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<link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/hint.css/2.4.1/hint.min.css"><h1 id="aaai-18-neural-response-generation-with-dynamic-vocabularies">AAAI-18 Neural Response Generation with Dynamic Vocabularies</h1>
<p><a href="https://arxiv.org/abs/1711.11191" target="_blank" rel="external">PDF</a></p>
<p>这是我本周要讲的论文，发表在18年AAAI会议上。本文针对采用静态词表解码容易生成不相关回复以及解码效率过低的问题，提出了使用动态词表解码来解决。</p>
<h1 id="motivation">Motivation</h1>
<p><strong>shortcomings(open domain conversation)</strong>:</p>
<ul>
<li>words that are semantically far from the current conversation also take part in decoding, irrelevant responses and generic responses.</li>
<li>the decoding process becomes unnecessarily slow.</li>
</ul>
<p><strong>solutions</strong>:</p>
<ul>
<li>dynamic vocabulary sequence-to-sequence (DVS2S) model</li>
<li>In training: vocabulary construction and response generation are jointly learned by maximizing a lower bound of the true objective with a Monte Carlo sampling method.</li>
<li>In inference: word prediction model dynamically allocates a small vocabulary for an input</li>
</ul>
<h1 id="problem-formalization">Problem Formalization</h1>
<p><span class="math display">\[p(Y_i|X_i) = p(Y_i|T_i,X_i)p(T_i|X_i)\]</span></p>
<p>target vocabulary : <span class="math inline">\(T_i\)</span> (sampled from a multivariate Bernoulli distribution)</p>
<p>response:<span class="math inline">\(Y_i\)</span> input:<span class="math inline">\(X_i\)</span></p>
<p>word selection model: <span class="math inline">\(f(X)\)</span></p>
<p>response generation model: <span class="math inline">\(g(X, T)\)</span></p>
<h1 id="model">Model</h1>
<img src="/2018-03-21.html/01.png" alt="01.png" title="">
<ul>
<li>[<strong>Sequence-to-Sequence Model</strong>]</li>
</ul>
<p>略</p>
<ul>
<li><p>[<strong>word selection model</strong>]</p></li>
<li><p><strong>Function words</strong></p>
<p>We collect words appearing more than times 10 in the training data, excluding nouns, verbs, adjectives and adverbs from them, and use the remaining ones to form a function word set.</p>
<p>There are 701 function words</p></li>
<li><p><strong>Content words</strong></p>
<div class="image-size-200" style="width:80%; text-align: center">
<p> <img src="/2018-03-21.html/02.png" alt="02.png" title=""></p>
</div>
<ul>
<li><p>The input vector is given by the last hidden state of the encoder</p></li>
<li><p>MLP is employed to predict the vocabulary</p></li>
</ul>
<p><span class="math display">\[\beta_{I(c)} = \sigma(W_c^Th_t + b_c)\]</span></p>
<ul>
<li>The word prediction loss is formulated as</li>
</ul>
<p><span class="math display">\[𝑃(𝑤_{𝑝𝑜𝑠} = 1|𝑋)+𝑝(𝑤_{𝑛𝑒𝑔} = 0|𝑋)\]</span></p>
<p>where <span class="math inline">\(𝑤_{𝑛𝑒𝑔}\)</span> are sampled by frequency, and $ 𝑤_{𝑝𝑜𝑠}$ are words in the ground-truth response.</p>
<p>-:)这边原文没有说明，这预训练的过程中，词表构造模型是通过负采样的方法进行的，负样本是通过词频进行采样的，因为频率高的词越容易导致在回复中出现，正样本是标注数据中的词。</p></li>
</ul>
<h1 id="model-training">Model Training</h1>
<ul>
<li><strong>Joint learning</strong></li>
</ul>
<p><span class="math display">\[\sum_{i=1}^{N}log(p(Y_i|X_i)) = \sum_{i=1}^{N}log(\sum_{Ti}log(\sum_{T_i}p(Y_i|T_i,X_i)p(T_i|X_i)))\]</span></p>
<ol style="list-style-type: decimal">
<li>With a latent variable T, it is difficult to optimize as logarithm is outside the summation.</li>
</ol>
<p>instead maximize a variational lower bound of <span class="math inline">\(\sum_{i=1}^{N}log(p(Y_i|X_i))\)</span>：</p>
<div class="image-size-200" style="width:60%; text-align: center">
<p> <img src="/2018-03-21.html/03.png" alt="03.png" title=""></p>
</div>
<ol start="2" style="list-style-type: decimal">
<li>log trick:</li>
</ol>
<p><span class="math display">\[\frac{dlog(f(x))}{dx} = \frac{1}{f(x)}\frac{df(x)}{dx}\]</span></p>
