### Paper-pdf

Authors: Abigail See, Peter J. Liu, Chris Manning (Stanford)

Published: April 25, 2017 (ACL)

### Summary

They extend the standard encoder-decoder architecture with a hybrid of pointer-generator network in their decoder. They also utilize a coverage mechanism to keep track of what has been already summarized to discourage repetition. Their results show improvements over CNN/Daily Mail datasets.

### Interesting Methods

#### Pointer-generator

They follow the Nallapati 2016 abstractive work as baseline which is an attentive sequence to sequence model and they extend it using a hybrid of pointer-generator network as well as a coverage mechanism.

• $h^e_i$ encoder hidden state
• $h^d_t$ decoder state at time $t$
• $a^t$ attention distribution (Bahdanau attention):

\begin{align} a^t=softmax\big(v^T \tanh([W_s h^d_t + W_h h^e_i + b_{attn})\big) \end{align}

• $h_t^*$ context vector, source representation.

\begin{align} h_t^* = \sum_i a_i^t h^e_i \end{align}

• $P_{vocab}$ vocabulary distribution, the probability of generating words at time step $t$.

\begin{align} P_{vocab} = softmax \big( V’(V[h^d_t, h_t^*] + b) + b’ \big) \end{align}

• $P_{vocab}(w)$: probability of generating word $w$.

• $P_{gen}$ probability of generating a word at time step $t$:

\begin{align} p_{gen} = \sigma \big( \mathrm{linear}(h_t^*, h^d_t, x_t) \big) \end{align}

• Copying words from input is according to attention weights at that time step.
• The final probability of generating a word $w$ at each time step is:

\begin{align} P(w) = p_{gen} P_{vocab} (w) + (1-p_{gen})\sum_{i:w_i=w}a_i^t \end{align}

• If $w$ is OOV, P_{vocab}(w)=0. Similarly, if $w$ is not in the source, $\sum_{i:w_i=w}a_i^t=0$.
• Pointer-generator is able to produce OOV words

#### Coverage

• In order to limit the repetition problem, they maintain a coverage vector $c_t$ which is sum of attention distributions over all previous decoder timesteps:

\begin{align} c^t = \sum_{t’=0}^{t-1} a^{t’} \end{align}

• Use coverage as an extra input to the attention mechanism:

\begin{align} e_t^i = v^T \tanh \big(\mathrm{linear}(h^e_i, h^d_t, c_i^t)\big) \end{align}

• They find it necessary to add a coverage loss to penalize repeatedly attending to the same locations:

\begin{align} \mathrm{covloss}_t = \sum_i \min (a_i^t , c_i^t) \end{align}

• Final loss:

\begin{align} \mathrm{loss} = -\log P(w^{*}_t) + \gamma \sum_i \min (a_i^t , c_i^t) \end{align}

• They first train the model without coverage until convergence and then add the coverage loss.