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<h1>
[Sequential Models] week3. Sequence models & Attention mechanism
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<time datetime="2018-02-28T00:00:00+01:00"><i class="fa fa-calendar"></i> Wed, 28 Feb 2018</time>
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Part 16 of «Andrew Ng Deep Learning MOOC»
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目录
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<div id="toc"><ul><li><a class="toc-href" href="#i-various-sequence-to-sequence-architectures" title="I-Various sequence to sequence architectures">I-Various sequence to sequence architectures</a><ul><li><a class="toc-href" href="#basic-models" title="Basic Models">Basic Models</a></li><li><a class="toc-href" href="#picking-the-most-likely-sentence" title="Picking the most likely sentence">Picking the most likely sentence</a></li><li><a class="toc-href" href="#beam-search" title="Beam Search">Beam Search</a></li><li><a class="toc-href" href="#refinements-to-beam-search" title="Refinements to Beam Search">Refinements to Beam Search</a></li><li><a class="toc-href" href="#error-analysis-in-beam-search" title="Error analysis in beam search">Error analysis in beam search</a></li><li><a class="toc-href" href="#bleu-score-optional" title="Bleu Score (optional)">Bleu Score (optional)</a></li><li><a class="toc-href" href="#attention-model-intuition" title="Attention Model Intuition">Attention Model Intuition</a></li><li><a class="toc-href" href="#attention-model" title="Attention Model">Attention Model</a></li></ul></li><li><a class="toc-href" href="#ii-speech-recognition-audio-data_1" title="II-Speech recognition - Audio data">II-Speech recognition - Audio data</a><ul><li><a class="toc-href" href="#speech-recognition" title="Speech recognition">Speech recognition</a></li><li><a class="toc-href" href="#trigger-word-detection" title="Trigger Word Detection">Trigger Word Detection</a></li></ul></li><li><a class="toc-href" href="#conclusion-and-thank-you_1" title="Conclusion and thank you">Conclusion and thank you</a></li></ul></div>
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<p>This week: seq2seq. </p>
<h2 id="i-various-sequence-to-sequence-architectures">I-Various sequence to sequence architectures</h2>
<h3 id="basic-models">Basic Models</h3>
<p>e.g. Machine translation<br/>
<strong>encoder network</strong>: many-to-one RNN<br/>
<strong>decoder network</strong>: one-to-many RNN<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image001.png"/><br/>
This architecture also works for image captioning: <em>use ConvNet as encoder</em><br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image002.png"/><br/>
Difference between seq2seq and generating new text with language model: seq2seq don't <em>randomly</em> choose a translation, but choose <em>most likely</em> output sequence. </p>
<h3 id="picking-the-most-likely-sentence">Picking the most likely sentence</h3>
<p>Machine translation (or seq2seq in general): a <em>conditional</em> language model. </p>
<ul>
<li>language model: <code>P(y<1>,...,y<T>)</code>, <code>x<i> = y<i-1></code>, initial activation = <code>a<0></code> </li>
<li>seq2seq: feed encoder output as initial activation → <code>P(y<1>...y<T>|x=input seq)</code> </li>
</ul>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image003.png"/><br/>
Want to sample most likely output sequence (instead of random sampling) <br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image004.png"/> </p>
<ul>
<li>For output sequence of length L, there are |V|^L possiblilities. </li>
<li>greedy search: pick most likely word at each step → doesn't work well </li>
<li>→ <em>approximate(not guaranteed)</em> search algo: beam search (next section). </li>
</ul>
<h3 id="beam-search">Beam Search</h3>
<p>Approximately find most likely output sequence.<br/>
<strong>algo</strong><br/>
parameter: beam width <code>B</code> = 3 (beam serach = greedy for B=1) </p>
<ul>
<li>step 1: find <code>B</code> most likely choices for first word argmax <code>P(y<1>|x)</code> </li>
