def rescore_with_n_best_list(lats: k2.Fsa, G: k2.Fsa, num_paths: int,
lm_scale_list: List[float]) -> Dict[str, k2.Fsa]:
'''Decode using n-best list with LM rescoring.
`lats` is a decoding lattice, which has 3 axes. This function first
extracts `num_paths` paths from `lats` for each sequence using
`k2.random_paths`. The `am_scores` of these paths are computed.
For each path, its `lm_scores` is computed using `G` (which is an LM).
The final `tot_scores` is the sum of `am_scores` and `lm_scores`.
The path with the greatest `tot_scores` within a sequence is used
as the decoding output.
Args:
lats:
An FsaVec. It can be the output of `k2.intersect_dense_pruned`.
G:
An FsaVec representing the language model (LM). Note that it
is an FsaVec, but it contains only one Fsa.
num_paths:
It is the size `n` in `n-best` list.
lm_scale_list:
A list containing lm_scale values.
Returns:
A dict of FsaVec, whose key is a lm_scale and the value represents the
best decoding path for each sequence in the lattice.
'''
device = lats.device
assert len(lats.shape) == 3
assert hasattr(lats, 'aux_labels')
assert hasattr(lats, 'lm_scores')
assert G.shape == (1, None, None)
assert G.device == device
assert hasattr(G, 'aux_labels') is False
# First, extract `num_paths` paths for each sequence.
# paths is a k2.RaggedInt with axes [seq][path][arc_pos]
paths = k2.random_paths(lats, num_paths=num_paths, use_double_scores=True)
# word_seqs is a k2.RaggedInt sharing the same shape as `paths`
# but it contains word IDs. Note that it also contains 0s and -1s.
# The last entry in each sublist is -1.
word_seqs = k2.index(lats.aux_labels, paths)
# Remove epsilons and -1 from word_seqs
word_seqs = k2.ragged.remove_values_leq(word_seqs, 0)
# Remove repeated sequences to avoid redundant computation later.
#
# unique_word_seqs is still a k2.RaggedInt with 3 axes [seq][path][word]
# except that there are no repeated paths with the same word_seq
# within a seq.
#
# num_repeats is also a k2.RaggedInt with 2 axes containing the
# multiplicities of each path.
# num_repeats.num_elements() == unique_word_seqs.num_elements()
#
# Since k2.ragged.unique_sequences will reorder paths within a seq,
# `new2old` is a 1-D torch.Tensor mapping from the output path index
# to the input path index.
# new2old.numel() == unique_word_seqs.num_elements()
unique_word_seqs, num_repeats, new2old = k2.ragged.unique_sequences(
word_seqs, need_num_repeats=True, need_new2old_indexes=True)
seq_to_path_shape = k2.ragged.get_layer(unique_word_seqs.shape(), 0)
# path_to_seq_map is a 1-D torch.Tensor.
# path_to_seq_map[i] is the seq to which the i-th path
# belongs.
path_to_seq_map = seq_to_path_shape.row_ids(1)
# Remove the seq axis.
# Now unique_word_seqs has only two axes [path][word]
unique_word_seqs = k2.ragged.remove_axis(unique_word_seqs, 0)
# word_fsas is an FsaVec with axes [path][state][arc]
word_fsas = k2.linear_fsa(unique_word_seqs)
word_fsas_with_epsilon_loops = k2.add_epsilon_self_loops(word_fsas)
am_scores = compute_am_scores(lats, word_fsas_with_epsilon_loops,
path_to_seq_map)
# Now compute lm_scores
b_to_a_map = torch.zeros_like(path_to_seq_map)
lm_path_lats = _intersect_device(G,
word_fsas_with_epsilon_loops,
b_to_a_map=b_to_a_map,
sorted_match_a=True)
lm_path_lats = k2.top_sort(k2.connect(lm_path_lats.to('cpu')).to(device))
lm_scores = lm_path_lats.get_tot_scores(use_double_scores=True, log_semiring=False)
ans = dict()
for lm_scale in lm_scale_list:
