# Sequence Generation with Sampling and Beam Search¶

This tutorial demonstrates how to sample sequences using a pre-trained language model in the following two ways: with a beam search sampler and with a sequence sampler.

Let’s use `V`

to denote the vocabulary size, and `T`

to denote the
sequence length. Given a language model, we can sample sequences
according to the probability that they would occur according to our
model. At each time step, a language model predicts the likelihood of
each word occurring, given the context from prior time steps. The
outputs at any time step can be any word from the vocabulary whose size
is `V`

and thus the number of all possible outcomes for a sequence of
length `T`

is thus

.

While sometimes we might want to sample sentences according to their
probability of occurring, at other times we want to find the sentences
that *are most likely to occur*. This is especially true in the case of
language translation where we don’t just want to see *a* translation. We
want the *best* translation. While finding the optimal outcome quickly
becomes intractable as time increases, there are still many ways to
sample reasonably good sequences. GluonNLP provides two samplers for
generating from a language model: `BeamSearchSampler`

and
`SequenceSampler`

.

## Loading a pre-trained language model (LM)¶

Firstly, let’s load a pre-trained language model, from which we will sample sequences. GluonNLP makes this a painless process.

```
In [1]:
```

```
import mxnet as mx
import gluonnlp as nlp
ctx = mx.cpu()
lm_model, vocab = nlp.model.get_model(name='awd_lstm_lm_1150',
dataset_name='wikitext-2',
pretrained=True,
ctx=ctx)
```

```
Vocab file is not found. Downloading.
Downloading /root/.mxnet/models/1562943107.0388463wikitext-2-be36dc52.zip from https://apache-mxnet.s3-accelerate.dualstack.amazonaws.com/gluon/dataset/vocab/wikitext-2-be36dc52.zip...
Downloading /root/.mxnet/models/awd_lstm_lm_1150_wikitext-2-f9562ed0.zip from https://apache-mxnet.s3-accelerate.dualstack.amazonaws.com/gluon/models/awd_lstm_lm_1150_wikitext-2-f9562ed0.zip...
```

## Sampling a Sequence with `BeamSearchSampler`

¶

To overcome the exponential complexity in sequence decoding, beam search
decodes greedily, keeping those sequences that are most likely based on
the probability up to the current time step. The size of this subset is
called the *beam size*. Suppose the beam size is `K`

and the output
vocabulary size is `V`

. When selecting the beams to keep, the beam
search algorithm first predicts all possible successor words from the
previous `K`

beams, each of which has `V`

possible outputs. This
becomes a total of `K*V`

paths. Out of these `K*V`

paths, beam
search ranks them by their score keeping only the top `K`

paths.

Let’s take a look how to construct a `BeamSearchSampler`

. The
`nlp.model.BeamSearchSampler`

class takes the following arguments for
customization and extension:

- beam_size : the beam size
- decoder : callable function of the one-step-ahead decoder
- eos_id : the id of the EOS token
- scorer: the score function used in beam search
- max_length: the maximum search length

For beam search to work, we need a scorer function.

### The scorer function¶

In this tutorial, we will use the `BeamSearchScorer`

as the scorer
function, which implements the scoring function with length penalty in
the Google NMT paper:

```
In [2]:
```

```
scorer = nlp.model.BeamSearchScorer(alpha=0, K=5, from_logits=False)
```

Defining the scorer is as simple as this one line.

### The decoder function¶

Next, we define the decoder based on the pre-trained language model.

```
In [3]:
```

```
class LMDecoder(object):
def __init__(self, model):
self._model = model
def __call__(self, inputs, states):
outputs, states = self._model(mx.nd.expand_dims(inputs, axis=0), states)
return outputs[0], states
def state_info(self, *arg, **kwargs):
return self._model.state_info(*arg, **kwargs)
decoder = LMDecoder(lm_model)
```

### Beam Search Sampler¶

Given a scorer and a decoder, we are ready to create a sampler. We use
the symbol `.`

to indicate the end of sentence (EOS). We can use vocab
to get the index of the EOS to then feed the index to the sampler. The
following code shows how to construct a beam search sampler. We will
create a sampler with 4 beams and a maximum sample length of 20.

```
In [4]:
```

```
eos_id = vocab['.']
beam_sampler = nlp.model.BeamSearchSampler(beam_size=5,
decoder=decoder,
eos_id=eos_id,
scorer=scorer,
max_length=20)
```

It’s really that simple!

