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<a href="https://github.com/labmlai/annotated_deep_learning_paper_implementations/tree/master/labml_nn/sampling/nucleus.py" target="_blank">
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<h1>Nucleus Sampling</h1>
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<p>This is an implementation of nucleus sampling, introduced in the paper <a href="https://arxiv.org/abs/1904.09751">The Curious Case of Neural Text Degeneration</a>.</p>
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<p>The paper discusses the problems with other sampling methods such as Beam Search, <a href="temperature.html">Pure sampling</a>, <a href="temperature.html">Temperature sampling</a>, and <a href="top_k.html">Top-k sampling</a>. The paper introduces the idea of nucleus sampling, which practically performs better than other sampling methods for text generation.</p>
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<p>Nucleus sampling first picks a subset of the vocabulary <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.9270999999999999em;vertical-align:-0.0391em;"></span><span class="mord coloredeq eqd" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8879999999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mopen mtight" style="">(</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqe" style="">p</span></span><span class="mclose mtight" style="">)</span></span></span></span></span></span></span></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:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span></span></span></span></span>, where <span ><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:0.8879999999999999em;vertical-align:0em;"></span><span class="mord coloredeq eqd" style=""><span class="mord" style=""><span class="mord mathnormal" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8879999999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mopen mtight" style="">(</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqe" style="">p</span></span><span class="mclose mtight" style="">)</span></span></span></span></span></span></span></span></span></span></span></span></span></span> is smallest set of tokens such that</p>
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<p><span ><span class="katex-display"><span class="katex"><span aria-hidden="true" class="katex-html"><span class="base"><span class="strut" style="height:2.541535em;vertical-align:-1.49153em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.75857em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mrel mtight">∈</span><span class="mord mtight coloredeq eqd" style=""><span class="mord mtight" style=""><span class="mord mathnormal mtight" style="margin-right:0.22222em">V</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8220357142857143em;"><span style="top:-2.8220357142857138em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5357142857142856em;"></span><span class="sizing reset-size3 size1 mtight" style=""><span class="mord mtight" style=""><span class="mopen mtight" style="">(</span><span class="mord mtight" style=""><span class="mord mathnormal mtight coloredeq eqe" style="">p</span></span><span class="mclose mtight" style="">)</span></span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:1.49153em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord coloredeq eqb" style=""><span class="mord mathnormal" style="margin-right:0.13889em">P</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</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="mord" style="">∣</span><span class="mord" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">1</span><span class="mrel mtight" style="">:</span><span class="mord mathnormal mtight" style="">i</span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mclose" style="">)</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 eqe" style=""><span class="mord mathnormal" style="">p</span></span></span></span></span></span></span></p>
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<p>That is, we pick the highest probable tokens until the sum of their probabilities is less that <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 eqe" style=""><span class="mord mathnormal" style="">p</span></span></span></span></span></span>.</p>
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<p>Then we sample from the selected tokens.</p>
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<p>Here's an <a href="experiment.html">experiment</a> that uses these sampling techniques.</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">29</span><span></span><span class="kn">import</span> <span class="nn">torch</span>
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<span class="lineno">30</span><span class="kn">from</span> <span class="nn">torch</span> <span class="kn">import</span> <span class="n">nn</span>
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<span class="lineno">31</span>
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<span class="lineno">32</span><span class="kn">from</span> <span class="nn">labml_nn.sampling</span> <span class="kn">import</span> <span class="n">Sampler</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-1'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-1'>#</a>
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</div>
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<h2>Nucleus Sampler</h2>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">35</span><span class="k">class</span> <span class="nc">NucleusSampler</span><span class="p">(</span><span class="n">Sampler</span><span class="p">):</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-2'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-2'>#</a>
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</div>
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<ul><li><code class="highlight"><span></span><span class="n">p</span></code>
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is the sum of probabilities of tokens to pick <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 eqe" style=""><span class="mord mathnormal" style="">p</span></span></span></span></span></span> </li>
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<li><code class="highlight"><span></span><span class="n">sampler</span></code>
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is the sampler to use for the selected tokens</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">39</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">p</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span> <span class="n">sampler</span><span class="p">:</span> <span class="n">Sampler</span><span class="p">):</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-3'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-3'>#</a>
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</div>
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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="bp">self</span><span class="o">.</span><span class="n">p</span> <span class="o">=</span> <span class="n">p</span>
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<span class="lineno">45</span> <span class="bp">self</span><span class="o">.</span><span class="n">sampler</span> <span class="o">=</span> <span class="n">sampler</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-4'>
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<div class='docs'>
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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>Softmax to compute <span ><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 eqb" style=""><span class="mord mathnormal" style="margin-right:0.13889em">P</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</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="mord" style="">∣</span><span class="mord" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">1</span><span class="mrel mtight" style="">:</span><span class="mord mathnormal mtight" style="">i</span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span></span></span> from the logits </p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">47</span> <span class="bp">self</span><span class="o">.</span><span class="n">softmax</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Softmax</span><span class="p">(</span><span class="n">dim</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-5'>
