# Copyright (c) 2021 PaddlePaddle Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import paddle
from paddle import nn
from paddlespeech.s2t.utils.log import Log
logger = Log(__name__).getlog()
__all__ = ['CRF']
class CRF(nn.Layer):
"""
Linear-chain Conditional Random Field (CRF).
Args:
nb_labels (int): number of labels in your tagset, including special symbols.
bos_tag_id (int): integer representing the beginning of sentence symbol in
your tagset.
eos_tag_id (int): integer representing the end of sentence symbol in your tagset.
pad_tag_id (int, optional): integer representing the pad symbol in your tagset.
If None, the model will treat the PAD as a normal tag. Otherwise, the model
will apply constraints for PAD transitions.
batch_first (bool): Whether the first dimension represents the batch dimension.
"""
def __init__(self,
nb_labels: int,
bos_tag_id: int,
eos_tag_id: int,
pad_tag_id: int=None,
batch_first: bool=True):
super().__init__()
self.nb_labels = nb_labels
self.BOS_TAG_ID = bos_tag_id
self.EOS_TAG_ID = eos_tag_id
self.PAD_TAG_ID = pad_tag_id
self.batch_first = batch_first
# initialize transitions from a random uniform distribution between -0.1 and 0.1
self.transitions = self.create_parameter(
[self.nb_labels, self.nb_labels],
default_initializer=nn.initializer.Uniform(-0.1, 0.1))
self.init_weights()
def init_weights(self):
# enforce contraints (rows=from, columns=to) with a big negative number
# so exp(-10000) will tend to zero
# no transitions allowed to the beginning of sentence
self.transitions[:, self.BOS_TAG_ID] = -10000.0
# no transition alloed from the end of sentence
self.transitions[self.EOS_TAG_ID, :] = -10000.0
if self.PAD_TAG_ID is not None:
# no transitions from padding
self.transitions[self.PAD_TAG_ID, :] = -10000.0
# no transitions to padding
self.transitions[:, self.PAD_TAG_ID] = -10000.0
# except if the end of sentence is reached
# or we are already in a pad position
self.transitions[self.PAD_TAG_ID, self.EOS_TAG_ID] = 0.0
self.transitions[self.PAD_TAG_ID, self.PAD_TAG_ID] = 0.0
def forward(self,
emissions: paddle.Tensor,
tags: paddle.Tensor,
mask: paddle.Tensor=None) -> paddle.Tensor:
"""Compute the negative log-likelihood. See `log_likelihood` method."""
nll = -self.log_likelihood(emissions, tags, mask=mask)
return nll
def log_likelihood(self, emissions, tags, mask=None):
"""Compute the probability of a sequence of tags given a sequence of
emissions scores.
Args:
emissions (paddle.Tensor): Sequence of emissions for each label.
Shape of (batch_size, seq_len, nb_labels) if batch_first is True,
(seq_len, batch_size, nb_labels) otherwise.
tags (paddle.LongTensor): Sequence of labels.
Shape of (batch_size, seq_len) if batch_first is True,
(seq_len, batch_size) otherwise.
mask (paddle.FloatTensor, optional): Tensor representing valid positions.
If None, all positions are considered valid.
Shape of (batch_size, seq_len) if batch_first is True,
(seq_len, batch_size) otherwise.
Returns:
paddle.Tensor: sum of the log-likelihoods for each sequence in the batch.
Shape of ()
"""
# fix tensors order by setting batch as the first dimension
if not self.batch_first:
emissions = emissions.transpose(0, 1)
tags = tags.transpose(0, 1)
if mask is None:
mask = paddle.ones(emissions.shape[:2], dtype=paddle.float)
scores = self._compute_scores(emissions, tags, mask=mask)
partition = self._compute_log_partition(emissions, mask=mask)
return paddle.sum(scores - partition)
def decode(self, emissions, mask=None):
"""Find the most probable sequence of labels given the emissions using
the Viterbi algorithm.
Args:
emissions (paddle.Tensor): Sequence of emissions for each label.
Shape (batch_size, seq_len, nb_labels) if batch_first is True,
(seq_len, batch_size, nb_labels) otherwise.
mask (paddle.FloatTensor, optional): Tensor representing valid positions.
If None, all positions are considered valid.
Shape (batch_size, seq_len) if batch_first is True,
(seq_len, batch_size) otherwise.
Returns:
paddle.Tensor: the viterbi score for the for each batch.
