def test_no_repeated(self):
# standard ctc topo and modified ctc topo
# should be equivalent if there are no
# repeated neighboring symbols in the transcript
max_token = 3
standard = k2.ctc_topo(max_token, modified=False)
modified = k2.ctc_topo(max_token, modified=True)
transcript = k2.linear_fsa([1, 2, 3])
standard_graph = k2.compose(standard, transcript)
modified_graph = k2.compose(modified, transcript)
input1 = k2.linear_fsa([1, 1, 1, 0, 0, 2, 2, 3, 3])
input2 = k2.linear_fsa([1, 1, 0, 0, 2, 2, 0, 3, 3])
inputs = [input1, input2]
for i in inputs:
lattice1 = k2.intersect(standard_graph,
i,
treat_epsilons_specially=False)
lattice2 = k2.intersect(modified_graph,
i,
treat_epsilons_specially=False)
lattice1 = k2.connect(lattice1)
lattice2 = k2.connect(lattice2)
aux_labels1 = lattice1.aux_labels[lattice1.aux_labels != 0]
aux_labels2 = lattice2.aux_labels[lattice2.aux_labels != 0]
aux_labels1 = aux_labels1[:-1] # remove -1
aux_labels2 = aux_labels2[:-1]
assert torch.all(torch.eq(aux_labels1, aux_labels2))
assert torch.all(torch.eq(aux_labels2, torch.tensor([1, 2, 3])))
def test_with_repeated(self):
max_token = 2
standard = k2.ctc_topo(max_token, modified=False)
modified = k2.ctc_topo(max_token, modified=True)
transcript = k2.linear_fsa([1, 2, 2])
standard_graph = k2.compose(standard, transcript)
modified_graph = k2.compose(modified, transcript)
# There is a blank separating 2 in the input
# so standard and modified ctc topo should be equivalent
input = k2.linear_fsa([1, 1, 2, 2, 0, 2, 2, 0, 0])
lattice1 = k2.intersect(standard_graph,
input,
treat_epsilons_specially=False)
lattice2 = k2.intersect(modified_graph,
input,
treat_epsilons_specially=False)
lattice1 = k2.connect(lattice1)
lattice2 = k2.connect(lattice2)
aux_labels1 = lattice1.aux_labels[lattice1.aux_labels != 0]
aux_labels2 = lattice2.aux_labels[lattice2.aux_labels != 0]
aux_labels1 = aux_labels1[:-1] # remove -1
aux_labels2 = aux_labels2[:-1]
assert torch.all(torch.eq(aux_labels1, aux_labels2))
assert torch.all(torch.eq(aux_labels1, torch.tensor([1, 2, 2])))
# There are no blanks separating 2 in the input.
# The standard ctc topo requires that there must be a blank
# separating 2, so lattice1 in the following is empty
input = k2.linear_fsa([1, 1, 2, 2, 0, 0])
lattice1 = k2.intersect(standard_graph,
input,
treat_epsilons_specially=False)
lattice2 = k2.intersect(modified_graph,
input,
treat_epsilons_specially=False)
lattice1 = k2.connect(lattice1)
lattice2 = k2.connect(lattice2)
assert lattice1.num_arcs == 0
# Since there are two 2s in the input and there are also two 2s
# in the transcript, the final output contains only one path.
# If there were more than two 2s in the input, the output
# would contain more than one path
aux_labels2 = lattice2.aux_labels[lattice2.aux_labels != 0]
aux_labels2 = aux_labels2[:-1]
assert torch.all(torch.eq(aux_labels1, torch.tensor([1, 2, 2])))
def test_compose(self):
s = '''
0 1 11 1 1.0
0 2 12 2 2.5
1 3 -1 -1 0
2 3 -1 -1 2.5
3
'''
a_fsa = k2.Fsa.from_str(s, num_aux_labels=1).requires_grad_(True)
s = '''
0 1 1 1 1.0
0 2 2 3 3.0
1 2 3 2 2.5
2 3 -1 -1 2.0
3
'''
b_fsa = k2.Fsa.from_str(s, num_aux_labels=1).requires_grad_(True)
ans = k2.compose(a_fsa, b_fsa, inner_labels='inner')
ans = k2.connect(ans)
ans = k2.create_fsa_vec([ans])
scores = ans.get_tot_scores(log_semiring=True, use_double_scores=False)
# The reference values for `scores`, `a_fsa.grad` and `b_fsa.grad`
# are computed using GTN.
# See https://bit.ly/3heLAJq
assert scores.item() == 10
scores.backward()
assert torch.allclose(a_fsa.grad, torch.tensor([0., 1., 0., 1.]))
assert torch.allclose(b_fsa.grad, torch.tensor([0., 1., 0., 1.]))
