Conditional Language Modeling

Chris DyerDeepMind

Carnegie Mellon University

August 30, 2017MT Marathon 2017

A language model assigns probabilities to sequences of words, .w = (w1, w2, . . . , w`)

p(w) = p(w1)⇥ p(w2 | w1)⇥ p(w3 | w1, w2)⇥ · · ·⇥p(w` | w1, . . . , w`�1)

p(wt | w1, . . . , wt�1)

We saw that it is helpful to decompose this probability using the chain rule, as follows:

This reduces the language modeling problem to modeling the probability of the next word, given the history of preceding words.

Review: Unconditional LMs

Unconditional LMs with RNNs

softmax

p(tom | hsi)

softmax

p(tom | hsi)

softmaxsoftmax

p(tom | hsi)

softmaxsoftmax

p(tom | hsi)

⇠likes

⇥p(likes | hsi, tom)

softmaxsoftmax

p(tom | hsi)

⇠likes

softmax

⇥p(beer | hsi, tom, likes)

softmaxsoftmax

p(tom | hsi)

⇠likes

softmax

⇥p(beer | hsi, tom, likes)

softmax

⇥p(h/si | hsi, tom, likes, beer)

softmaxsoftmax

tom⇠

softmax

Unconditional LMs with RNNsTraining

softmaxsoftmax

tom likes

softmax

cost1 cost2 cost3 cost4

softmaxsoftmax

tom likes

softmax

cost1 cost2 cost3 cost4{log lo

softmaxsoftmax

tom likes

softmax

{log lo

softmaxsoftmax

tom likes

softmax

{log lo

softmax

w1 w2 w3 w4

w4w3w2w1

p(W5|w1,w2,w3,w4)z }| {

vector(word embedding)

observedcontext word

random variable

RNN hidden state vector, length=|vocab|

A conditional language model assigns probabilities to sequences of words, , given some conditioning context, .

w = (w1, w2, . . . , w`)

Conditional LMs

p(w | x) =Y

p(wt | x, w1, w2, . . . , wt�1)

As with unconditional models, it is again helpful to use the chain rule to decompose this probability:

What is the probability of the next word, given the history of previously generated words and conditioning context ?

Conditional LMs “input” “text output”An author A document written by that authorA topic label An article about that topic{SPAM, NOT_SPAM} An emailA sentence in Portuguese Its English translationA sentence in English Its Portuguese translationA sentence in English Its Chinese translationAn image A text description of the imageA document Its summaryA document Its translationMeterological measurements A weather reportAcoustic signal Transcription of speechConversational history + database Dialogue system responseA question + a document Its answerA question + an image Its answer

Data for training conditional LMs

To train conditional language models, we need paired samples, .{(xi,wi)}Ni=1

Data availability varies. It’s easy to think of tasks that could be solved by conditional language models, but the data just doesn’t exist.

Relatively large amounts of data for:Translation, summarisation, caption generation, speech recognition

Section overviewThe rest of this section will look at “encoder-decoder” models that learn a function that maps into a fixed-size vector and then uses a language model to “decode” that vector into a sequence of words, .w

Kunst kann nicht gelehrt werden…

Artistry can’t be taught…

Section overviewThe rest of this section will look at “encoder-decoder” models that learn a function that maps into a fixed-size vector and then uses a language model to “decode” that vector into a sequence of words, .w

A dog is playing on the beach.

• Two questions

• How do we encode as a fixed-size vector, ?

• How do we condition on in the decoding model?