Shape of (batch_size,)
list of lists: the best viterbi sequence of labels for each batch. [B, T]
"""
# fix tensors order by setting batch as the first dimension
if not self.batch_first:
emissions = emissions.transpose(0, 1)
tags = tags.transpose(0, 1)
if mask is None:
mask = paddle.ones(emissions.shape[:2], dtype=paddle.float)
scores, sequences = self._viterbi_decode(emissions, mask)
return scores, sequences
def _compute_scores(self, emissions, tags, mask):
"""Compute the scores for a given batch of emissions with their tags.
Args:
emissions (paddle.Tensor): (batch_size, seq_len, nb_labels)
tags (Paddle.LongTensor): (batch_size, seq_len)
mask (Paddle.FloatTensor): (batch_size, seq_len)
Returns:
paddle.Tensor: Scores for each batch.
Shape of (batch_size,)
"""
batch_size, seq_length = tags.shape
scores = paddle.zeros([batch_size])
# save first and last tags to be used later
first_tags = tags[:, 0]
last_valid_idx = mask.int().sum(1) - 1
# TODO(Hui Zhang): not support fancy index.
# last_tags = tags.gather(last_valid_idx.unsqueeze(1), axis=1).squeeze()
batch_idx = paddle.arange(batch_size, dtype=last_valid_idx.dtype)
gather_last_valid_idx = paddle.stack(
[batch_idx, last_valid_idx], axis=-1)
last_tags = tags.gather_nd(gather_last_valid_idx)
# add the transition from BOS to the first tags for each batch
# t_scores = self.transitions[self.BOS_TAG_ID, first_tags]
t_scores = self.transitions[self.BOS_TAG_ID].gather(first_tags)
# add the [unary] emission scores for the first tags for each batch
# for all batches, the first word, see the correspondent emissions
# for the first tags (which is a list of ids):
# emissions[:, 0, [tag_1, tag_2, ..., tag_nblabels]]
# e_scores = emissions[:, 0].gather(1, first_tags.unsqueeze(1)).squeeze()
gather_first_tags_idx = paddle.stack([batch_idx, first_tags], axis=-1)
e_scores = emissions[:, 0].gather_nd(gather_first_tags_idx)
# the scores for a word is just the sum of both scores
scores += e_scores + t_scores
# now lets do this for each remaining word
for i in range(1, seq_length):
# we could: iterate over batches, check if we reached a mask symbol
# and stop the iteration, but vecotrizing is faster due to gpu,
# so instead we perform an element-wise multiplication
is_valid = mask[:, i]
previous_tags = tags[:, i - 1]
current_tags = tags[:, i]
# calculate emission and transition scores as we did before
# e_scores = emissions[:, i].gather(1, current_tags.unsqueeze(1)).squeeze()
gather_current_tags_idx = paddle.stack(
[batch_idx, current_tags], axis=-1)
e_scores = emissions[:, i].gather_nd(gather_current_tags_idx)
# t_scores = self.transitions[previous_tags, current_tags]
gather_transitions_idx = paddle.stack(
[previous_tags, current_tags], axis=-1)
t_scores = self.transitions.gather_nd(gather_transitions_idx)
# apply the mask
e_scores = e_scores * is_valid
t_scores = t_scores * is_valid
scores += e_scores + t_scores
# add the transition from the end tag to the EOS tag for each batch
# scores += self.transitions[last_tags, self.EOS_TAG_ID]
scores += self.transitions.gather(last_tags)[:, self.EOS_TAG_ID]
return scores
def _compute_log_partition(self, emissions, mask):
"""Compute the partition function in log-space using the forward-algorithm.
Args:
emissions (paddle.Tensor): (batch_size, seq_len, nb_labels)
mask (Paddle.FloatTensor): (batch_size, seq_len)
Returns:
paddle.Tensor: the partition scores for each batch.
