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[Sequential Models] week1. Recurrent Neural Networks
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目录
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<div id="toc"><ul><li><a class="toc-href" href="#week1" title="week1">week1</a><ul><li><a class="toc-href" href="#why-sequence-models" title="Why sequence models">Why sequence models</a></li><li><a class="toc-href" href="#notation" title="Notation">Notation</a></li><li><a class="toc-href" href="#recurrent-neural-network-model" title="Recurrent Neural Network Model">Recurrent Neural Network Model</a><ul><li><a class="toc-href" href="#rnn" title="RNN">RNN</a></li><li><a class="toc-href" href="#rnn-forward-prop" title="RNN Forward prop">RNN Forward prop</a></li></ul></li><li><a class="toc-href" href="#backpropagation-through-time_1" title="Backpropagation through time">Backpropagation through time</a></li><li><a class="toc-href" href="#different-types-of-rnns" title="Different types of RNNs">Different types of RNNs</a></li><li><a class="toc-href" href="#language-model-and-sequence-generation" title="Language model and sequence generation">Language model and sequence generation</a></li><li><a class="toc-href" href="#sampling-novel-sequences" title="Sampling novel sequences">Sampling novel sequences</a></li><li><a class="toc-href" href="#vanishing-gradients-with-rnns" title="Vanishing gradients with RNNs">Vanishing gradients with RNNs</a></li><li><a class="toc-href" href="#gated-recurrent-unit-gru" title="Gated Recurrent Unit (GRU)">Gated Recurrent Unit (GRU)</a></li><li><a class="toc-href" href="#long-short-term-memory-lstm" title="Long Short Term Memory (LSTM)">Long Short Term Memory (LSTM)</a></li><li><a class="toc-href" href="#bidirectional-rnn" title="Bidirectional RNN">Bidirectional RNN</a></li><li><a class="toc-href" href="#deep-rnns" title="Deep RNNs">Deep RNNs</a></li></ul></li></ul></div>
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</div>
<h1 id="week1">week1</h1>
<p>Created Friday 02 February 2018 </p>
<h3 id="why-sequence-models">Why sequence models</h3>
<p>examples of seq data (<em>either input or output</em>): </p>
<ul>
<li>speech recognition </li>
<li>music generation </li>
<li>sentiment classification </li>
<li>DNA seq analysis </li>
<li>Machine translation </li>
<li>video activity recognition </li>
<li>name entity recognition (<strong>NER</strong>) </li>
</ul>
<p>→ in this course: learn models applicable to these different settings. </p>
<h3 id="notation">Notation</h3>
<p>motivating example: NER (Each word: whether the word is part of a person's name.) </p>
<ul>
<li><code>x^<t></code> / <code>y^<t></code>: t-th element in input/output sequence. </li>
<li><code>X^(i)</code>: i-th training example </li>
<li><code>T_x^(i)</code>: length of i-th training example sequence </li>
</ul>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image001.png"/><br/>
<strong>how to repr each words in a sentences (x<i>)</i></strong> </p>
<ul>
<li><em>vocabulary</em>: list of ~10k possible tokens (+"<unk>" for unknown words) </unk></li>
<li><em>one-hot</em> repr for each word </li>
</ul>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image003.png"/> </p>
<h3 id="recurrent-neural-network-model">Recurrent Neural Network Model</h3>
<p><strong>why not a standard NN</strong> </p>
<ul>
<li>input/output are of different length (padding might not be a good representation) </li>
<li>doesn't share features learned across different positions in text </li>
</ul>
<p>→ using a better representation helps to reduce number of parameters. </p>
<h4 id="rnn">RNN</h4>
<p>motivation example: output length = input length </p>
<ul>
<li>for each input <code>x<t></code>, → feed to RNN → compute <em>activation</em>(hidden state) <code>a<t></code>, and output <code>y<t></code>, </li>
<li><code>y<t>=f(a<t>)</code>, <code>a<t>=f(x<t>, a<t-1>)</code>, i.e. a<t> depends on previous state and current input. </t></li>
<li>parameters <code>W_ax</code> / <code>W_aa</code> / <code>W_ya</code> are shared across all time steps. </li>
</ul>
<p>⇒ <code>y<t></code> depends on <code>x<1>...x<t></code>, limit: only depend on <em>previous</em> words ("unidirectional"). </p>
<p>Unrolled diagram:<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image006.png"/><br/>
Or drawing a recurrent loop (harder to understand than unrolled version):<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image007.png"/> </p>
<h4 id="rnn-forward-prop">RNN Forward prop</h4>
<p>formula to calculate <code>a<t></code> and <code>y<t></code>:<br/>
a<t> = g(W_aa * a<t-1> + W_ax * x<t> + b_a)<br/>
y<t> = g(W_ya * a<t> + b_y)<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image008.png"/><br/>