Section overview

- Problem (or at least modality) specific- Think about assumptions

- Less problem specific- We will review solution/architectures

Kalchbrenner and Blunsom 2013

c = embed(x)

s = Vc

Encoder

Recurrent decoderSource sentence

Embedding of wt�1

Recurrent connection

Recall unconditional RNNht = g(W[ht�1;wt�1] + b])

Learnt biasht = g(W[ht�1;wt�1] + s+ b])

ut = Pht + b0

p(Wt | x,w<t) = softmax(ut)

K&B 2013: EncoderHow should we define ?c = embed(x)

The simplest model possible:

What do you think of this model?

x1 x2 x3 x4 x5 x6

x2 x3 x4 x5 x6

K&B 2013: CSM EncoderHow should we define ?c = embed(x)

Convolutional sentence model (CSM)

K&B 2013: RNN Decoder

c = embed(x)

s = Vc

Encoder

Recurrent decoderSource sentence

Embedding of wt�1

Recurrent connection

Recall unconditional RNNht = g(W[ht�1;wt�1] + b])

Learnt biasht = g(W[ht�1;wt�1] + s+ b])

ut = Pht + b0

softmax

p(tom | s, hsi)

softmax

p(tom | s, hsi)

softmax

⇠likes

⇥p(likes | s, hsi, tom)

softmax

p(tom | s, hsi)

softmax

⇠likes

softmax

⇥p(beer | s, hsi, tom, likes)

softmax

p(tom | s, hsi)

softmax

⇠likes

softmax

⇥p(beer | s, hsi, tom, likes)

softmax

⇥p(h\si | s, hsi, tom, likes, beer)

Sutskever et al. (2014)LSTM encoder

LSTM decoder

(c0,h0) are parameters

The encoding is where .

w0 = hsi

(ci,hi) = LSTM(xi, ci�1,hi�1)

(ct+`,ht+`) = LSTM(wt�1, ct+`�1,ht+`�1)

(c`,h`) ` = |x|

ut = Pht+` + b

Aller Anfang ist schwer STOP

Sutskever et al. (2014)

Aller Anfang ist schwer STOP

Beginnings

Aller Anfang ist schwer

Beginnings

difficultBeginnings

difficult STOPBeginnings

• Good

• RNNs deal naturally with sequences of various lengths

• LSTMs in principle can propagate gradients a long distance

• Very simple architecture!

• Bad

• The hidden state has to remember a lot of information!

Sutskever et al. (2014): Tricks

Sutskever et al. (2014): TricksRead the input sequence “backwards”: +4 BLEU

Ensemble of 2 models: +3 BLEU

Decoder:

u(j)t = Ph(j)

t + b(j)

Ensemble of 5 models: +4.5 BLEU

Use an ensemble of J independently trained models.

(c(j)t+`,h(j)t+`) = LSTM(j)(wt�1, c

(j)t+`�1,h

(j)t+`�1)

A word about decoding

⇤= argmax

wp(w | x)

= argmax

log p(wt | x,w<t)

In general, we want to find the most probable (MAP) output given the input, i.e.

⇤= argmax

wp(w | x)

= argmax

log p(wt | x,w<t)

This is, for general RNNs, a hard problem. We therefore approximate it with a greedy search:

w⇤1 = argmax

p(w1 | x)

w⇤2 = argmax

p(w2 | x, w⇤1)

w⇤t = argmax

p(wt | x,w⇤<t)

⇤= argmax

wp(w | x)

= argmax

log p(wt | x,w<t)

This is, for general RNNs, a hard problem. We therefore approximate it with a greedy search:

w⇤1 = argmax

p(w1 | x)

w⇤2 = argmax

p(w2 | x, w⇤1)

w⇤t = argmax

p(wt | x,w⇤<t)

undecidable :(

A word about decodingA slightly better approximation is to use a beam search withbeam size b. Key idea: keep track of top b hypothesis.