def test_ragged_aux_labels(self):
s1 = '''
0 1 1 0.1
0 2 5 0.6
1 2 3 0.3
2 3 3 0.5
2 4 2 0.6
3 5 -1 0.7
4 5 -1 0.8
5
'''
s2 = '''
0 0 2 1 1
0 1 4 3 2
0 1 6 2 2
0 2 -1 -1 0
1 1 2 5 3
1 2 -1 -1 4
2
'''
# https://git.io/JqNok
fsa1 = k2.Fsa.from_str(s1)
fsa1.aux_labels = k2.RaggedInt('[[2] [2 4] [5] [3] [2] [-1] [-1]]')
# https://git.io/JqNaJ
fsa2 = k2.Fsa.from_str(s2, num_aux_labels=1)
# https://git.io/JqNon
ans = k2.connect(k2.compose(fsa1, fsa2, inner_labels='phones'))
assert torch.all(torch.eq(ans.labels, torch.tensor([5, 0, 2, -1])))
assert torch.all(torch.eq(ans.phones, torch.tensor([2, 4, 2, -1])))
assert str(ans.aux_labels) == str(k2.RaggedInt('[[1] [3] [5] [-1]]'))
def test_compose_inner_labels(self):
s1 = '''
0 1 1 2 0.1
0 2 0 2 0.2
1 3 3 5 0.3
2 3 5 4 0.4
3 4 3 3 0.5
3 5 2 2 0.6
4 6 -1 -1 0.7
5 6 -1 -1 0.8
6
'''
s2 = '''
0 0 2 1 1
0 1 4 3 2
0 1 6 2 2
0 2 -1 -1 0
1 1 2 5 3
1 2 -1 -1 4
2
'''
# https://git.io/JqN2j
fsa1 = k2.Fsa.from_str(s1, num_aux_labels=1)
# https://git.io/JqNaJ
fsa2 = k2.Fsa.from_str(s2, num_aux_labels=1)
# https://git.io/JqNaT
ans = k2.connect(k2.compose(fsa1, fsa2, inner_labels='phones'))
assert torch.all(torch.eq(ans.labels, torch.tensor([0, 5, 2, -1])))
assert torch.all(torch.eq(ans.phones, torch.tensor([2, 4, 2, -1])))
assert torch.all(torch.eq(ans.aux_labels, torch.tensor([1, 3, 5, -1])))
def compile(self, texts: Iterable[str],
P: k2.Fsa) -> Tuple[k2.Fsa, k2.Fsa]:
'''Create numerator and denominator graphs from transcripts
and the bigram phone LM.
Args:
texts:
A list of transcripts. Within a transcript, words are
separated by spaces.
P:
The bigram phone LM created by :func:`create_bigram_phone_lm`.
Returns:
A tuple (num_graph, den_graph), where
- `num_graph` is the numerator graph. It is an FsaVec with
shape `(len(texts), None, None)`.
- `den_graph` is the denominator graph. It is an FsaVec with the same
shape of the `num_graph`.
'''
assert P.is_cpu()
ctc_topo_P = k2.intersect(self.ctc_topo, P).invert_()
ctc_topo_P = k2.connect(ctc_topo_P)
num_graphs = k2.create_fsa_vec(
[self.compile_one_and_cache(text) for text in texts])
num = k2.compose(ctc_topo_P, num_graphs)
num = k2.connect(num)
num = k2.arc_sort(num)
den = k2.create_fsa_vec([ctc_topo_P.detach()] * len(texts))
return num, den
def compile(self,
texts: Iterable[str],
P: k2.Fsa,
replicate_den: bool = True) -> Tuple[k2.Fsa, k2.Fsa]:
'''Create numerator and denominator graphs from transcripts
and the bigram phone LM.
Args:
texts:
A list of transcripts. Within a transcript, words are
separated by spaces.
P:
The bigram phone LM created by :func:`create_bigram_phone_lm`.
replicate_den:
If True, the returned den_graph is replicated to match the number
of FSAs in the returned num_graph; if False, the returned den_graph
contains only a single FSA
Returns:
A tuple (num_graph, den_graph), where
- `num_graph` is the numerator graph. It is an FsaVec with
shape `(len(texts), None, None)`.
- `den_graph` is the denominator graph. It is an FsaVec with the same
shape of the `num_graph` if replicate_den is True; otherwise, it
is an FsaVec containing only a single FSA.
