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<h1>原子核采样</h1>
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<p>这是原子核采样的一种实现，在论文<a href="https://papers.labml.ai/paper/1904.09751">《神经文本变性的好奇案例》</a>中进行了介绍。</p>
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<p>本文讨论了其他采样方法（例如光束搜索、<a href="temperature.html">纯采样、<a href="temperature.html">温度</a>采样</a>和T <a href="top_k.html">op-K采样</a>）存在的问题。本文介绍了原子核采样的概念，在文本生成方面，核采样的效果实际上比其他采样方法要好。</p>
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<p>Nucleus 采样首先选择词汇的一个子集<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 coloredeq eqe" style=""><span class="mord mathnormal mtight" 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>，其中<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 coloredeq eqe" style=""><span class="mord mathnormal mtight" style="">p</span></span><span class="mclose mtight" style="">)</span></span></span></span></span></span></span></span></span></span></span></span></span></span>是最小的令牌集合</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 coloredeq eqe" style=""><span class="mord mathnormal mtight" 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>也就是说，我们选择可能性最高的代币，直到它们的概率总和小于该值为止<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>然后我们从选定的令牌中抽样。</p>
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<p>这是一个使用这些采样技术的<a href="experiment.html">实验</a>。</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 采样器</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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<ul><li><code class="highlight"><span></span><span class="n">p</span></code>
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是要选择的代币概率之和<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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是用于选定令牌的采样器</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 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>
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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 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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<p>要根据对数计算<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>的 softmax</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>使用 Nucleus 采样从 logits 中提取样本</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>获取概率<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>按降序对概率进行排序</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 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>按排序顺序获取概率的累积总和</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>找出小于的累计总和<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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在@@ <p>前面加一个，这样我们就可以在累积概率小于该值的最小代币数量之后添加一个令牌<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>
|
||
<div class='code'>
|
||
<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>
|
||
</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'>
|
||
<a href='#section-11'>#</a>
|
||
</div>
|
||
<p>获取对数概率并掩盖非核</p>
|
||
|
||
</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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||
</div>
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||
<div class='section' id='section-12'>
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<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-12'>#</a>
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</div>
|
||
<p>来自采样器的样本</p>
|
||
|
||
</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>
|
||
</div>
|
||
<div class='section' id='section-13'>
|
||
<div class='docs'>
|
||
<div class='section-link'>
|
||
<a href='#section-13'>#</a>
|
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</div>
|
||
<p>获取实际索引</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>
|
||
</div>
|
||
</div>
|
||
<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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