### Generate Sequences with Beam Search¶

Next, we are going to generate sentences starting with “I love it” using beam search first. We feed [‘I’, ‘Love’] to the language model to get the initial states and set the initial input to be the word ‘it’. We will then print the top-3 generations.

```
In [5]:
```

```
bos = 'I love it'.split()
bos_ids = [vocab[ele] for ele in bos]
begin_states = lm_model.begin_state(batch_size=1, ctx=ctx)
if len(bos_ids) > 1:
_, begin_states = lm_model(mx.nd.expand_dims(mx.nd.array(bos_ids[:-1]), axis=1),
begin_states)
inputs = mx.nd.full(shape=(1,), ctx=ctx, val=bos_ids[-1])
```

Here we define the helper function to generate the sequences so we can simply use one line to generate new sequences for any given input.

```
In [6]:
```

```
def generate_sequences(sampler, inputs, begin_states, num_print_outcomes):
samples, scores, valid_lengths = sampler(inputs, begin_states)
samples = samples[0].asnumpy()
scores = scores[0].asnumpy()
valid_lengths = valid_lengths[0].asnumpy()
print('Generation Result:')
for i in range(num_print_outcomes):
sentence = bos[:-1]
for ele in samples[i][:valid_lengths[i]]:
sentence.append(vocab.idx_to_token[ele])
print([' '.join(sentence), scores[i]])
```

And then below, we have the one-liner to generate the sequences.

```
In [7]:
```

```
generate_sequences(beam_sampler, inputs, begin_states, 5)
```

```
Generation Result:
['I love it .', -1.1080625]
['I love it , and the <unk> of the <unk> .', -13.386151]
['I love it , but it was not until the end of the year that it was not until the end of the .', -25.007336]
['I love it , but it was not until the end of the 20th century that it was not until the end of .', -26.333736]
['I love it , but it was not until the end of the 20th century that it was not until the early 1990s .', -28.628922]
```

## Sampling a Sequence with `SequenceSampler`

¶

The previous generation results may look a bit boring. Instead, let’s now use the sequence sampler to get relatively more interesting results.

A `SequenceSampler`

samples from the contextual multinomial
distribution produced by the language model at each time step. Since we
may want to control how “sharp” the distribution is to tradeoff
diversity with correctness, we can use the temperature option in
`SequenceSampler`

, which controls the temperature of the softmax
activation function.

For each input, sequence sampler can sample multiple **independent**
sequences at once. The number of independent sequences to sample can be
specified through the argument `beam_size`

.

Defining the `SequenceSampler`

is as simple as this:

```
In [8]:
```

```
seq_sampler = nlp.model.SequenceSampler(beam_size=5,
decoder=decoder,
eos_id=eos_id,
max_length=100,
temperature=0.97)
```

### Generate Sequences with Sequence Sampler¶

Now, instead of using the beam sampler for our `generate_sequences`

function, we can use the `SequenceSampler`

instead to sample sequences
based on the same inputs used previously.

```
In [9]:
```

```
generate_sequences(seq_sampler, inputs, begin_states, 5)
```

```
Generation Result:
['I love it and enjoy one of their series , Schafer or Clive .', -56.322575]
['I love it in a television vein and rid him of his adventures .', -46.98534]
['I love it for news .', -12.868879]
['I love it ; it is not until the end of the year that a relative <unk> to a EEC owner is now raised .', -68.121025]
['I love it in an AIL report .', -25.607042]
```

Et voila! We’ve generated the most likely sentences based on our given input.

### Exercises for the keen reader¶

- Tweak alpha and K in BeamSearchScorer, how are the results changed? Does it do relatively better or worse than the sequence SequenceSampler?
- Try different samples to decode and figure out which results the BeamSearchSampler does better than the SequenceSampler