tot_scores = am_scores / lm_scale + lm_scores
# Remember that we used `k2.ragged.unique_sequences` to remove repeated
# paths to avoid redundant computation in `k2.intersect_device`.
# Now we use `num_repeats` to correct the scores for each path.
#
# NOTE(fangjun): It is commented out as it leads to a worse WER
# tot_scores = tot_scores * num_repeats.values()
# TODO(fangjun): We may need to add `k2.RaggedDouble`
ragged_tot_scores = k2.RaggedFloat(seq_to_path_shape,
tot_scores.to(torch.float32))
argmax_indexes = k2.ragged.argmax_per_sublist(ragged_tot_scores)
# Use k2.index here since argmax_indexes' dtype is torch.int32
best_path_indexes = k2.index(new2old, argmax_indexes)
paths_2axes = k2.ragged.remove_axis(paths, 0)
# best_path is a k2.RaggedInt with 2 axes [path][arc_pos]
best_paths = k2.index(paths_2axes, best_path_indexes)
# labels is a k2.RaggedInt with 2 axes [path][phone_id]
# Note that it contains -1s.
labels = k2.index(lats.labels.contiguous(), best_paths)
labels = k2.ragged.remove_values_eq(labels, -1)
# lats.aux_labels is a k2.RaggedInt tensor with 2 axes, so
# aux_labels is also a k2.RaggedInt with 2 axes
aux_labels = k2.index(lats.aux_labels, best_paths.values())
best_path_fsas = k2.linear_fsa(labels)
best_path_fsas.aux_labels = aux_labels
key = f'lm_scale_{lm_scale}'
ans[key] = best_path_fsas
return ans
def nbest_decoding(lats: k2.Fsa, num_paths: int):
'''
(Ideas of this function are from Dan)
It implements something like CTC prefix beam search using n-best lists
The basic idea is to first extra n-best paths from the given lattice,
build a word seqs from these paths, and compute the total scores
of these sequences in the log-semiring. The one with the max score
is used as the decoding output.
'''
# First, extract `num_paths` paths for each sequence.
# paths is a k2.RaggedInt with axes [seq][path][arc_pos]
paths = k2.random_paths(lats, num_paths=num_paths, use_double_scores=True)
# word_seqs is a k2.RaggedInt sharing the same shape as `paths`
# but it contains word IDs. Note that it also contains 0s and -1s.
# The last entry in each sublist is -1.
word_seqs = k2.index(lats.aux_labels, paths)
# Note: the above operation supports also the case when
# lats.aux_labels is a ragged tensor. In that case,
# `remove_axis=True` is used inside the pybind11 binding code,
# so the resulting `word_seqs` still has 3 axes, like `paths`.
# The 3 axes are [seq][path][word]
# Remove epsilons and -1 from word_seqs
word_seqs = k2.ragged.remove_values_leq(word_seqs, 0)
# Remove repeated sequences to avoid redundant computation later.
#
# Since k2.ragged.unique_sequences will reorder paths within a seq,
# `new2old` is a 1-D torch.Tensor mapping from the output path index
# to the input path index.
# new2old.numel() == unique_word_seqs.num_elements()
unique_word_seqs, _, new2old = k2.ragged.unique_sequences(
word_seqs, need_num_repeats=False, need_new2old_indexes=True)
# Note: unique_word_seqs still has the same axes as word_seqs
seq_to_path_shape = k2.ragged.get_layer(unique_word_seqs.shape(), 0)
# path_to_seq_map is a 1-D torch.Tensor.
# path_to_seq_map[i] is the seq to which the i-th path
# belongs.
path_to_seq_map = seq_to_path_shape.row_ids(1)
# Remove the seq axis.
# Now unique_word_seqs has only two axes [path][word]
unique_word_seqs = k2.ragged.remove_axis(unique_word_seqs, 0)
# word_fsas is an FsaVec with axes [path][state][arc]
word_fsas = k2.linear_fsa(unique_word_seqs)
word_fsas_with_epsilon_loops = k2.add_epsilon_self_loops(word_fsas)
# lats has phone IDs as labels and word IDs as aux_labels.
# inv_lats has word IDs as labels and phone IDs as aux_labels
inv_lats = k2.invert(lats)
inv_lats = k2.arc_sort(inv_lats) # no-op if inv_lats is already arc-sorted
path_lats = k2.intersect_device(inv_lats,
word_fsas_with_epsilon_loops,
b_to_a_map=path_to_seq_map,
sorted_match_a=True)
# path_lats has word IDs as labels and phone IDs as aux_labels
path_lats = k2.top_sort(k2.connect(path_lats.to('cpu')).to(lats.device))
tot_scores = path_lats.get_tot_scores(True, True)
# RaggedFloat currently supports float32 only.
# We may bind Ragged<double> as RaggedDouble if needed.
ragged_tot_scores = k2.RaggedFloat(seq_to_path_shape,
tot_scores.to(torch.float32))
argmax_indexes = k2.ragged.argmax_per_sublist(ragged_tot_scores)