'''
assert P.device == self.device
P_with_self_loops = k2.add_epsilon_self_loops(P)
ctc_topo_P = k2.intersect(self.ctc_topo_inv,
P_with_self_loops,
treat_epsilons_specially=False).invert()
ctc_topo_P = k2.arc_sort(ctc_topo_P)
num_graphs = self.build_num_graphs(texts)
num_graphs_with_self_loops = k2.remove_epsilon_and_add_self_loops(
num_graphs)
num_graphs_with_self_loops = k2.arc_sort(num_graphs_with_self_loops)
num = k2.compose(ctc_topo_P,
num_graphs_with_self_loops,
treat_epsilons_specially=False)
num = k2.arc_sort(num)
ctc_topo_P_vec = k2.create_fsa_vec([ctc_topo_P.detach()])
if replicate_den:
indexes = torch.zeros(len(texts),
dtype=torch.int32,
device=self.device)
den = k2.index_fsa(ctc_topo_P_vec, indexes)
else:
den = ctc_topo_P_vec
return num, den
def compile_one_and_cache(self, text: str) -> k2.Fsa:
tokens = (token if token in self.words else self.oov
for token in text.split(' '))
word_ids = [self.words[token] for token in tokens]
fsa = k2.linear_fsa(word_ids)
decoding_graph = k2.connect(k2.intersect(fsa, self.L_inv)).invert_()
decoding_graph = k2.arc_sort(decoding_graph)
decoding_graph = k2.compose(self.ctc_topo, decoding_graph)
decoding_graph = k2.connect(decoding_graph)
return decoding_graph
def test_case1(self):
for device in self.devices:
# suppose we have four symbols: <blk>, a, b, c, d
torch_activation = torch.tensor([0.2, 0.2, 0.2, 0.2,
0.2]).to(device)
k2_activation = torch_activation.detach().clone()
# (T, N, C)
torch_activation = torch_activation.reshape(
1, 1, -1).requires_grad_(True)
# (N, T, C)
k2_activation = k2_activation.reshape(1, 1,
-1).requires_grad_(True)
torch_log_probs = torch.nn.functional.log_softmax(
torch_activation, dim=-1) # (T, N, C)
# we have only one sequence and its label is `a`
targets = torch.tensor([1]).to(device)
input_lengths = torch.tensor([1]).to(device)
target_lengths = torch.tensor([1]).to(device)
torch_loss = torch.nn.functional.ctc_loss(
log_probs=torch_log_probs,
targets=targets,
input_lengths=input_lengths,
target_lengths=target_lengths,
reduction='mean')
assert torch.allclose(torch_loss,
torch.tensor([1.6094379425049]).to(device))
# (N, T, C)
k2_log_probs = torch.nn.functional.log_softmax(k2_activation,
dim=-1)
supervision_segments = torch.tensor([[0, 0, 1]], dtype=torch.int32)
dense_fsa_vec = k2.DenseFsaVec(k2_log_probs,
supervision_segments).to(device)
ctc_topo = k2.ctc_topo(4)
linear_fsa = k2.linear_fsa([1])
decoding_graph = k2.compose(ctc_topo, linear_fsa).to(device)
k2_loss = k2.ctc_loss(decoding_graph,
dense_fsa_vec,
reduction='mean',
target_lengths=target_lengths)
assert torch.allclose(torch_loss, k2_loss)
torch_loss.backward()
k2_loss.backward()
assert torch.allclose(torch_activation.grad, k2_activation.grad)
def test_case3(self):
for device in self.devices:
# (T, N, C)
torch_activation = torch.tensor([[
[-5, -4, -3, -2, -1],
[-10, -9, -8, -7, -6],
[-15, -14, -13, -12, -11.],
]]).permute(1, 0, 2).to(device).requires_grad_(True)
torch_activation = torch_activation.to(torch.float32)
torch_activation.requires_grad_(True)
k2_activation = torch_activation.detach().clone().requires_grad_(
True)
torch_log_probs = torch.nn.functional.log_softmax(
torch_activation, dim=-1) # (T, N, C)
# we have only one sequence and its labels are `b,c`
targets = torch.tensor([2, 3]).to(device)
input_lengths = torch.tensor([3]).to(device)
target_lengths = torch.tensor([2]).to(device)
torch_loss = torch.nn.functional.ctc_loss(
log_probs=torch_log_probs,
targets=targets,
input_lengths=input_lengths,
target_lengths=target_lengths,
reduction='mean')
act = k2_activation.permute(1, 0, 2) # (T, N, C) -> (N, T, C)
k2_log_probs = torch.nn.functional.log_softmax(act, dim=-1)
supervision_segments = torch.tensor([[0, 0, 3]], dtype=torch.int32)
dense_fsa_vec = k2.DenseFsaVec(k2_log_probs,
supervision_segments).to(device)
ctc_topo = k2.ctc_topo(4)
linear_fsa = k2.linear_fsa([2, 3])
decoding_graph = k2.compose(ctc_topo, linear_fsa).to(device)
k2_loss = k2.ctc_loss(decoding_graph,
dense_fsa_vec,
reduction='mean',
target_lengths=target_lengths)
expected_loss = torch.tensor([4.938850402832],
device=device) / target_lengths
assert torch.allclose(torch_loss, k2_loss)
assert torch.allclose(torch_loss, expected_loss)
torch_loss.backward()
k2_loss.backward()
assert torch.allclose(torch_activation.grad, k2_activation.grad)
def compile(self, texts: Iterable[str],
P: k2.Fsa) -> Tuple[k2.Fsa, k2.Fsa, k2.Fsa]:
'''Create numerator and denominator graphs from transcripts
and the bigram phone LM.