<li>step 2: for each of <code>B</code> previous choices → compute second word probabilities </li>
</ul>
<p>→ compuate <code>P(y<1>, y<2>|x)</code> by Bayes<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image005.png"/><br/>
initialize <strong>B</strong> copies of the network, hardwiring each of the B choices of first word from last step<br/>
⇒ keep top <code>B</code> most likely first 2 words {y<1>,y<2>}<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image006.png"/> </p>
<ul>
<li>step 3: similar </li>
</ul>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image007.png"/> </p>
<h3 id="refinements-to-beam-search">Refinements to Beam Search</h3>
<p><strong>Length normalization</strong><br/>
original object to optimize: <br/>
P(y<1>...y<t>) = product of conditional proba: P(y<1>|x)<em>P(y<2>|y<1>,x)</em>...<br/>
(in practice: taking log → sum of log-probas, more numerically stable)<br/>
with original object function, tends to prefer shorter output sequences<br/>
⇒ normalize the probability by output length, i.e. average proba of each word<br/>
"<strong>normlized log-likelihood</strong>"<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image010.png"/><br/>
In practice: use a softer normalization: normalize by <code>T^alpha</code> (typical value: alpha=0.7) </t></p>
<ul>
<li>alpha=1: fully normalizing by length </li>
<li>alpha=0: no normalization </li>
</ul>
<p><strong>Beam width choice</strong> </p>
<ul>
<li>large B: better approximation, better result, slower </li>
<li>small B: worse result, but faster </li>
</ul>
<p>In production: B=10<br/>
In research: B=~1000 </p>
<h3 id="error-analysis-in-beam-search">Error analysis in beam search</h3>
<p>When error occurs: figure out whether it's due to beam search or RNN model.<br/>
Given <code>yhat</code> and <code>y*</code>(human result):<br/>
→ feed <code>yhat</code> and <code>y*</code> to RNN language model, compute the <em>probability of each sequence</em> <br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image011.png"/> </p>
<ul>
<li>If <code>P(y*)>P(yhat)</code>⇒ beam seach needs improvement </li>
<li>If <code>P(y*)<P(yhat)</code> ⇒ RNN needs improvement </li>
</ul>
<h3 id="bleu-score-optional">Bleu Score (optional)</h3>
<p>How to evaluate machine translation systems (multiple correct answers).<br/>
→ <strong>BLEU </strong>(bilingual evaluation understudy): pretty good single-number eval metrics.<br/>
<strong>Precision</strong> </p>
<ul>
<li>(word-level) Precision: fraction of words in MT output that appears in reference translation </li>
<li>Modified precision: each word has a <em>credit</em>: max number of appearance in reference sentences (i.e. clip the count of a word) </li>
</ul>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image012.png"/><br/>
<strong>Precision on bigrams</strong><br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image013.png"/><br/>
For n-grams:<br/>
<code>Pn = sum(count_clip of ngram in yhat) / sum(count of ngram in yhat)</code> </p>
<p><strong>Bleu score</strong><br/>
Combined Bleu score: exp of avearged precision.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image015.png"/><br/>
<strong>BP</strong>: brevety penalty (penalize short translations)<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image014.png"/> </p>
<h3 id="attention-model-intuition">Attention Model Intuition</h3>
<p>Human translator: generate translation one part after another, instead of memorize (encode) whole sentence before translate.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image016.png"/> </p>
<ul>
<li>Input: run B-RNN to get hidden features for each word <code>a<t></code> </li>
<li>Output: also an RNN, </li>
</ul>
<p>at each step, using <strong>context</strong> with <strong>attention weights</strong> <code>alpha</code> to focus on only parts of input features.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image017.png"/><br/>
Attention <code>alpha<t,t'></code>: how much attention to pay to <code>t</code>'th input word when generating <code>t</code>th output word: depends on previous output <code>s<t-1></code>, and RNN input feature <code>a<t'></code>.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image018.png"/> </p>
