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<h1>Parity Task</h1>
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<p>This creates data for Parity Task from the paper <a href="https://papers.labml.ai/paper/1603.08983">Adaptive Computation Time for Recurrent Neural Networks</a>.</p>
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<p>The input of the parity task is a vector with <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>'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>'s and <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. The output is the parity of <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>'s - one if there is an odd number of <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>'s and zero otherwise. The input is generated by making a random number of elements in the vector either <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> or <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.</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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<div class='docs doc-strings'>
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<a href='#section-1'>#</a>
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<h3>Parity dataset</h3>
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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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is the number of samples </li>
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<li><code class="highlight"><span></span><span class="n">n_elems</span></code>
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is the number of elements in the input vector</li></ul>
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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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<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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<p> Size of the dataset</p>
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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="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='docs doc-strings'>
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<a href='#section-6'>#</a>
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<p> Generate a sample</p>
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</div>
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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='section' id='section-7'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-7'>#</a>
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<p>Empty vector </p>
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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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<a href='#section-8'>#</a>
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<p>Number of non-zero elements - a random number between <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> and total number of elements </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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<a href='#section-9'>#</a>
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<p>Fill non-zero elements with <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>'s and <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 </p>
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</div>
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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 class='section' id='section-10'>
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<a href='#section-10'>#</a>
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<p>Randomly permute the elements </p>
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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 class='section-link'>
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<a href='#section-11'>#</a>
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<p>The parity </p>
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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='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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