Args:
texts:
A list of transcripts. Within a transcript, words are
separated by spaces.
P:
The bigram phone LM created by :func:`create_bigram_phone_lm`.
Returns:
A tuple (num_graph, den_graph, decoding_graph), where
- `num_graph` is the numerator graph. It is an FsaVec with
shape `(len(texts), None, None)`.
It is the result of compose(ctc_topo, P, L, transcript)
- `den_graph` is the denominator graph. It is an FsaVec with the same
shape of the `num_graph`.
It is the result of compose(ctc_topo, P).
- decoding_graph: It is the result of compose(ctc_topo, L_disambig, G)
Note that it is a single Fsa, not an FsaVec.
'''
assert P.device == self.device
P_with_self_loops = k2.add_epsilon_self_loops(P)
ctc_topo_P = k2.intersect(self.ctc_topo_inv,
P_with_self_loops,
treat_epsilons_specially=False).invert()
ctc_topo_P = k2.arc_sort(ctc_topo_P)
num_graphs = self.build_num_graphs(texts)
num_graphs_with_self_loops = k2.remove_epsilon_and_add_self_loops(
num_graphs)
num_graphs_with_self_loops = k2.arc_sort(num_graphs_with_self_loops)
num = k2.compose(ctc_topo_P,
num_graphs_with_self_loops,
treat_epsilons_specially=False,
inner_labels='phones')
num = k2.arc_sort(num)
ctc_topo_P_vec = k2.create_fsa_vec([ctc_topo_P.detach()])
indexes = torch.zeros(len(texts),
dtype=torch.int32,
device=self.device)
den = k2.index_fsa(ctc_topo_P_vec, indexes)
return num, den, self.decoding_graph
def test_random_case1(self):
# 1 sequence
for device in self.devices:
T = torch.randint(10, 100, (1, )).item()
C = torch.randint(20, 30, (1, )).item()
torch_activation = torch.rand((1, T + 10, C),
dtype=torch.float32,
device=device).requires_grad_(True)
k2_activation = torch_activation.detach().clone().requires_grad_(
True)
# [N, T, C] -> [T, N, C]
torch_log_probs = torch.nn.functional.log_softmax(
torch_activation.permute(1, 0, 2), dim=-1)
input_lengths = torch.tensor([T]).to(device)
target_lengths = torch.randint(1, T, (1, )).to(device)
targets = torch.randint(1, C - 1,
(target_lengths.item(), )).to(device)
torch_loss = torch.nn.functional.ctc_loss(
log_probs=torch_log_probs,
targets=targets,
input_lengths=input_lengths,
target_lengths=target_lengths,
reduction='mean')
k2_log_probs = torch.nn.functional.log_softmax(k2_activation,
dim=-1)
supervision_segments = torch.tensor([[0, 0, T]], dtype=torch.int32)
dense_fsa_vec = k2.DenseFsaVec(k2_log_probs,
supervision_segments).to(device)
ctc_topo = k2.ctc_topo(C - 1)
linear_fsa = k2.linear_fsa([targets.tolist()])
decoding_graph = k2.compose(ctc_topo, linear_fsa).to(device)
k2_loss = k2.ctc_loss(decoding_graph,
dense_fsa_vec,
reduction='mean',
target_lengths=target_lengths)
assert torch.allclose(torch_loss, k2_loss)
scale = torch.rand_like(torch_loss) * 100
(torch_loss * scale).sum().backward()
(k2_loss * scale).sum().backward()
assert torch.allclose(torch_activation.grad,
k2_activation.grad,
atol=1e-2)
def test_compose(self):
s = '''
0 1 11 1 1.0
0 2 12 2 2.5
1 3 -1 -1 0
2 3 -1 -1 2.5
3
'''
a_fsa = k2.Fsa.from_str(s).requires_grad_(True)
s = '''
0 1 1 1 1.0
0 2 2 3 3.0
1 2 3 2 2.5
2 3 -1 -1 2.0
3
'''
b_fsa = k2.Fsa.from_str(s).requires_grad_(True)
ans = k2.compose(a_fsa, b_fsa, inner_labels='inner')
ans = k2.connect(ans)
# Convert a single FSA to a FsaVec.
# It will retain `requires_grad_` of `ans`.
ans.__dict__['arcs'] = _k2.create_fsa_vec([ans.arcs])
scores = k2.get_tot_scores(ans,
log_semiring=True,
use_double_scores=False)
# The reference values for `scores`, `a_fsa.grad` and `b_fsa.grad`
# are computed using GTN.
# See https://bit.ly/3heLAJq
assert scores.item() == 10
scores.backward()
assert torch.allclose(a_fsa.grad, torch.tensor([0., 1., 0., 1.]))
