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View code on Github</a>
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<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 実験</a></h1>
<p><a href="index.html">これは、FNetモデルをトレーニングするための注釈付きのPyTorch実験です。</a></p>
<p>これは、<a href="../../experiments/nlp_classification.html">AG News分類タスクの一般的なトレーニングループと構成に基づいています</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>トランスフォーマーベースの分類器モデル</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>
<a href="../models.html#Encoder">変圧器エンコーダです</a></li>
<li><code class="highlight"><span></span><span class="n">src_embed</span></code>
<a href="../models.html#EmbeddingsWithLearnedPositionalEncoding">はトークン埋め込みモジュールです (位置エンコーディング付き)</a></li>
</ul><li><code class="highlight"><span></span><span class="n">generator</span></code>
<a href="../models.html#Generator">ロジットを生成する最後の完全接続層です</a>。</li>
</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>位置エンコーディングによるトークンの埋め込みを取得</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>トランスエンコーダー</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>分類用のロジットを取得します。</p>
<p><code class="highlight"><span></span><span class="p">[</span><span class="n">CLS</span><span class="p">]</span></code>
シーケンスの最後の位置にトークンを設定します。これは、<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>
<code class="highlight"><span></span><span class="n">x</span></code>
形状がどこにあるかによって抽出されます <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">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>結果を返します（トレーナーはRNNでも使用されるため、2番目の値は状態用です）</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>コンフィギュレーション</h2>
<p>これは以下から継承されます <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>分類モデル</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>変圧器</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>変圧器構成</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><a href="../configs.html#TransformerConfigs">設定可能なトランス実装を使用しています</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>埋め込みやロジットの生成に使用するボキャブラリーサイズを設定</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><code class="highlight"><span></span><span class="n">FNetMix</span></code>
<a href="../models.html#TransformerLayer">トランスエンコーダー層のセルフアテンションに代わるモジュールを作成してください</a>。</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>分類モデルの作成</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>実験を作成</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>コンフィグの作成</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>オーバーライド設定</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>ワールドレベルのトークナイザーを使う</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><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>時代に合わせた列車</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>エポックごとにトレーニングと検証を切り替える <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></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>
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<p>変圧器構成 (デフォルトと同じ)</p>
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<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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<p><a href="index.html">自己アテンションの代わりにFNetを使う</a></p>
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<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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<p><a href="../../optimizers/noam.html">Noam</a> オプティマイザを使う</p>
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<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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<p>保存および読み込み用のモデルを設定する</p>
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<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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<p>実験を始める</p>
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<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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<a href='#section-32'>#</a>
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<p>トレーニングを実行</p>
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<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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<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: フーリエ変換によるトークンの混合</h1>
<p>これは、論文「<a href="https://papers.labml.ai/paper/2105.03824">FNet: トークンをフーリエ変換と混合する」<a href="https://pytorch.org">をPyTorchで実装したものです</a></a>。</p>
<p><em>この論文では、<a href="../mha.html"><a href="https://en.wikipedia.org/wiki/Discrete_Fourier_transform">セルフアテンション層を2つのフーリエ変換に置き換えてトークンを混合します</a></a>。</em><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>これは自己注意よりも効率的です。<a href="https://paperswithcode.com/method/bert">BERT</a> on <a href="https://paperswithcode.com/dataset/glue">GLUE</a> ベンチマークでは、自己注意よりもこれを使用した場合の精度の低下は約 92%</p> です。
<h2>2 つのフーリエ変換によるトークンの混合</h2>
<p>フーリエ変換を非表示次元 (埋め込み次元) に沿って適用し、次にシーケンス次元に沿って適用します。</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>ここで、<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>は埋め込み入力で、<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><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>フーリエ変換を表し、複素数の実数成分を表します。</p>
<p>これをPyTorchに実装するのはとても簡単です。たった1行のコードです。この論文では、事前に計算されたDFT行列を使用し、行列の乗算を行ってフーリエ変換を行うことを提案しています</p>。
<p>以下は<a href="experiment.html">、<a href="https://paperswithcode.com/dataset/ag-news">FNetベースのモデルを使用してAG</a> Newsを分類するためのトレーニングコードです</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>
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<div class='section' id='section-1'>
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<div class='section-link'>
<a href='#section-1'>#</a>
</div>
<h2>FNet-ミックストークン</h2>
<p>このモジュールは単純に実装します <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>このモジュールの構造は、<a href="../mha.html">標準的なアテンションモジュールと同様の構造になっているため</a>、簡単に交換できます。</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">通常のアテンションモジュールには</a>、、、<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>マスクにさまざまなトークンを埋め込むことができます。<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></p>
<p>同じ関数シグネチャに従うので、直接置換できます。</p>
<p>FNetミキシングの場合<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>、マスキングはできません。<code class="highlight"><span></span><span class="n">query</span></code>
(<code class="highlight"><span></span><span class="n">key</span></code>
と<code class="highlight"><span></span><span class="n">value</span></code>
) の形はです<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'>
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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:0.69444em;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 ><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>そしてトークンのミキシングではすべてが等しくなければなりません</p>
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<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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<p>トークンのミキシングはマスキングをサポートしていません。つまり、すべてのトークンに他のすべてのトークンの埋め込みが表示されます。</p>
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<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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<p><code class="highlight"><span></span><span class="n">x</span></code>
わかりやすいように割り当てる</p>
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<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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<p>フーリエ変換を非表示 (埋め込み) 次元に沿って適用します <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><a href="https://pytorch.org/docs/stable/complex_numbers.html">フーリエ変換の出力は複素数のテンソルです</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>シーケンスの次元に沿ってフーリエ変換を適用します <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='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>本物のコンポーネントを手に入れよう <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: フーリエ変換によるトークンの混合</a></h1>
<p>これは、論文「<a href="https://papers.labml.ai/paper/2105.03824">FNet: トークンをフーリエ変換と混合する」<a href="https://pytorch.org">をPyTorchで実装したものです</a></a>。</p>
<p><em>この論文では、<a href="https://nn.labml.ai/transformers//mha.html"><a href="https://en.wikipedia.org/wiki/Discrete_Fourier_transform">自己注意層を2つのフーリエ変換に置き換えてトークンを混合します</a></a>。</em>これは自己処理よりも7倍効率的です。<a href="https://paperswithcode.com/method/bert">BERT</a> on <a href="https://paperswithcode.com/dataset/glue">GLUE</a> ベンチマークでは、自己注意よりもこれを使用した場合の精度の低下は約 92%</p> です。
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