# Since we invoked `k2.ragged.unique_sequences`, which reorders
# the index from `paths`, we use `new2old`
# here to convert argmax_indexes to the indexes into `paths`.
#
# Use k2.index here since argmax_indexes' dtype is torch.int32
best_path_indexes = k2.index(new2old, argmax_indexes)
paths_2axes = k2.ragged.remove_axis(paths, 0)
# best_paths is a k2.RaggedInt with 2 axes [path][arc_pos]
best_paths = k2.index(paths_2axes, best_path_indexes)
# labels is a k2.RaggedInt with 2 axes [path][phone_id]
# Note that it contains -1s.
labels = k2.index(lats.labels.contiguous(), best_paths)
labels = k2.ragged.remove_values_eq(labels, -1)
# lats.aux_labels is a k2.RaggedInt tensor with 2 axes, so
# aux_labels is also a k2.RaggedInt with 2 axes
aux_labels = k2.index(lats.aux_labels, best_paths.values())
best_path_fsas = k2.linear_fsa(labels)
best_path_fsas.aux_labels = aux_labels
return best_path_fsas
def rescore_with_whole_lattice(lats: k2.Fsa, G_with_epsilon_loops: k2.Fsa,
lm_scale_list: List[float]
) -> Dict[str, k2.Fsa]:
'''Use whole lattice to rescore.
Args:
lats:
An FsaVec It can be the output of `k2.intersect_dense_pruned`.
G_with_epsilon_loops:
An FsaVec representing the language model (LM). Note that it
is an FsaVec, but it contains only one Fsa.
lm_scale_list:
A list containing lm_scale values.
Returns:
A dict of FsaVec, whose key is a lm_scale and the value represents the
best decoding path for each sequence in the lattice.
'''
assert len(lats.shape) == 3
assert hasattr(lats, 'lm_scores')
assert G_with_epsilon_loops.shape == (1, None, None)
device = lats.device
lats.scores = lats.scores - lats.lm_scores
# We will use lm_scores from G, so remove lats.lm_scores here
del lats.lm_scores
assert hasattr(lats, 'lm_scores') is False
# lats.scores = scores / lm_scale
# Now, lats.scores contains only am_scores
# inverted_lats has word IDs as labels.
# Its aux_labels are phone IDs, which is a ragged tensor k2.RaggedInt
inverted_lats = k2.invert(lats)
num_seqs = lats.shape[0]
b_to_a_map = torch.zeros(num_seqs, device=device, dtype=torch.int32)
try:
rescoring_lats = k2.intersect_device(G_with_epsilon_loops,
inverted_lats,
b_to_a_map,
sorted_match_a=True)
except RuntimeError as e:
print(f'Caught exception:\n{e}\n')
print(f'Number of FSAs: {inverted_lats.shape[0]}')
print('num_arcs before pruning: ', inverted_lats.arcs.num_elements())
# NOTE(fangjun): The choice of the threshold 0.01 is arbitrary here
# to avoid OOM. We may need to fine tune it.
inverted_lats = k2.prune_on_arc_post(inverted_lats, 0.001, True)
print('num_arcs after pruning: ', inverted_lats.arcs.num_elements())
rescoring_lats = k2.intersect_device(G_with_epsilon_loops,
inverted_lats,
b_to_a_map,
sorted_match_a=True)
rescoring_lats = k2.top_sort(k2.connect(rescoring_lats.to('cpu')).to(device))
# inv_lats has phone IDs as labels
# and word IDs as aux_labels.
inv_lats = k2.invert(rescoring_lats)
ans = dict()
#
# The following implements
# scores = (scores - lm_scores)/lm_scale + lm_scores
# = scores/lm_scale + lm_scores*(1 - 1/lm_scale)
#
saved_am_scores = inv_lats.scores - inv_lats.lm_scores
for lm_scale in lm_scale_list:
am_scores = saved_am_scores / lm_scale
inv_lats.scores = am_scores + inv_lats.lm_scores
best_paths = k2.shortest_path(inv_lats, use_double_scores=True)
key = f'lm_scale_{lm_scale}'
ans[key] = best_paths
return ans
def whole_lattice_rescoring(lats: Fsa, G_with_epsilon_loops: Fsa) -> Fsa:
'''Rescore the 1st pass lattice with an LM.
In general, the G in HLG used to obtain `lats` is a 3-gram LM.
This function replaces the 3-gram LM in `lats` with a 4-gram LM.
Args:
lats:
The decoding lattice from the 1st pass. We assume it is the result
of intersecting HLG with the network output.
G_with_epsilon_loops:
An LM. It is usually a 4-gram LM with epsilon self-loops.
It should be arc sorted.
Returns:
Return a new lattice rescored with a given G.