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<div class='docs doc-strings'>
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<div class='section-link'>
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<a href='#section-5'>#</a>
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</div>
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<p> Sample from logits with Nucleus Sampling</p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">49</span> <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">logits</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>
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</div>
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<div class='section' id='section-6'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-6'>#</a>
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</div>
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<p>Get probabilities <span ><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 eqb" style=""><span class="mord mathnormal" style="margin-right:0.13889em">P</span><span class="mopen" style="">(</span><span class="mord" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mathnormal mtight" style="">i</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="mord" style="">∣</span><span class="mord" style=""><span class="mord mathnormal" style="">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style=""><span class="mord mtight" style=""><span class="mord mtight" style="">1</span><span class="mrel mtight" style="">:</span><span class="mord mathnormal mtight" style="">i</span><span class="mbin mtight" style="">−</span><span class="mord mtight" style="">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mclose" style="">)</span></span></span></span></span></span> </p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">55</span> <span class="n">probs</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">softmax</span><span class="p">(</span><span class="n">logits</span><span class="p">)</span></pre></div>
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</div>
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</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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</div>
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<p>Sort probabilities in descending order </p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">58</span> <span class="n">sorted_probs</span><span class="p">,</span> <span class="n">indices</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">probs</span><span class="p">,</span> <span class="n">dim</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">descending</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span></pre></div>
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</div>
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</div>
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<div class='section' id='section-8'>
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<div class='docs'>
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<div class='section-link'>
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<a href='#section-8'>#</a>
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</div>
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<p>Get the cumulative sum of probabilities in the sorted order </p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">60</span> <span class="n">cum_sum_probs</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">cumsum</span><span class="p">(</span><span class="n">sorted_probs</span><span class="p">,</span> <span class="n">dim</span><span class="o">=-</span><span class="mi">1</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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<p>Find the cumulative sums less than <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 eqe" style=""><span class="mord mathnormal" style="">p</span></span></span></span></span></span>. </p>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">62</span> <span class="n">nucleus</span> <span class="o">=</span> <span class="n">cum_sum_probs</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">p</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>Prepend ones so that we add one token after the minimum number of tokens with cumulative probability less that <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 eqe" style=""><span class="mord mathnormal" style="">p</span></span></span></span></span></span>. </p>
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</div>
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<div class='code'>
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<div class="highlight"><pre><span class="lineno">65</span> <span class="n">nucleus</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">cat</span><span class="p">([</span><span class="n">nucleus</span><span class="o">.</span><span class="n">new_ones</span><span class="p">(</span><span class="n">nucleus</span><span class="o">.</span><span class="n">shape</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span><span class="p">,)),</span> <span class="n">nucleus</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="p">:</span><span class="o">-</span><span class="mi">1</span><span class="p">]],</span> <span class="n">dim</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span></pre></div>
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</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>
|
||
<p>Get log probabilities and mask out the non-nucleus </p>
|
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||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">68</span> <span class="n">sorted_log_probs</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">sorted_probs</span><span class="p">)</span>
|
||
<span class="lineno">69</span> <span class="n">sorted_log_probs</span><span class="p">[</span><span class="o">~</span><span class="n">nucleus</span><span class="p">]</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="s1">'-inf'</span><span class="p">)</span></pre></div>
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||
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||
</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>Sample from the sampler </p>
|
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||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">72</span> <span class="n">sampled_sorted_indexes</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sampler</span><span class="p">(</span><span class="n">sorted_log_probs</span><span class="p">)</span></pre></div>
|
||
</div>
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||
</div>
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||
<div class='section' id='section-13'>
|
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<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-13'>#</a>
|
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</div>
|
||
<p>Get the actual indexes </p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">75</span> <span class="n">res</span> <span class="o">=</span> <span class="n">indices</span><span class="o">.</span><span class="n">gather</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">sampled_sorted_indexes</span><span class="o">.</span><span class="n">unsqueeze</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span></pre></div>
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||
</div>
|
||
</div>
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||
<div class='section' id='section-14'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-14'>#</a>
|
||
</div>
|
||
<p> </p>
|
||
|
||
</div>
|
||
<div class='code'>
|
||
<div class="highlight"><pre><span class="lineno">78</span> <span class="k">return</span> <span class="n">res</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span></pre></div>
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