Simplified annotation: stack <code>a<t-1></code> and <code>x<t></code>, <code>W_a = [W_aa, W_ax]</code><br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image009.png"/> </t></t></t></t-1></t></p>
<h3 id="backpropagation-through-time_1">Backpropagation through time</h3>
<p>Parameters: <code>W_y</code> and <code>W_a</code><br/>
loss function: log loss at each timestep (assume predictions y<t> are binary)<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image011.png"/><br/>
→ backporp through the computation graph:<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image012.png"/> </t></p>
<h3 id="different-types-of-rnns">Different types of RNNs</h3>
<p><strong>many-to-many</strong>: </p>
<ul>
<li>T_x = T_y, one prediction per timestep. </li>
</ul>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image013.png"/> </p>
<ul>
<li>T_x != T_y, e.g. machine translation </li>
</ul>
<p>having a <em>encoder</em> and a <em>decoder</em>:<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image017.png"/><br/>
<strong>many-to-one</strong>:<br/>
e.g. sentence classification<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image014.png"/><br/>
<strong>one-to-many</strong>:<br/>
e.g. music generation<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image015.png"/> </p>
<h3 id="language-model-and-sequence-generation">Language model and sequence generation</h3>
<p><strong>Language model</strong><br/>
motivation example: speech recognition, <br/>
<em>"The apple and the pear salad" </em>VS<em> "The apple and the pair salad"</em><br/>
language model: <em>give probability of a sentence</em> P(sentence). </p>
<p><strong>Building language model with RNN</strong><br/>
Training set: large corpus of text. </p>
<ul>
<li>tokenize </li>
<li>vocabulary size </li>
<li>unknow word "<unk>". </unk></li>
</ul>
<p><strong>RNN for seq generation</strong> </p>
<ul>
<li>output <code>y<t></code>: softmax of <em>probability for each word</em>. </li>
<li><code>y<t+1></code>: make prediction <em>given the correct previous word</em> </li>
<li>like this predict one word at a time. </li>
</ul>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image019.png"/><br/>
Loss function: cross entropy (<em>actual word VS probability of this word</em>) at each timestep.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image020.png"/> </p>
<h3 id="sampling-novel-sequences">Sampling novel sequences</h3>
<p>Get a sense of what's learned: sample nouvel seqs.<br/>
From training, the RNN has a distribution of sequences <code>P(y<t> | y<1...t-1>)</code>.<br/>
In sample: let the model generate sequences (<code>np.random.choice</code>): </p>
<ul>
<li>feed previously gen word as input to next step </li>
<li>include <eos> token in vocab to finish </eos></li>
<li>reject <unk> tokens </unk></li>
</ul>
<p><strong>char-level language model</strong><br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image021.png"/> </p>
<ul>
<li>pro: no <unk> token </unk></li>
<li>con: much longer sequences, more expensive to train. </li>
</ul>
<h3 id="vanishing-gradients-with-rnns">Vanishing gradients with RNNs</h3>
<p>long-range dependencies are hard to capture: <br/>
e.g. "<em>the cat ........ was full</em>" VS "<em>the cats ...... were full</em>" </p>
<p>this is due to vanishing gradients:<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image022.png"/> </p>
<p>For exploding gradients: apply <em>gradient clipping</em> (restrict gradient norm). </p>
<h3 id="gated-recurrent-unit-gru">Gated Recurrent Unit (GRU)</h3>
<p>Modification of RNN to capture long range dependencies. </p>
<p><em>Visualization of a RNN unit:</em><br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image023.png"/> </p>
<p><strong>(simplified) GRU</strong> </p>
<ul>
<li>Extra <em>memory cell</em>: <code>c<t>=a<t></code>, (replaces output activation). </li>
<li><em>Candidate</em> value of c<t>: <code>c_tilde<t>=tanh(Wc * [c<t-1>, x<t>] + b_c)</code> </t></li>
<li><strong>Gate</strong><em> (between 0 and 1, conceptually consider it as binary)</em>: </li>
</ul>
<p><code>Gamme_u = sigmoid(W_u * [c<t-1>, x<t>] + b_u)</code><br/>
subscript "<em>u</em>" stands for "<em>update</em>", i.e. whether we want to update current memory cell </p>
<ul>
<li>Actual value of <code>c<t> = Gamme_u * c_tilde<t> + (1-Gamma_u) * c<t-1></code> (<code>*</code> is element-wise multiplication) </li>
</ul>
<p>i.e. <code>c<t></code> can be conserved for long range before being updated<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image024.png"/><br/>
Visualization of GRU unit (maybe equations are more understandable...):<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image025.png"/> </p>
<p><strong>full GRU</strong><br/>