Shape of (batch_size,)
"""
batch_size, seq_length, nb_labels = emissions.shape
# in the first iteration, BOS will have all the scores
alphas = self.transitions[self.BOS_TAG_ID, :].unsqueeze(
0) + emissions[:, 0]
for i in range(1, seq_length):
# (bs, nb_labels) -> (bs, 1, nb_labels)
e_scores = emissions[:, i].unsqueeze(1)
# (nb_labels, nb_labels) -> (bs, nb_labels, nb_labels)
t_scores = self.transitions.unsqueeze(0)
# (bs, nb_labels) -> (bs, nb_labels, 1)
a_scores = alphas.unsqueeze(2)
scores = e_scores + t_scores + a_scores
new_alphas = paddle.logsumexp(scores, axis=1)
# set alphas if the mask is valid, otherwise keep the current values
is_valid = mask[:, i].unsqueeze(-1)
alphas = is_valid * new_alphas + (1 - is_valid) * alphas
# add the scores for the final transition
last_transition = self.transitions[:, self.EOS_TAG_ID]
end_scores = alphas + last_transition.unsqueeze(0)
# return a *log* of sums of exps
return paddle.logsumexp(end_scores, axis=1)
def _viterbi_decode(self, emissions, mask):
"""Compute the viterbi algorithm to find the most probable sequence of labels
given a sequence of emissions.
Args:
emissions (paddle.Tensor): (batch_size, seq_len, nb_labels)
mask (Paddle.FloatTensor): (batch_size, seq_len)
Returns:
paddle.Tensor: the viterbi score for the for each batch.
Shape of (batch_size,)
list of lists of ints: the best viterbi sequence of labels for each batch
"""
batch_size, seq_length, nb_labels = emissions.shape
# in the first iteration, BOS will have all the scores and then, the max
alphas = self.transitions[self.BOS_TAG_ID, :].unsqueeze(
0) + emissions[:, 0]
backpointers = []
for i in range(1, seq_length):
# (bs, nb_labels) -> (bs, 1, nb_labels)
e_scores = emissions[:, i].unsqueeze(1)
# (nb_labels, nb_labels) -> (bs, nb_labels, nb_labels)
t_scores = self.transitions.unsqueeze(0)
# (bs, nb_labels) -> (bs, nb_labels, 1)
a_scores = alphas.unsqueeze(2)
# combine current scores with previous alphas
scores = e_scores + t_scores + a_scores
# so far is exactly like the forward algorithm,
# but now, instead of calculating the logsumexp,
# we will find the highest score and the tag associated with it
# max_scores, max_score_tags = paddle.max(scores, axis=1)
max_scores = paddle.max(scores, axis=1)
max_score_tags = paddle.argmax(scores, axis=1)
# set alphas if the mask is valid, otherwise keep the current values
is_valid = mask[:, i].unsqueeze(-1)
alphas = is_valid * max_scores + (1 - is_valid) * alphas
# add the max_score_tags for our list of backpointers
# max_scores has shape (batch_size, nb_labels) so we transpose it to
# be compatible with our previous loopy version of viterbi
backpointers.append(max_score_tags.t())
# add the scores for the final transition
last_transition = self.transitions[:, self.EOS_TAG_ID]
end_scores = alphas + last_transition.unsqueeze(0)
# get the final most probable score and the final most probable tag
# max_final_scores, max_final_tags = paddle.max(end_scores, axis=1)
max_final_scores = paddle.max(end_scores, axis=1)
max_final_tags = paddle.argmax(end_scores, axis=1)
# find the best sequence of labels for each sample in the batch
best_sequences = []
emission_lengths = mask.int().sum(axis=1)
for i in range(batch_size):
# recover the original sentence length for the i-th sample in the batch
sample_length = emission_lengths[i].item()
# recover the max tag for the last timestep
sample_final_tag = max_final_tags[i].item()
# limit the backpointers until the last but one
# since the last corresponds to the sample_final_tag
sample_backpointers = backpointers[:sample_length - 1]
# follow the backpointers to build the sequence of labels
sample_path = self._find_best_path(i, sample_final_tag,
sample_backpointers)
# add this path to the list of best sequences
best_sequences.append(sample_path)
return max_final_scores, best_sequences
def _find_best_path(self, sample_id, best_tag, backpointers):
"""Auxiliary function to find the best path sequence for a specific sample.
Args:
sample_id (int): sample index in the range [0, batch_size)
best_tag (int): tag which maximizes the final score
backpointers (list of lists of tensors): list of pointers with
shape (seq_len_i-1, nb_labels, batch_size) where seq_len_i
represents the length of the ith sample in the batch
Returns:
list of ints: a list of tag indexes representing the bast path
"""
# add the final best_tag to our best path
best_path = [best_tag]
# traverse the backpointers in backwards
for backpointers_t in reversed(backpointers):
# recover the best_tag at this timestep
best_tag = backpointers_t[best_tag][sample_id].item()
# append to the beginning of the list so we don't need to reverse it later
best_path.insert(0, best_tag)
return best_path