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docs/adaptive_computation/parity.html

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</div>
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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 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>&#x27;s <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 eqb" style=""><span class="mord" style="">1</span></span></span></span></span>&#x27;s and <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"></span><span class="mord coloredeq eqb" style=""><span class="mord" style="">1</span></span></span></span></span>&#x27;s. The output is the parity of <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 eqb" style=""><span class="mord" style="">1</span></span></span></span></span>&#x27;s - one if there is an odd number of <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 eqb" style=""><span class="mord" style="">1</span></span></span></span></span>&#x27;s and zero otherwise. The input is generated by making a random number of elements in the vector either <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 eqb" style=""><span class="mord" style="">1</span></span></span></span></span> or <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"></span><span class="mord coloredeq eqb" style=""><span class="mord" style="">1</span></span></span></span></span>&#x27;s.</p>
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<p>The input of the parity task is a vector with <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>&#x27;s <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>&#x27;s and <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"></span><span class="mord coloredeq eqc" style=""><span class="mord" style="">1</span></span></span></span></span>&#x27;s. The output is the parity of <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>&#x27;s - one if there is an odd number of <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>&#x27;s and zero otherwise. The input is generated by making a random number of elements in the vector either <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> or <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"></span><span class="mord coloredeq eqc" style=""><span class="mord" style="">1</span></span></span></span></span>&#x27;s.</p>
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<p>Number of non-zero elements - a random number between <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 eqb" style=""><span class="mord" style="">1</span></span></span></span></span> and total number of elements </p>
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<p>Number of non-zero elements - a random number between <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> and total number of elements </p>
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<p>Fill non-zero elements with <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 eqb" style=""><span class="mord" style="">1</span></span></span></span></span>&#x27;s and <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"></span><span class="mord coloredeq eqb" style=""><span class="mord" style="">1</span></span></span></span></span>&#x27;s </p>
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<p>Fill non-zero elements with <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>&#x27;s and <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"></span><span class="mord coloredeq eqc" style=""><span class="mord" style="">1</span></span></span></span></span>&#x27;s </p>
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