上实现起来非常简单-只需一行代码。本文建议使用预先计算的DFT矩阵并进行矩阵乘法来获得傅里叶变换。</p>
<p><a href="experiment.html">以下是使用基于 FNet 的模型对 <a href="https://paperswithcode.com/dataset/ag-news">AG News</a> 进行分类的训练代码</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-混合代币</h2>
<p>这个模块简单地实现了<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>该模块的结构类似于<a href="../mha.html">标准的注意力模块</a>，因此我们可以简单地替换它。</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>
</div>
</div>
<div class='section' id='section-2'>
<div class='docs doc-strings'>
<div class='section-link'>
<a href='#section-2'>#</a>
</div>
<p><a href="../mha.html">普通注意力模块</a>可以使用<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>和的不同令牌嵌入<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>以及掩码进行馈送。</p>
<p>我们遵循相同的函数签名，以便我们可以直接替换它。</p>
<p>对于 FNet 混合<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>，屏蔽是不可能的。<code class="highlight"><span></span><span class="n">query</span></code>
（和<code class="highlight"><span></span><span class="n">key</span></code>
和<code class="highlight"><span></span><span class="n">value</span></code>
）的形状为<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>
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<div class='section-link'>
<a href='#section-3'>#</a>
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<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>、，<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>对于令牌混合，al<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> l 应该等于</p>
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<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>
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<div class='section-link'>
<a href='#section-4'>#</a>
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<p>令牌混合不支持掩码。即所有令牌都将看到所有其他令牌嵌入。</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>
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</div>
<div class='section' id='section-5'>
<div class='docs'>
<div class='section-link'>
<a href='#section-5'>#</a>
</div>
<p>为了清楚起见，<code class="highlight"><span></span><span class="n">x</span></code>
请分配给</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>
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<div class='section' id='section-6'>
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<a href='#section-6'>#</a>
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<p>沿隐藏（嵌入）维度应用傅里叶变换<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>傅里叶变换的输出是<a href="https://pytorch.org/docs/stable/complex_numbers.html">复数</a>张量。</p>
</div>
<div class='code'>
<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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<a href='#section-7'>#</a>
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<p>沿序列维度应用傅里叶变换<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>
</div>
<div class='code'>
<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>获取真正的组件<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='code'>
<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：将令牌与傅里叶变换混合</a></h1>
<p>这是论文《<a href="https://arxiv.org/abs/2105.03824">FNet：将代币与傅里叶变换混合》的 PyTor</a> <a href="https://pytorch.org">ch</a> 实现。</p>
<p>本文用两个<a href="https://en.wikipedia.org/wiki/Discrete_Fourier_transform">傅里叶变</a>换取代了<a href="https://nn.labml.ai/transformers//mha.html">自我注意力层</a>，以<em>混合</em>令牌。这比自我注意力高7倍。在 GLUE <a href="https://paperswithcode.com/dataset/glue">基准测试</a>中，<a href="https://paperswithcode.com/method/bert">BERT</a> 使用它而不是自我注意力的准确性损失约为92％。</p>
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