assert torch.allclose(b_fsa.grad, torch.tensor([0., 1., 0., 1.]))
print(ans)
def compile_HLG(L: Fsa, G: Fsa, H: Fsa, labels_disambig_id_start: int,
aux_labels_disambig_id_start: int) -> Fsa:
"""
Creates a decoding graph using a lexicon fst ``L`` and language model fsa ``G``.
Involves arc sorting, intersection, determinization, removal of disambiguation symbols
and adding epsilon self-loops.
Args:
L:
An ``Fsa`` that represents the lexicon (L), i.e. has phones as ``symbols``
and words as ``aux_symbols``.
G:
An ``Fsa`` that represents the language model (G), i.e. it's an acceptor
with words as ``symbols``.
H: An ``Fsa`` that represents a specific topology used to convert the network
outputs to a sequence of phones.
Typically, it's a CTC topology fst, in which when 0 appears on the left
side, it represents the blank symbol; when it appears on the right side,
it indicates an epsilon.
labels_disambig_id_start:
An integer ID corresponding to the first disambiguation symbol in the
phonetic alphabet.
aux_labels_disambig_id_start:
An integer ID corresponding to the first disambiguation symbol in the
words vocabulary.
:return:
"""
L = k2.arc_sort(L)
G = k2.arc_sort(G)
logging.info("Intersecting L and G")
LG = k2.compose(L, G)
logging.info(f'LG shape = {LG.shape}')
logging.info("Connecting L*G")
LG = k2.connect(LG)
logging.info(f'LG shape = {LG.shape}')
logging.info("Determinizing L*G")
LG = k2.determinize(LG)
logging.info(f'LG shape = {LG.shape}')
logging.info("Connecting det(L*G)")
LG = k2.connect(LG)
logging.info(f'LG shape = {LG.shape}')
logging.info("Removing disambiguation symbols on L*G")
LG.labels[LG.labels >= labels_disambig_id_start] = 0
if isinstance(LG.aux_labels, torch.Tensor):
LG.aux_labels[LG.aux_labels >= aux_labels_disambig_id_start] = 0
else:
LG.aux_labels.values()[
LG.aux_labels.values() >= aux_labels_disambig_id_start] = 0
logging.info("Removing epsilons")
LG = k2.remove_epsilon(LG)
logging.info(f'LG shape = {LG.shape}')
logging.info("Connecting rm-eps(det(L*G))")
LG = k2.connect(LG)
logging.info(f'LG shape = {LG.shape}')
LG.aux_labels = k2.ragged.remove_values_eq(LG.aux_labels, 0)
logging.info("Arc sorting LG")
LG = k2.arc_sort(LG)
logging.info("Composing ctc_topo LG")
HLG = k2.compose(H, LG, inner_labels='phones')
logging.info("Connecting LG")
HLG = k2.connect(HLG)
logging.info("Arc sorting LG")
HLG = k2.arc_sort(HLG)
logging.info(
f'LG is arc sorted: {(HLG.properties & k2.fsa_properties.ARC_SORTED) != 0}'
)
# Attach a new attribute `lm_scores` so that we can recover
# the `am_scores` later.
# The scores on an arc consists of two parts:
# scores = am_scores + lm_scores
# NOTE: we assume that both kinds of scores are in log-space.
HLG.lm_scores = HLG.scores.clone()
return HLG
def visualize_ctc_topo():
'''This function shows how to visualize
standard/modified ctc topologies. It's for
demonstration only, not for testing.