<p><span class="math display">\[\nabla log(f(x)) = \frac{\nabla f(x)}{f(x)}\]</span></p>
<p><span class="math display">\[\nabla p(T_i|X_i) = p(T_i|X_i)\frac{\nabla p(T_i|X_i)}{p(T_i|X_i)} = p(T_i|X_i)\nabla logp(T_i|X_i)\]</span></p>
<p><span class="math inline">\(\frac{\partial L_i(\theta)}{\partial \theta}\)</span> :</p>
<div class="image-size-200" style="width:60%; text-align: center">
<p> <img src="/2018-03-21.html/04.png" alt="04.png" title=""></p>
</div>
<ol start="3" style="list-style-type: decimal">
<li>we employ the Monte Carlo sampling technique to approximate <span class="math inline">\(\frac{\partial L_i(\theta)}{\partial \theta}\)</span>:</li>
</ol>
<div class="image-size-200" style="width:60%; text-align: center">
<p> <img src="/2018-03-21.html/05.png" alt="05.png" title=""></p>
</div>
<p>$T_{(i,s)} $ a multivariate Bernoulli distribution <span class="math inline">\((\{\beta\}^{|V|})\)</span></p>
<ol start="4" style="list-style-type: decimal">
<li>To reduce variance, we normalize the gradient with the length of the response:</li>
</ol>
<div class="image-size-200" style="width:60%; text-align: center">
<p> <img src="/2018-03-21.html/06.png" alt="06.png" title=""></p>
</div>
<div class="image-size-200" style="width:60%; text-align: center">
<p> <img src="/2018-03-21.html/07.png" alt="07.png" title=""></p>
</div>
<ul>
<li><strong>Algorithm</strong></li>
</ul>
<div class="image-size-200" style="width:60%; text-align: center">
<p> <img src="/2018-03-21.html/08.png" alt="08.png" title=""></p>
</div>
<h1 id="experiment">Experiment</h1>
<ul>
<li><p><strong>Experiment Setup</strong></p></li>
<li><p><strong>dataset</strong>: Baidu Tieba</p>
<p>training set: 5 million pairs validation set: 10000 pairs test set: 1; 000 pairs</p></li>
<li><p>samples S: 5</p>
<p>function words: 701</p>
<p>content words: rank according to <span class="math inline">\(\{\beta_i\}\)</span> and select top 1000 words to form a target vocabulary</p>
<p>beam size: 20</p></li>
<li><p><strong>Evaluation Metrics</strong></p></li>
<li>Word overlap based metrics</li>
<li>Embedding based metrics</li>
<li>Distinct-1 & distinct-2</li>
<li><p>3-scale human annotation</p></li>
<li><p><strong>Comparison Methods</strong></p></li>
<li>S2SA: https://github.com/mila-udem/blocks</li>
<li>S2SA-MMI: https://github.com/jiweil/Neural-Dialogue-Generation</li>
<li>TA-S2S: https://github.com/LynetteXing1991/TAJA-Seq2Seq</li>
<li>CVAE: https://github.com/snakeztc/NeuralDialog-CVAE</li>
<li><p>S-DVS2S: separately learn a generation model and a word prediction model</p></li>
<li><p><strong>Evaluation Results</strong></p></li>
<li><p>automatic metrics evaluation:</p>
<img src="/2018-03-21.html/09.png" alt="09.png" title=""></li>
<li><p>human evaluation:</p>
<div class="image-size-200" style="width:70%; text-align: center">
<p> <img src="/2018-03-21.html/10.png" alt="10.png" title=""></p>
</div></li>
<li><p>efficiency of decoding:</p>
<div class="image-size-200" style="width:90%; text-align: center">
<p> <img src="/2018-03-21.html/11.png" alt="11.png" title=""></p>
</div>
<p></p></li>
</ul>
<h1 id="discussions">Discussions</h1>
<ul>
<li><strong>Dynamic vocabulary coverage</strong>:</li>
</ul>
<div class="image-size-200" style="width:80%; text-align: center">
<p> <img src="/2018-03-21.html/12.png" alt="12.png" title=""></p>
</div>
<ul>
<li><strong>Performance across different dynamic vocabulary sizes</strong></li>
</ul>
<div class="image-size-200" style="width:80%; text-align: center">
<p> <img src="/2018-03-21.html/13.png" alt="13.png" title=""></p>
</div>
<ul>
<li><strong>Case study</strong></li>
</ul>
<img src="/2018-03-21.html/14.png" alt="14.png" title="">
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