for candidate <code>c_tilde<t></code>, add one more gate <code>Gamme_r</code>: controlling how much <code>c<t-1></code> contributes to <code>c_tilde<t></code>("<em>r</em>" for "<em>relevance</em>", i.e. how relevant <code>c<t-1></code> is for <code>c_tilde<t></code>)<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image026.png"/> </p>
<h3 id="long-short-term-memory-lstm">Long Short Term Memory (LSTM)</h3>
<p>More powerful and general version of GRU. </p>
<ul>
<li>output <code>a<t></code> no longer equals to memory cell <code>c<t></code> (but a <em>gated</em> version of it, see below) </li>
<li>candidate <code>c_tilde<t></code> depends on <code>a<t-1></code> instead of <code>c<t-1></code> </li>
<li><em>two update gates</em>: <code>Gamma_u</code> (<em>update gate</em>) and <code>Gamma_f</code> (<em>forget gate</em>) </li>
<li><em>output gate</em>: <code>Gamma_o</code> </li>
<li>value of <code>c<t> = Gamma_u * c_tilde<t> + Gamma_f * c<t-1></code> </li>
<li>value of <code>a<t> = Gamma_o * c<t></code> </li>
</ul>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image027.png"/><br/>
Visualization:<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image028.png"/><br/>
Intuition: c<t> can be kept for long time if gates are set properly.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image029.png"/> </t></p>
<p>Variant: let the gates depend on c<t-1> as well ("<em>peephole connection</em>")<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image030.png"/> </t-1></p>
<p><strong>GRU vs LSTM</strong> </p>
<ul>
<li>LSTM is proposed earlier </li>
<li>GRU as a simplified version of LSTM </li>
<li>GRU easier to train larger NN (2 gates instead of 3) </li>
<li>LSTM more powerful, recommended default choice to try </li>
</ul>
<h3 id="bidirectional-rnn">Bidirectional RNN</h3>
<p>Getting information from the future.<br/>
motivation example: <br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image031.png"/> </p>
<p><strong>Bidirectional RNN (BRNN)</strong> </p>
<ul>
<li><em>forward and backword</em> recurrent components </li>
<li>computation graph is still acyclic </li>
<li>at t, both information from the past and the future are passed in </li>
<li><em>BRNN with LSTM blocks</em> are typically the first thing to try in NLP problems </li>
</ul>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image032.png"/> </p>
<h3 id="deep-rnns">Deep RNNs</h3>
<p>Complex NN: stack multiple RNNs (having 3 RNN layers is already a lot).0<br/>
notation: <code>a[l]<t></code> for activation in layer <code>l</code> and time <code>t</code>.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c5wk1/pasted_image033.png"/> </p>
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<li class="list-group-item"><a class="btn btn-primary" href='https://x-wei.github.io/Ng_DLMooc_c5wk1.html' style="text-align:left">[Sequential Models] week1. Recurrent Neural Networks</a></li>
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<div id="toc"><ul><li><a class="toc-href" href="#week1" title="week1">week1</a><ul><li><a class="toc-href" href="#why-sequence-models" title="Why sequence models">Why sequence models</a></li><li><a class="toc-href" href="#notation" title="Notation">Notation</a></li><li><a class="toc-href" href="#recurrent-neural-network-model" title="Recurrent Neural Network Model">Recurrent Neural Network Model</a><ul><li><a class="toc-href" href="#rnn" title="RNN">RNN</a></li><li><a class="toc-href" href="#rnn-forward-prop" title="RNN Forward prop">RNN Forward prop</a></li></ul></li><li><a class="toc-href" href="#backpropagation-through-time_1" title="Backpropagation through time">Backpropagation through time</a></li><li><a class="toc-href" href="#different-types-of-rnns" title="Different types of RNNs">Different types of RNNs</a></li><li><a class="toc-href" href="#language-model-and-sequence-generation" title="Language model and sequence generation">Language model and sequence generation</a></li><li><a class="toc-href" href="#sampling-novel-sequences" title="Sampling novel sequences">Sampling novel sequences</a></li><li><a class="toc-href" href="#vanishing-gradients-with-rnns" title="Vanishing gradients with RNNs">Vanishing gradients with RNNs</a></li><li><a class="toc-href" href="#gated-recurrent-unit-gru" title="Gated Recurrent Unit (GRU)">Gated Recurrent Unit (GRU)</a></li><li><a class="toc-href" href="#long-short-term-memory-lstm" title="Long Short Term Memory (LSTM)">Long Short Term Memory (LSTM)</a></li><li><a class="toc-href" href="#bidirectional-rnn" title="Bidirectional RNN">Bidirectional RNN</a></li><li><a class="toc-href" href="#deep-rnns" title="Deep RNNs">Deep RNNs</a></li></ul></li></ul></div>
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