'''
max_token = 2
labels_sym = k2.SymbolTable.from_str('''
<blk> 0
z 1
o 2
''')
aux_labels_sym = k2.SymbolTable.from_str('''
z 1
o 2
''')
word_sym = k2.SymbolTable.from_str('''
zoo 1
''')
standard = k2.ctc_topo(max_token, modified=False)
modified = k2.ctc_topo(max_token, modified=True)
standard.labels_sym = labels_sym
standard.aux_labels_sym = aux_labels_sym
modified.labels_sym = labels_sym
modified.aux_labels_sym = aux_labels_sym
standard.draw('standard_topo.svg', title='standard CTC topo')
modified.draw('modified_topo.svg', title='modified CTC topo')
fsa = k2.linear_fst([1, 2, 2], [1, 0, 0])
fsa.labels_sym = labels_sym
fsa.aux_labels_sym = word_sym
fsa.draw('transcript.svg', title='transcript')
standard_graph = k2.compose(standard, fsa)
modified_graph = k2.compose(modified, fsa)
standard_graph.draw('standard_graph.svg', title='standard graph')
modified_graph.draw('modified_graph.svg', title='modified graph')
# z z <blk> <blk> o o <blk> o <blk>
inputs = k2.linear_fsa([1, 1, 0, 0, 2, 2, 0, 2, 0])
inputs.labels_sym = labels_sym
inputs.draw('inputs.svg', title='inputs')
standard_lattice = k2.intersect(standard_graph,
inputs,
treat_epsilons_specially=False)
standard_lattice.draw('standard_lattice.svg', title='standard lattice')
modified_lattice = k2.intersect(modified_graph,
inputs,
treat_epsilons_specially=False)
modified_lattice = k2.connect(modified_lattice)
modified_lattice.draw('modified_lattice.svg', title='modified lattice')
# z z <blk> <blk> o o o <blk>
inputs2 = k2.linear_fsa([1, 1, 0, 0, 2, 2, 2, 0])
inputs2.labels_sym = labels_sym
inputs2.draw('inputs2.svg', title='inputs2')
standard_lattice2 = k2.intersect(standard_graph,
inputs2,
treat_epsilons_specially=False)
standard_lattice2 = k2.connect(standard_lattice2)
# It's empty since the topo requires that there must be a blank
# between the two o's in zoo
assert standard_lattice2.num_arcs == 0
standard_lattice2.draw('standard_lattice2.svg',
title='standard lattice2')
modified_lattice2 = k2.intersect(modified_graph,
inputs2,
treat_epsilons_specially=False)
modified_lattice2 = k2.connect(modified_lattice2)
modified_lattice2.draw('modified_lattice2.svg',
title='modified lattice2')
def compile_LG(L: Fsa, G: Fsa, ctc_topo_inv: Fsa,
labels_disambig_id_start: int,
aux_labels_disambig_id_start: int) -> Fsa:
"""
Creates a decoding graph using a lexicon fst ``L`` and language model fsa ``G``.
Involves arc sorting, intersection, determinization, removal of disambiguation symbols
and adding epsilon self-loops.
Args:
L:
An ``Fsa`` that represents the lexicon (L), i.e. has phones as ``symbols``
and words as ``aux_symbols``.
G:
An ``Fsa`` that represents the language model (G), i.e. it's an acceptor
with words as ``symbols``.
ctc_topo_inv: Epsilons are in `aux_labels` and `labels` contain phone IDs.
labels_disambig_id_start:
An integer ID corresponding to the first disambiguation symbol in the
phonetic alphabet.
aux_labels_disambig_id_start:
An integer ID corresponding to the first disambiguation symbol in the
words vocabulary.
:return:
"""
L_inv = k2.arc_sort(L.invert_())
G = k2.arc_sort(G)
logging.debug("Intersecting L and G")
LG = k2.intersect(L_inv, G)
logging.debug(f'LG shape = {LG.shape}')
logging.debug("Connecting L*G")
LG = k2.connect(LG).invert_()
logging.debug(f'LG shape = {LG.shape}')
logging.debug("Determinizing L*G")
LG = k2.determinize(LG)
logging.debug(f'LG shape = {LG.shape}')
logging.debug("Connecting det(L*G)")
LG = k2.connect(LG)
logging.debug(f'LG shape = {LG.shape}')
logging.debug("Removing disambiguation symbols on L*G")
LG.labels[LG.labels >= labels_disambig_id_start] = 0
if isinstance(LG.aux_labels, torch.Tensor):
LG.aux_labels[LG.aux_labels >= aux_labels_disambig_id_start] = 0
else:
LG.aux_labels.values()[
LG.aux_labels.values() >= aux_labels_disambig_id_start] = 0
logging.debug("Removing epsilons")
LG = k2.remove_epsilons_iterative_tropical(LG)
logging.debug(f'LG shape = {LG.shape}')
logging.debug("Connecting rm-eps(det(L*G))")
LG = k2.connect(LG)
logging.debug(f'LG shape = {LG.shape}')