E.g., for b=2:

w0 w1 w2 w3

hsilogprob=0

x = Bier trinke ichbeer drink I

E.g., for b=2:

w0 w1 w2 w3

hsilogprob=0

logprob=-2.11

logprob=-1.82beer

E.g., for b=2:

w0 w1 w2 w3

hsilogprob=0

logprob=-2.11

logprob=-1.82beer

logprob=-6.93

logprob=-5.80

E.g., for b=2:

w0 w1 w2 w3

hsilogprob=0

logprob=-2.11

logprob=-1.82beer

logprob=-6.93

logprob=-5.80

logprob=-8.66

logprob=-2.87drink

E.g., for b=2:

w0 w1 w2 w3

hsilogprob=0

logprob=-2.11

logprob=-1.82beer

logprob=-8.66

logprob=-2.87

logprob=-6.93

logprob=-5.80

E.g., for b=2:

w0 w1 w2 w3

hsilogprob=0

logprob=-2.11

logprob=-1.82beer

logprob=-8.66

logprob=-2.87

logprob=-6.93

logprob=-5.80

logprob=-3.04

logprob=-5.12

logprob=-6.28

logprob=-7.31

beer beer

E.g., for b=2:

w0 w1 w2 w3

hsilogprob=0

logprob=-2.11

logprob=-1.82beer

logprob=-8.66

logprob=-2.87

logprob=-6.93

logprob=-5.80

logprob=-3.04

logprob=-5.12

logprob=-6.28

logprob=-7.31

beer beer

E.g., for b=2:

w0 w1 w2 w3

hsilogprob=0

logprob=-2.11

logprob=-1.82beer

logprob=-8.66

logprob=-2.87

logprob=-6.93

logprob=-5.80

logprob=-3.04

logprob=-5.12

logprob=-6.28

logprob=-7.31

beer beer

Use beam search: +1 BLEU

hsilogprob=0

logprob=-2.11

logprob=-1.82beer

logprob=-8.66

logprob=-2.87

logprob=-6.93

logprob=-5.80

logprob=-3.04

logprob=-5.12

logprob=-6.28

logprob=-7.31

beer beer

w0 w1 w2 w3

A conceptual digression

A car bomb exploded downtownIn der Innenstadt explodierte eine Autobombe

In der Innenstadt explodierte eine Autobombe A car bomb exploded downtown

In der Innenstadt explodierte eine Autobombe

A car bomb exploded downtown

detonate :arg0 bomb :arg1 car :loc downtown :time past

Semantics“logical form”

Syntax

report_event[ factivity=true explode(e, bomb, car) loc(e, downtown)]

explodieren :arg0 Bombe :arg1 Auto :loc Innenstadt :tempus imperf

Interlingua“meaning”

report_event[ factivity=true explode(e, bomb, car) loc(e, downtown)]

explodieren :arg0 Bombe :arg1 Auto :loc Innenstadt :tempus imperf

Interlingua“meaning”

Hidden

Interlingua?

Conditioning with vectors

We are compressing a lot of information in a finite-sized vector.

“You can't cram the meaning of a whole %&!$#sentence into a single $&!#* vector!”

Prof. Ray Mooney

Gradients have a long way to travel. Even LSTMs forget!

What is to be done?

Outline of Final Section

• Machine translation with attention

• Image caption generation with attention

Outline of Final Section

• Machine translation with attention

• Image caption generation with attention

Solving the Vector Problem in Translation

• Represent a source sentence as a matrix

• Generate a target sentence from a matrix

• This will

• Solve the capacity problem

• Solve the gradient flow problem

Sentences as Matrices• Problem with the fixed-size vector model

• Sentences are of different sizes but vectors are of the same size

• Solution: use matrices instead

• Fixed number of rows, but number of columns depends on the number of words

• Usually |f| = #cols

Sentences as Matrices

Ich mochte ein Bier

Mach’s gut

Ich mochte ein Bier

Mach’s gut Die Wahrheiten der Menschen sind die unwiderlegbaren Irrtumer

Ich mochte ein Bier

Mach’s gut Die Wahrheiten der Menschen sind die unwiderlegbaren Irrtumer

Question: How do we build these matrices?

With Concatenation• Each word type is represented by an n-dimensional

vector

• Take all of the vectors for the sentence and concatenate them into a matrix

• Simplest possible model

• So simple, no one has bothered to publish how well/badly it works!

