# Source code for fairseq.modules.dynamic_crf_layer

```# Copyright (c) Facebook, Inc. and its affiliates.
#
# LICENSE file in the root directory of this source tree.

"""
This file is to re-implemented the low-rank and beam approximation of CRF layer
Proposed by:

Sun, Zhiqing, et al.
Fast Structured Decoding for Sequence Models
https://arxiv.org/abs/1910.11555

The CRF implementation is mainly borrowed from
https://github.com/kmkurn/pytorch-crf/blob/master/torchcrf/__init__.py

"""

import numpy as np
import torch
import torch.nn as nn

def logsumexp(x, dim=1):

[docs]class DynamicCRF(nn.Module):
"""Dynamic CRF layer is used to approximate the traditional
Conditional Random Fields (CRF)
\$P(y | x) = 1/Z(x) exp(sum_i s(y_i, x) + sum_i t(y_{i-1}, y_i, x))\$

where in this function, we assume the emition scores (s) are given,
and the transition score is a |V| x |V| matrix \$M\$

in the following two aspects:
(1) it used a low-rank approximation for the transition matrix:
\$M = E_1 E_2^T\$
(2) it used a beam to estimate the normalizing factor Z(x)
"""

def __init__(self, num_embedding, low_rank=32, beam_size=64):
super().__init__()

self.E1 = nn.Embedding(num_embedding, low_rank)
self.E2 = nn.Embedding(num_embedding, low_rank)

self.vocb = num_embedding
self.rank = low_rank
self.beam = beam_size

[docs]    def extra_repr(self):
return "vocab_size={}, low_rank={}, beam_size={}".format(
self.vocb, self.rank, self.beam
)

[docs]    def forward(self, emissions, targets, masks, beam=None):
"""
Compute the conditional log-likelihood of a sequence of target tokens given emission scores

Args:
emissions (`~torch.Tensor`): Emission score are usually the unnormalized decoder output
``(batch_size, seq_len, vocab_size)``. We assume batch-first
targets (`~torch.LongTensor`): Sequence of target token indices
``(batch_size, seq_len)

Returns:
`~torch.Tensor`: approximated log-likelihood
"""
denominator = self._compute_normalizer(emissions, targets, masks, beam)
return numerator - denominator

[docs]    def forward_decoder(self, emissions, masks=None, beam=None):
"""
Find the most likely output sequence using Viterbi algorithm.

Args:
emissions (`~torch.Tensor`): Emission score are usually the unnormalized decoder output
``(batch_size, seq_len, vocab_size)``. We assume batch-first

Returns:
`~torch.LongTensor`: decoded sequence from the CRF model
"""

batch_size, seq_len = targets.size()
emission_scores = emissions.gather(2, targets[:, :, None])[:, :, 0]  # B x T
transition_scores = (self.E1(targets[:, :-1]) * self.E2(targets[:, 1:])).sum(2)

scores = emission_scores
scores[:, 1:] += transition_scores

return scores.sum(-1)

def _compute_normalizer(self, emissions, targets=None, masks=None, beam=None):
# HACK: we include "target" which is a hueristic for training
# HACK: we use a beam of tokens to approximate the normalizing factor (which is bad?)

beam = beam if beam is not None else self.beam
batch_size, seq_len = emissions.size()[:2]
if targets is not None:
_emissions = emissions.scatter(2, targets[:, :, None], np.float("inf"))
beam_targets = _emissions.topk(beam, 2)
beam_emission_scores = emissions.gather(2, beam_targets)
else:
beam_emission_scores, beam_targets = emissions.topk(beam, 2)
beam_transition_score1 = self.E1(beam_targets[:, :-1])  # B x (T-1) x K x D
beam_transition_score2 = self.E2(beam_targets[:, 1:])  # B x (T-1) x K x D
beam_transition_matrix = torch.bmm(
beam_transition_score1.view(-1, beam, self.rank),
beam_transition_score2.view(-1, beam, self.rank).transpose(1, 2),
)
beam_transition_matrix = beam_transition_matrix.view(batch_size, -1, beam, beam)

# compute the normalizer in the log-space
score = beam_emission_scores[:, 0]  # B x K
for i in range(1, seq_len):
next_score = score[:, :, None] + beam_transition_matrix[:, i - 1]
next_score = logsumexp(next_score, dim=1) + beam_emission_scores[:, i]

score = torch.where(masks[:, i : i + 1], next_score, score)
else:
score = next_score

# Sum (log-sum-exp) over all possible tags
return logsumexp(score, dim=1)

# HACK: we use a beam of tokens to approximate the normalizing factor (which is bad?)

beam = beam if beam is not None else self.beam
batch_size, seq_len = emissions.size()[:2]
beam_emission_scores, beam_targets = emissions.topk(beam, 2)
beam_transition_score1 = self.E1(beam_targets[:, :-1])  # B x (T-1) x K x D
beam_transition_score2 = self.E2(beam_targets[:, 1:])  # B x (T-1) x K x D
beam_transition_matrix = torch.bmm(
beam_transition_score1.view(-1, beam, self.rank),
beam_transition_score2.view(-1, beam, self.rank).transpose(1, 2),
)
beam_transition_matrix = beam_transition_matrix.view(batch_size, -1, beam, beam)

traj_tokens, traj_scores = [], []
finalized_tokens, finalized_scores = [], []

# compute the normalizer in the log-space
score = beam_emission_scores[:, 0]  # B x K
dummy = (
torch.arange(beam, device=score.device).expand(*score.size()).contiguous()
)

for i in range(1, seq_len):
traj_scores.append(score)
_score = score[:, :, None] + beam_transition_matrix[:, i - 1]
_score, _index = _score.max(dim=1)
_score = _score + beam_emission_scores[:, i]

score = torch.where(masks[:, i : i + 1], _score, score)
index = torch.where(masks[:, i : i + 1], _index, dummy)
else:
score, index = _score, _index
traj_tokens.append(index)

# now running the back-tracing and find the best
best_score, best_index = score.max(dim=1)
finalized_tokens.append(best_index[:, None])
finalized_scores.append(best_score[:, None])

for idx, scs in zip(reversed(traj_tokens), reversed(traj_scores)):
previous_index = finalized_tokens[-1]
finalized_tokens.append(idx.gather(1, previous_index))
finalized_scores.append(scs.gather(1, previous_index))

finalized_tokens.reverse()
finalized_tokens = torch.cat(finalized_tokens, 1)
finalized_tokens = beam_targets.gather(2, finalized_tokens[:, :, None])[:, :, 0]

finalized_scores.reverse()
finalized_scores = torch.cat(finalized_scores, 1)
finalized_scores[:, 1:] = finalized_scores[:, 1:] - finalized_scores[:, :-1]

return finalized_scores, finalized_tokens
```