LG.aux_labels = k2.ragged.remove_values_eq(LG.aux_labels, 0)
logging.debug("Arc sorting")
LG = k2.arc_sort(LG)
logging.debug("Composing")
LG = k2.compose(ctc_topo_inv, LG)
logging.debug("Connecting")
LG = k2.connect(LG)
logging.debug("Arc sorting")
LG = k2.arc_sort(LG)
logging.debug(
f'LG is arc sorted: {(LG.properties & k2.fsa_properties.ARC_SORTED) != 0}'
)
return LG
def test_case4(self):
for device in self.devices:
# put case3, case2 and case1 into a batch
torch_activation_1 = torch.tensor(
[[0., 0., 0., 0., 0.]]).to(device).requires_grad_(True)
torch_activation_2 = torch.arange(1, 16).reshape(3, 5).to(
torch.float32).to(device).requires_grad_(True)
torch_activation_3 = torch.tensor([
[-5, -4, -3, -2, -1],
[-10, -9, -8, -7, -6],
[-15, -14, -13, -12, -11.],
]).to(device).requires_grad_(True)
k2_activation_1 = torch_activation_1.detach().clone(
).requires_grad_(True)
k2_activation_2 = torch_activation_2.detach().clone(
).requires_grad_(True)
k2_activation_3 = torch_activation_3.detach().clone(
).requires_grad_(True)
# [T, N, C]
torch_activations = torch.nn.utils.rnn.pad_sequence(
[torch_activation_3, torch_activation_2, torch_activation_1],
batch_first=False,
padding_value=0)
# [N, T, C]
k2_activations = torch.nn.utils.rnn.pad_sequence(
[k2_activation_3, k2_activation_2, k2_activation_1],
batch_first=True,
padding_value=0)
# [[b,c], [c,c], [a]]
targets = torch.tensor([2, 3, 3, 3, 1]).to(device)
input_lengths = torch.tensor([3, 3, 1]).to(device)
target_lengths = torch.tensor([2, 2, 1]).to(device)
torch_log_probs = torch.nn.functional.log_softmax(
torch_activations, dim=-1) # (T, N, C)
torch_loss = torch.nn.functional.ctc_loss(
log_probs=torch_log_probs,
targets=targets,
input_lengths=input_lengths,
target_lengths=target_lengths,
reduction='sum')
expected_loss = torch.tensor(
[4.938850402832, 7.355742931366, 1.6094379425049]).sum()
assert torch.allclose(torch_loss, expected_loss.to(device))
k2_log_probs = torch.nn.functional.log_softmax(k2_activations,
dim=-1)
supervision_segments = torch.tensor(
[[0, 0, 3], [1, 0, 3], [2, 0, 1]], dtype=torch.int32)
dense_fsa_vec = k2.DenseFsaVec(k2_log_probs,
supervision_segments).to(device)
ctc_topo = k2.ctc_topo(4)
# [ [b, c], [c, c], [a]]
linear_fsa = k2.linear_fsa([[2, 3], [3, 3], [1]])
decoding_graph = k2.compose(ctc_topo, linear_fsa).to(device)
k2_loss = k2.ctc_loss(decoding_graph,
dense_fsa_vec,
reduction='sum',
target_lengths=target_lengths)
assert torch.allclose(torch_loss, k2_loss)
scale = torch.tensor([1., -2, 3.5]).to(device)
(torch_loss * scale).sum().backward()
(k2_loss * scale).sum().backward()
assert torch.allclose(torch_activation_1.grad,
k2_activation_1.grad)
assert torch.allclose(torch_activation_2.grad,
k2_activation_2.grad)
assert torch.allclose(torch_activation_3.grad,
k2_activation_3.grad)
def compose_with_self_loops(base_graph: 'k2.Fsa', aux_graph: 'k2.Fsa') -> 'k2.Fsa':
"""Composition helper function.
"""
aux_graph_with_self_loops = k2.arc_sort(k2.add_epsilon_self_loops(aux_graph)).to(base_graph.device)
return k2.compose(base_graph, aux_graph_with_self_loops, treat_epsilons_specially=False, inner_labels="phones",)
def compile_LG(L: Fsa, G: Fsa, ctc_topo: Fsa, labels_disambig_id_start: int,
aux_labels_disambig_id_start: int) -> Fsa:
"""
Creates a decoding graph using a lexicon fst ``L`` and language model fsa ``G``.
Involves arc sorting, intersection, determinization, removal of disambiguation symbols
and adding epsilon self-loops.
Args:
L:
An ``Fsa`` that represents the lexicon (L), i.e. has phones as ``symbols``
and words as ``aux_symbols``.
G:
An ``Fsa`` that represents the language model (G), i.e. it's an acceptor
with words as ``symbols``.
ctc_topo: CTC topology fst, in which when 0 appears on the left side, it represents
the blank symbol; when it appears on the right side,
it indicates an epsilon.
labels_disambig_id_start:
An integer ID corresponding to the first disambiguation symbol in the
phonetic alphabet.
aux_labels_disambig_id_start:
An integer ID corresponding to the first disambiguation symbol in the
words vocabulary.