Ich möchte ein Bier

x1 x2 x3 x4

fi = xi

x1 x2 x3 x4

Ich mochte ein Bier

fi = xi

F 2 Rn⇥|f |

x1 x2 x3 x4

With Convolutional Nets• Apply convolutional networks to transform the naive

concatenated matrix to obtain a context-dependent matrix

• Explored in a recent ICLR submission by Gehring et al., 2016 (from FAIR)

• Closely related to the neural translation model proposed by Kalchbrenner and Blunsom, 2013

• Note: convnets usually have a “pooling” operation at the top level that results in a fixed-sized representation. For sentences, leave this out.

x1 x2 x3 x4

Filter 1

x1 x2 x3 x4

⇤ ⇤

Filter 1 Filter 2

x1 x2 x3 x4

⇤ ⇤

Ich mochte ein Bier

F 2 Rf(n)⇥g(|f |)

Filter 1 Filter 2

With Bidirectional RNNs• By far the most widely used matrix representation, due to

Bahdanau et al (2015)

• One column per word

• Each column (word) has two halves concatenated together:

• a “forward representation”, i.e., a word and its left context

• a “reverse representation”, i.e., a word and its right context

• Implementation: bidirectional RNNs (GRUs or LSTMs) to read f from left to right and right to left, concatenate representations

x1 x2 x3 x4

�!h 1

�!h 2

�!h 3

�!h 4

x1 x2 x3 x4

�!h 1

�!h 2

�!h 3

�!h 4

�h 1

�h 2

�h 3

�h 4

x1 x2 x3 x4

�!h 1

�!h 2

�!h 3

�!h 4

�h 1

�h 2

�h 3

�h 4

fi = [ �h i;�!h i]

x1 x2 x3 x4

�!h 1

�!h 2

�!h 3

�!h 4

�h 1

�h 2

�h 3

�h 4

fi = [ �h i;�!h i]

x1 x2 x3 x4

�!h 1

�!h 2

�!h 3

�!h 4

�h 1

�h 2

�h 3

�h 4

fi = [ �h i;�!h i]

x1 x2 x3 x4

�!h 1

�!h 2

�!h 3

�!h 4

�h 1

�h 2

�h 3

�h 4

fi = [ �h i;�!h i]

x1 x2 x3 x4

�!h 1

�!h 2

�!h 3

�!h 4

�h 1

�h 2

�h 3

�h 4

Ich mochte ein Bier

F 2 R2n⇥|f |

fi = [ �h i;�!h i]

Where are we in 2017?• There are lots of ways to construct F

• And currently lots of work looking at alternatives!

• Some particularly exciting trends want to get rid of recurrences when processing the input.

• Convolutions are making a comeback (especially at Facebook)

• “Stacked self-attention” (aka “All you need is attention” from Google Brain) is another strategy.

• Still many innovations possible, particularly targeting lower-resource scenarios and domain adaptation (two problems the big players aren’t as interested in)

Generation from Matrices• We have a matrix F representing the input, now we need to generate from it

• Bahdanau et al. (2015) were the first to propose using attention for translating from matrix-encoded sentences

• High-level idea

• Generate the output sentence word by word using an RNN

• At each output position t, the RNN receives two inputs (in addition to any recurrent inputs)

• a fixed-size vector embedding of the previously generated output symbol et-1

• a fixed-size vector encoding a “view” of the input matrix

• How do we get a fixed-size vector from a matrix that changes over time?

• Bahdanau et al: do a weighted sum of the columns of F (i.e., words) based on how important they are at the current time step. (i.e., just a matrix-vector product Fat)

• The weighting of the input columns at each time-step (at) is called attention

Recall RNNs…

→ I'd

Recall RNNs…

Ich mochte ein Bier

Attention history:a>1

Ich mochte ein Bier

z }| {Attention history:

c1 = Fa1

Ich mochte ein Bier

c1 = Fa1

Ich mochte ein Bier

c1 = Fa1

Ich mochte ein Bier

I'd →

Ich mochte ein Bier

I'd →

Ich mochte ein Bier

c2 = Fa2

I'd →

Ich mochte ein Bier

c2 = Fa2

I'd →

Ich mochte ein Bier

I'd →

Ich mochte ein Bier

I'd →

stopSTOP

Ich mochte ein Bier

Attention

• How do we know what to attend to at each time-step?

