Sequence Model - Sequence Models & Attention Mechanism

Various Sequence To Sequence Architectures

Basic Models

Sequence to sequence model

Image captioning

use CNN(AlexNet) first to get a 4096-dimensional vector, feed it to a RNN

Picking the Most Likely Sentence

translate a French sentence \(x\) to the most likely English sentence \(y\) .

it's to find

\[\argmax_{y^{<1>}, \dots, y^{<T_y>}} P(y^{<1>}, \dots, y^{<T_y>} | x) \]

• Why not a greedy search?

  (Find the most likely words one by one) Because it may be verbose and long.

Beam Search

• set the \(B = 3 \text{(beam width)}\), find \(3\) most likely English outputs

• consider each for the most likely second word, and then find \(B\) most likely words

  

• do it again until \(<EOS>\)

if \(B = 1\), it's just greedy search.

Refinements to beam search

Length normalization

\[\argmax_{y} \prod_{t = 1}^{T_y} P(y^{<t>}|x, y^{<1>}, y^{<t - 1>}) \]

\(P\) is much less than \(1\) (close to \(0\)) take \(\log\)

\[\argmax_{y} \sum_{t = 1}^{T_y} \log P(y^{<t>}|x, y^{<1>}, y^{<t - 1>}) \]

it tends to give the short sentences.

So you can normalize it (\(\alpha\) is a hyperparameter)

\[\argmax_{y} \frac 1 {T_y^{\alpha}} \sum_{t = 1}^{T_y} \log P(y^{<t>}|x, y^{<1>}, y^{<t - 1>}) \]

Beam search discussion

• large \(B\) : better result, slower
• small \(B\) : worse result, faster

Error Analysis in Beam Search

let \(y^*\) be human high quality translation, and \(\hat y\) be algorithm output.

• \(P(y^* | x) > P(\hat y | x)\) : Beam search is at fault
• \(P(y^* | x) \le P(\hat y | x)\) : RNN model is at fault

Bleu(bilingual evaluation understudy) Score

if you have some good referrences to evaluate the score.

\[p_n = \frac{\sum_{\text{n-grams} \in \hat y} \text{Count}_{\text{clip}}(\text{n-grams})} {\sum_{\text{n-grams} \in \hat y} \text{Count}(\text{n-grams})} \]

Bleu details

calculate it with \(\exp(\frac{1}{4} \sum_{n = 1}^4 p_n)\)

BP = brevity penalty

\[BP = \begin{cases} 1 & \text{if~~MT\_output\_length > reference\_output\_length}\\ \exp(1 - \text{reference\_output\_length / MT\_output\_length}) & \text{otherwise} \end{cases} \]

don't want short translation.

Attention Model Intuition

it's hard for network to memorize the whole sentence.

compute the attention weight to predict the word from the context

Attention Model

Use a BiRNN or BiLSTM.

\[\begin{aligned} a^{<t'>} &= (\vec a^{<t'>}, \overleftarrow a^{<t'>})\\ \sum_{t'} \alpha^{<i, t'>} &= 1\\ c^{<i>} &= \sum_{t'} \alpha^{<i, t'>} \alpha^{<t'>} \end{aligned} \]

Computing attention

\[\begin{aligned} \alpha^{<t, t'>} &= \text{amount of "attention" } y^{<t>} \text{ should pay to } a^{<t'>}\\ &= \frac{\exp(e^{<t, t'>})}{\sum_{t' = 1}^{T_x} \exp(e^{<t, t'>})} \end{aligned} \]

train a very small network to learn what the function is

the complexity is \(\mathcal O(T_x T_y)\) , which is so big (quadratic cost)

Speech Recognition - Audio Data

Speech recognition

\(x(\text{audio clip}) \to y(\text{transcript})\)

Attention model for sppech recognition

generate character by character

CTC cost for speech recognition

CTC(Connectionist temporal classification)

"ttt_h_eee___ ____qqq\(\dots\)" \(\rightarrow\) "the quick brown fox"

Basic rule: collapse repeated characters not separated by "blank"

Trigger Word Detection

label the trigger word, let the output be \(1\)s