:return:
"""
L = k2.arc_sort(L)
G = k2.arc_sort(G)
logging.info("Intersecting L and G")
LG = k2.compose(L, G)
logging.info(f'LG shape = {LG.shape}')
logging.info("Connecting L*G")
LG = k2.connect(LG)
logging.info(f'LG shape = {LG.shape}')
logging.info("Determinizing L*G")
LG = k2.determinize(LG)
logging.info(f'LG shape = {LG.shape}')
logging.info("Connecting det(L*G)")
LG = k2.connect(LG)
logging.info(f'LG shape = {LG.shape}')
logging.info("Removing disambiguation symbols on L*G")
LG.labels[LG.labels >= labels_disambig_id_start] = 0
if isinstance(LG.aux_labels, torch.Tensor):
LG.aux_labels[LG.aux_labels >= aux_labels_disambig_id_start] = 0
else:
LG.aux_labels.values()[
LG.aux_labels.values() >= aux_labels_disambig_id_start] = 0
logging.info("Removing epsilons")
LG = k2.remove_epsilon(LG)
logging.info(f'LG shape = {LG.shape}')
logging.info("Connecting rm-eps(det(L*G))")
LG = k2.connect(LG)
logging.info(f'LG shape = {LG.shape}')
LG.aux_labels = k2.ragged.remove_values_eq(LG.aux_labels, 0)
logging.info("Arc sorting LG")
LG = k2.arc_sort(LG)
logging.info("Composing ctc_topo LG")
LG = k2.compose(ctc_topo, LG, inner_labels='phones')
logging.info("Connecting LG")
LG = k2.connect(LG)
logging.info("Arc sorting LG")
LG = k2.arc_sort(LG)
logging.info(
f'LG is arc sorted: {(LG.properties & k2.fsa_properties.ARC_SORTED) != 0}'
)
return LG
def test_random_case2(self):
# 2 sequences
for device in self.devices:
T1 = torch.randint(10, 200, (1, )).item()
T2 = torch.randint(9, 100, (1, )).item()
C = torch.randint(20, 30, (1, )).item()
if T1 < T2:
T1, T2 = T2, T1
torch_activation_1 = torch.rand((T1, C),
dtype=torch.float32,
device=device).requires_grad_(True)
torch_activation_2 = torch.rand((T2, C),
dtype=torch.float32,
device=device).requires_grad_(True)
k2_activation_1 = torch_activation_1.detach().clone(
).requires_grad_(True)
k2_activation_2 = torch_activation_2.detach().clone(
).requires_grad_(True)
# [T, N, C]
torch_activations = torch.nn.utils.rnn.pad_sequence(
[torch_activation_1, torch_activation_2],
batch_first=False,
padding_value=0)
# [N, T, C]
k2_activations = torch.nn.utils.rnn.pad_sequence(
[k2_activation_1, k2_activation_2],
batch_first=True,
padding_value=0)
target_length1 = torch.randint(1, T1, (1, )).item()
target_length2 = torch.randint(1, T2, (1, )).item()
target_lengths = torch.tensor([target_length1,
target_length2]).to(device)
targets = torch.randint(1, C - 1,
(target_lengths.sum(), )).to(device)
# [T, N, C]
torch_log_probs = torch.nn.functional.log_softmax(
torch_activations, dim=-1)
input_lengths = torch.tensor([T1, T2]).to(device)
torch_loss = torch.nn.functional.ctc_loss(
log_probs=torch_log_probs,
targets=targets,
input_lengths=input_lengths,
target_lengths=target_lengths,
reduction='mean')
assert T1 >= T2
supervision_segments = torch.tensor([[0, 0, T1], [1, 0, T2]],
dtype=torch.int32)
k2_log_probs = torch.nn.functional.log_softmax(k2_activations,
dim=-1)
dense_fsa_vec = k2.DenseFsaVec(k2_log_probs,
supervision_segments).to(device)
ctc_topo = k2.ctc_topo(C - 1)
linear_fsa = k2.linear_fsa([
targets[:target_length1].tolist(),
targets[target_length1:].tolist()
])
decoding_graph = k2.compose(ctc_topo, linear_fsa).to(device)
k2_loss = k2.ctc_loss(decoding_graph,
dense_fsa_vec,
reduction='mean',
target_lengths=target_lengths)
assert torch.allclose(torch_loss, k2_loss)
scale = torch.rand_like(torch_loss) * 100
(torch_loss * scale).sum().backward()
(k2_loss * scale).sum().backward()
assert torch.allclose(torch_activation_1.grad,
k2_activation_1.grad,
atol=1e-2)
assert torch.allclose(torch_activation_2.grad,
k2_activation_2.grad,
atol=1e-2)