• That is, how do we compute ?at

Computing Attention• At each time step (one time step = one output word), we want to be able to

“attend” to different words in the source sentence

• We need a weight for every column: this is an |f|-length vector at

• Here is a simplified version of Bahdanau et al.’s solution

• Use an RNN to predict model output, call the hidden states

• At time t compute the expected input embedding

• Take the dot product with every column in the source matrix to compute the attention energy.

• Exponentiate and normalize to 1:

• Finally, the input source vector for time t is

at = softmax(ut)

ct = Fat

(called in the paper)

ut = F>rt

rt = Vst�1( is a learned parameter)V

(Since F has |f| columns, has |f| rows)ut

(st has a fixed dimensionality, call it m)

• At time t compute the query key embedding

at = softmax(ut)

ct = Fat

ut = F>rt

at = softmax(ut)

ct = Fat

ut = F>rt

at = softmax(ut)

ct = Fat

ut = F>rt

at = softmax(ut)

ct = Fat

ut = F>rt

Nonlinear Attention-Energy Model

• In the actual model, Bahdanau et al. replace the dot product between the columns of F and rt with an MLP:

• Here, W and v are learned parameters of appropriate dimension and + “broadcasts” over the |f| columns in WF

• This can learn more complex interactions

• It is unclear if the added complexity is necessary for good performance

ut = F>rt

ut = tanh (WF+ rt)v

(simple model)(Bahdanau et al)

ut = F>rt (simple model)(Bahdanau et al)ut = v> tanh(WF+ rt)

Putting it all togethere0 = hsi

while et 6= h/si :

F = EncodeAsMatrix(f)

rt = Vst�1

s0 = w (Learned initial state; Bahdanau uses )U �h 1

at = softmax(ut)

ct = Fatst = RNN(st�1, [et�1; ct])

yt = softmax(Pst + b)

et | e<t ⇠ Categorical(yt)

}(Compute attention)

t = t+ 1

( is a learned embedding of )et�1 et

( and are learned parameters)P b

ut = v> tanh(WF+ rt)

while et 6= h/si :

F = EncodeAsMatrix(f)

rt = Vst�1

at = softmax(ut)

t = t+ 1

doesn’t depend on output decisionsut = v> tanh(WF+ rt)

while et 6= h/si :

F = EncodeAsMatrix(f) (Part 1 of lecture)

rt = Vst�1

at = softmax(ut)

t = t+ 1

X = WF

Xut = v> tanh(WF+ rt)

while et 6= h/si :

F = EncodeAsMatrix(f) (Part 1 of lecture)

rt = Vst�1

at = softmax(ut)

t = t+ 1

X = WF

ut = v> tanh(X+ rt)

Attention in MTAdd attention to seq2seq translation: +11 BLEU

A word about gradients

I'd →

Ich mochte ein Bier

I'd →

Ich mochte ein Bier

I'd →

Ich mochte ein Bier

Attention and Translation• Cho’s question: does a translator read and memorize

the input sentence/document and then generate the output?

• Compressing the entire input sentence into a vector basically says “memorize the sentence”

• Common sense experience says translators refer back and forth to the input. (also backed up by eye-tracking studies)

• Should humans be a model for machines?

Summary• Attention

• provides the ability to establish information flow directly from distant

• closely related to “pooling” operations in convnets (and other architectures)

• Traditional attention model seems to only cares about “content”

• No obvious bias in favor of diagonals, short jumps, fertility, etc.

• Some work has begun to add other “structural” biases (Luong et al., 2015; Cohn et al., 2016), but there are lots more opportunities

• Factorization into keys and values (Miller et al., 2016; Ba et al., 2016, Gulcehre et al., 2016)

• Attention weights provide interpretation you can look at

Questions?

Há perguntas?

Obrigado!

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