'''
assert len(lats.shape) == 3, f'{lats.shape}'
assert hasattr(lats, 'lm_scores')
assert G_with_epsilon_loops.shape == (1, None, None), \
f'{G_with_epsilon_loops.shape}'
device = lats.device
lats.scores = lats.scores - lats.lm_scores
# Now lats contains only acoustic scores
# We will use lm_scores from the given G, so remove lats.lm_scores here
del lats.lm_scores
assert hasattr(lats, 'lm_scores') is False
# inverted_lats has word IDs as labels.
# Its aux_labels are token IDs, which is a ragged tensor k2.RaggedInt
# if lats.aux_labels is a ragged tensor
inverted_lats = k2.invert(lats)
num_seqs = lats.shape[0]
b_to_a_map = torch.zeros(num_seqs, device=device, dtype=torch.int32)
while True:
try:
rescoring_lats = k2.intersect_device(G_with_epsilon_loops,
inverted_lats,
b_to_a_map,
sorted_match_a=True)
break
except RuntimeError as e:
logging.info(f'Caught exception:\n{e}\n')
# Usually, this is an OOM exception. We reduce
# the size of the lattice and redo k2.intersect_device()
# NOTE(fangjun): The choice of the threshold 1e-5 is arbitrary here
# to avoid OOM. We may need to fine tune it.
logging.info(f'num_arcs before: {inverted_lats.num_arcs}')
inverted_lats = k2.prune_on_arc_post(inverted_lats, 1e-5, True)
logging.info(f'num_arcs after: {inverted_lats.num_arcs}')
rescoring_lats = k2.top_sort(k2.connect(rescoring_lats))
# inv_rescoring_lats has token IDs as labels
# and word IDs as aux_labels.
inv_rescoring_lats = k2.invert(rescoring_lats)
return inv_rescoring_lats
def compute_am_scores_and_lm_scores(
lats: k2.Fsa,
word_fsas_with_epsilon_loops: k2.Fsa,
path_to_seq_map: torch.Tensor,
device: str = "cuda",
batch_size: int = 500,
) -> Tuple[torch.Tensor, torch.Tensor]:
"""Compute AM and LM scores of n-best lists (represented as word_fsas).
Args:
lats:
An FsaVec, which is the output of `k2.intersect_dense_pruned`.
It must have the attribute `lm_scores`.
word_fsas_with_epsilon_loops:
An FsaVec representing a n-best list. Note that it has been processed
by `k2.add_epsilon_self_loops`.
path_to_seq_map:
A 1-D torch.Tensor with dtype torch.int32. path_to_seq_map[i] indicates
which sequence the i-th Fsa in word_fsas_with_epsilon_loops belongs to.
path_to_seq_map.numel() == word_fsas_with_epsilon_loops.arcs.dim0().
batch_size:
Batchify the n-best list when intersecting with inverted_lats.
You could tune this to avoid GPU OOM issue or increase the GPU usage.
Returns:
Return a tuple of (1-D torch.Tensor, 1-D torch.Tensor) containing
the AM and LM scores of each path.
`am_scores.numel() == word_fsas_with_epsilon_loops.shape[0]`
`lm_scores.numel() == word_fsas_with_epsilon_loops.shape[0]`
"""
assert len(lats.shape) == 3
# k2.compose() currently does not support b_to_a_map. To void
# replicating `lats`, we use k2.intersect_device here.
#
# lats has phone IDs as `labels` and word IDs as aux_labels, so we
# need to invert it here.
inverted_lats = k2.invert(lats)
# Now the `labels` of inverted_lats are word IDs (a 1-D torch.Tensor)
# and its `aux_labels` are phone IDs ( a k2.RaggedInt with 2 axes)
# Remove its `aux_labels` since it is not needed in the
# following computation
del inverted_lats.aux_labels
inverted_lats = k2.arc_sort(inverted_lats)
am_path_lats = _intersect_device(
inverted_lats,
word_fsas_with_epsilon_loops,
b_to_a_map=path_to_seq_map,
sorted_match_a=True,
batch_size=batch_size,
)
am_path_lats = k2.top_sort(k2.connect(am_path_lats))
# The `scores` of every arc consists of `am_scores` and `lm_scores`
tot_score_device = "cpu"
if hasattr(lats, "lm_scores"):
am_path_lats.scores = am_path_lats.scores - am_path_lats.lm_scores
am_scores = (
am_path_lats.to(tot_score_device)
.get_tot_scores(use_double_scores=True, log_semiring=False)
.to(device)
)
# Start to compute lm_scores
am_path_lats.scores = am_path_lats.lm_scores
lm_scores = (
am_path_lats.to(tot_score_device)
.get_tot_scores(use_double_scores=True, log_semiring=False)
.to(device)
)
else:
am_scores = (
am_path_lats.to(tot_score_device)
.get_tot_scores(use_double_scores=True, log_semiring=False)
.to(device)
)
lm_scores = None
return am_scores, lm_scores