<h3 id="attention-model">Attention Model</h3>
<p>Recap of attention model:<br/>
Feature vector at <code>t</code>'th input word: <code>a<t'></code><br/>
<em>context</em>: input features, weighted by attention weights<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image019.png"/> </p>
<p><strong>Computing attention alpha<t,t'></t,t'></strong><br/>
Use <code>a<t,t'>=softmax(e<t,t'>)</code> to ensure attention is normalized (over all <code>t</code>'s) to one.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image020.png"/><br/>
⇒ The mapping function from <code>a<t'></code> and <code>s<t-1></code> to attention logits <code>e<t,t'></code> is unknown<br/>
→ plug in a NN: <code>e<t,t'> = W * (s<t-1>, a<t'>)</code>— and trust backprop ! </p>
<p>downside: quadratique time complexity (<code>Tx * Ty</code>) → acceptable in MT, since input/output seqs are not that long...<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image021.png"/> </p>
<h2 id="ii-speech-recognition-audio-data_1">II-Speech recognition - Audio data</h2>
<h3 id="speech-recognition">Speech recognition</h3>
<p>seq2seq, where x = audio clip / spectrum gram, y=transcript<br/>
pre-DL era: phonemes (hand-engineered basic unit of sound) → no longer necessary with end-to-end learning on large dataset.<br/>
Dataset: 300~3000 hours </p>
<p><strong>CTC cost</strong> : "Connectionist temporal classification".<br/>
Pb in speech recogintion with many-to-many RNN: number of input timesteps are <em>much longer</em> than output.<br/>
→ blank and repeated characters are considered correct (collapse repeated characters afterwards)<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image023.png"/> </p>
<h3 id="trigger-word-detection">Trigger Word Detection</h3>
<p>Train with an RNN.<br/>
Data: audio clips<br/>
→ set label 1 right after the trigger word.<br/>
pb: unbalanced dataset (a lot of 0s) → label = 1 for several timesteps after trigger word.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image025.png"/> </p>
<h2 id="conclusion-and-thank-you_1">Conclusion and thank you</h2>
<p><em>Deep learning is a super power.</em><br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk3/pasted_image026.png"/> </p>
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<div id="toc"><ul><li><a class="toc-href" href="#i-various-sequence-to-sequence-architectures" title="I-Various sequence to sequence architectures">I-Various sequence to sequence architectures</a><ul><li><a class="toc-href" href="#basic-models" title="Basic Models">Basic Models</a></li><li><a class="toc-href" href="#picking-the-most-likely-sentence" title="Picking the most likely sentence">Picking the most likely sentence</a></li><li><a class="toc-href" href="#beam-search" title="Beam Search">Beam Search</a></li><li><a class="toc-href" href="#refinements-to-beam-search" title="Refinements to Beam Search">Refinements to Beam Search</a></li><li><a class="toc-href" href="#error-analysis-in-beam-search" title="Error analysis in beam search">Error analysis in beam search</a></li><li><a class="toc-href" href="#bleu-score-optional" title="Bleu Score (optional)">Bleu Score (optional)</a></li><li><a class="toc-href" href="#attention-model-intuition" title="Attention Model Intuition">Attention Model Intuition</a></li><li><a class="toc-href" href="#attention-model" title="Attention Model">Attention Model</a></li></ul></li><li><a class="toc-href" href="#ii-speech-recognition-audio-data_1" title="II-Speech recognition - Audio data">II-Speech recognition - Audio data</a><ul><li><a class="toc-href" href="#speech-recognition" title="Speech recognition">Speech recognition</a></li><li><a class="toc-href" href="#trigger-word-detection" title="Trigger Word Detection">Trigger Word Detection</a></li></ul></li><li><a class="toc-href" href="#conclusion-and-thank-you_1" title="Conclusion and thank you">Conclusion and thank you</a></li></ul></div>
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