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<h1>パリティタスク</h1>
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<p>これにより、論文「<a href="https://papers.labml.ai/paper/1603.08983">リカレントニューラルネットワークの適応的計算時間</a>」からパリティタスクのデータが作成されます。</p>
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<p>パリティタスクの入力は、と <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 coloredeq eqa" style=""><span class="mord" style="">−</span><span class="mord" style=""><span class="mord coloredeq eqc" style="">1</span></span></span></span></span></span></span> s <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">0</span></span></span></span></span> <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord coloredeq eqc" style=""><span class="mord" style="">1</span></span></span></span></span></span> の付いたベクトルで、出力は s <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 coloredeq eqc" style=""><span class="mord" style="">1</span></span></span></span></span></span> のパリティです。s <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 coloredeq eqc" style=""><span class="mord" style="">1</span></span></span></span></span></span> の数が奇数の場合は 1、それ以外の場合は 0 です。入力は、<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 coloredeq eqc" style=""><span class="mord" style="">1</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:0.72777em;vertical-align:-0.08333em;"></span><span class="mord coloredeq eqa" style=""><span class="mord" style="">−</span><span class="mord" style=""><span class="mord coloredeq eqc" style="">1</span></span></span></span></span></span></span>ベクトル内のランダムな数の要素をまたはのいずれかにすることによって生成されます。</p>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">19</span><span></span><span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Tuple</span>
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<span class="lineno">20</span>
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<span class="lineno">21</span><span class="kn">import</span> <span class="nn">torch</span>
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<span class="lineno">22</span><span class="kn">from</span> <span class="nn">torch.utils.data</span> <span class="kn">import</span> <span class="n">Dataset</span></pre></div>
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<a href='#section-1'>#</a>
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<h3>パリティデータセット</h3>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">25</span><span class="k">class</span> <span class="nc">ParityDataset</span><span class="p">(</span><span class="n">Dataset</span><span class="p">):</span></pre></div>
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<ul><li><code class="highlight"><span></span><span class="n">n_samples</span></code>
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はサンプル数</li>
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<li><code class="highlight"><span></span><span class="n">n_elems</span></code>
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は入力ベクトルの要素数です</li></ul>
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</div>
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<div class='code'>
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<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">n_samples</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">n_elems</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">64</span><span class="p">):</span></pre></div>
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<div class='section' id='section-3'>
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<div class='docs'>
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<a href='#section-3'>#</a>
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<div class="highlight"><pre><span class="lineno">35</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_samples</span> <span class="o">=</span> <span class="n">n_samples</span>
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<span class="lineno">36</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_elems</span> <span class="o">=</span> <span class="n">n_elems</span></pre></div>
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<div class='section' id='section-4'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-4'>#</a>
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</div>
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<p>データセットのサイズ</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">38</span> <span class="k">def</span> <span class="fm">__len__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span></pre></div>
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<div class='docs'>
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<a href='#section-5'>#</a>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">42</span> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_samples</span></pre></div>
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<div class='section' id='section-6'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-6'>#</a>
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<p>サンプルを生成</p>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">44</span> <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">idx</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="n">Tuple</span><span class="p">[</span><span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">,</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">]:</span></pre></div>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-7'>#</a>
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<p>空のベクトル</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">50</span> <span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">n_elems</span><span class="p">,))</span></pre></div>
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<div class='section' id='section-8'>
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<a href='#section-8'>#</a>
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<p>ゼロ以外の要素の数-<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 coloredeq eqc" style=""><span class="mord" style="">1</span></span></span></span></span></span> 要素の数と要素数の間のランダムな数</p>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">52</span> <span class="n">n_non_zero</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_elems</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="mi">1</span><span class="p">,))</span><span class="o">.</span><span class="n">item</span><span class="p">()</span></pre></div>
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<div class='section' id='section-9'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-9'>#</a>
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</div>
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<p>0 以外の要素を「」と <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 coloredeq eqc" style=""><span class="mord" style="">1</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:0.72777em;vertical-align:-0.08333em;"></span><span class="mord coloredeq eqa" style=""><span class="mord" style="">−</span><span class="mord" style=""><span class="mord coloredeq eqc" style="">1</span></span></span></span></span></span></span>「」で埋める</p>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">54</span> <span class="n">x</span><span class="p">[:</span><span class="n">n_non_zero</span><span class="p">]</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="n">n_non_zero</span><span class="p">,))</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">-</span> <span class="mi">1</span></pre></div>
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</div>
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<div class='section' id='section-10'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-10'>#</a>
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</div>
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<p>要素をランダムに並べ替える</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">56</span> <span class="n">x</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="n">torch</span><span class="o">.</span><span class="n">randperm</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_elems</span><span class="p">)]</span></pre></div>
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</div>
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<div class='section' id='section-11'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-11'>#</a>
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</div>
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<p>パリティ</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">59</span> <span class="n">y</span> <span class="o">=</span> <span class="p">(</span><span class="n">x</span> <span class="o">==</span> <span class="mf">1.</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span> <span class="o">%</span> <span class="mi">2</span></pre></div>
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<div class='section' id='section-12'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-12'>#</a>
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</div>
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<p></p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">62</span> <span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span></pre></div>
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