-
Notifications
You must be signed in to change notification settings - Fork 26
/
ctc_cost.py
206 lines (177 loc) · 7.59 KB
/
ctc_cost.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
"""
CTC-Connectionist Temporal Classification
Code provided by Mohammad Pezeshki - May. 2015 -
Montreal Institute for Learning Algorithms
Referece: Graves, Alex, et al. "Connectionist temporal classification:
labelling unsegmented sequence data with recurrent neural networks."
Proceedings of the 23rd international conference on Machine learning.
ACM, 2006.
Credits: Shawn Tan, Rakesh Var
This code is distributed without any warranty, express or implied.
"""
import theano
from theano import tensor
floatX = theano.config.floatX
# T: INPUT_SEQUENCE_LENGTH
# B: BATCH_SIZE
# L: OUTPUT_SEQUENCE_LENGTH
# C: NUM_CLASSES
class CTC(object):
"""Connectionist Temporal Classification
y_hat : T x B x C+1
y : L x B
y_hat_mask : T x B
y_mask : L x B
"""
@staticmethod
def add_blanks(y, blank_symbol, y_mask=None):
"""Add blanks to a matrix and updates mask
Input shape: L x B
Output shape: 2L+1 x B
"""
# for y
y_extended = y.T.dimshuffle(0, 1, 'x')
blanks = tensor.zeros_like(y_extended) + blank_symbol
concat = tensor.concatenate([y_extended, blanks], axis=2)
res = concat.reshape((concat.shape[0],
concat.shape[1] * concat.shape[2])).T
begining_blanks = tensor.zeros((1, res.shape[1])) + blank_symbol
blanked_y = tensor.concatenate([begining_blanks, res], axis=0)
# for y_mask
if y_mask is not None:
y_mask_extended = y_mask.T.dimshuffle(0, 1, 'x')
concat = tensor.concatenate([y_mask_extended,
y_mask_extended], axis=2)
res = concat.reshape((concat.shape[0],
concat.shape[1] * concat.shape[2])).T
begining_blanks = tensor.ones((1, res.shape[1]), dtype=floatX)
blanked_y_mask = tensor.concatenate([begining_blanks, res], axis=0)
else:
blanked_y_mask = None
return blanked_y, blanked_y_mask
@staticmethod
def class_batch_to_labeling_batch(y, y_hat, y_hat_mask=None):
y_hat = y_hat * y_hat_mask.dimshuffle(0, 'x', 1)
batch_size = y_hat.shape[2]
res = y_hat[:, y.astype('int32'), tensor.arange(batch_size)]
return res
@staticmethod
def recurrence_relation(y, y_mask, blank_symbol):
n_y = y.shape[0]
blanks = tensor.zeros((2, y.shape[1])) + blank_symbol
ybb = tensor.concatenate((y, blanks), axis=0).T
sec_diag = (tensor.neq(ybb[:, :-2], ybb[:, 2:]) *
tensor.eq(ybb[:, 1:-1], blank_symbol) *
y_mask.T)
# r1: LxL
# r2: LxL
# r3: LxLxB
r2 = tensor.eye(n_y, k=1)
r3 = (tensor.eye(n_y, k=2).dimshuffle(0, 1, 'x') *
sec_diag.dimshuffle(1, 'x', 0))
return r2, r3
@classmethod
def path_probabs(cls, y, y_hat, y_mask, y_hat_mask, blank_symbol):
pred_y = cls.class_batch_to_labeling_batch(y, y_hat, y_hat_mask)
r2, r3 = cls.recurrence_relation(y, y_mask, blank_symbol)
def step(p_curr, p_prev):
# instead of dot product, we * first
# and then sum oven one dimension.
# objective: T.dot((p_prev)BxL, LxLxB)
# solusion: Lx1xB * LxLxB --> LxLxB --> (sumover)xLxB
dotproduct = (p_prev + tensor.dot(p_prev, r2) +
(p_prev.dimshuffle(1, 'x', 0) * r3).sum(axis=0).T)
return p_curr.T * dotproduct * y_mask.T # B x L
probabilities, _ = theano.scan(
step,
sequences=[pred_y],
outputs_info=[tensor.eye(y.shape[0])[0] * tensor.ones(y.T.shape)])
return probabilities, probabilities.shape
@classmethod
def cost(cls, y, y_hat, y_mask, y_hat_mask, blank_symbol):
y_hat_mask_len = tensor.sum(y_hat_mask, axis=0, dtype='int32')
y_mask_len = tensor.sum(y_mask, axis=0, dtype='int32')
probabilities, sth = cls.path_probabs(y, y_hat,
y_mask, y_hat_mask,
blank_symbol)
batch_size = probabilities.shape[1]
labels_probab = (probabilities[y_hat_mask_len - 1,
tensor.arange(batch_size),
y_mask_len - 1] +
probabilities[y_hat_mask_len - 1,
tensor.arange(batch_size),
y_mask_len - 2])
avg_cost = tensor.mean(-tensor.log(labels_probab))
return avg_cost, sth
@staticmethod
def _epslog(x):
return tensor.cast(tensor.log(tensor.clip(x, 1E-12, 1E12)),
theano.config.floatX)
@staticmethod
def log_add(a, b):
max_ = tensor.maximum(a, b)
return (max_ + tensor.log1p(tensor.exp(a + b - 2 * max_)))
@staticmethod
def log_dot_matrix(x, z):
inf = 1E12
log_dot = tensor.dot(x, z)
zeros_to_minus_inf = (z.max(axis=0) - 1) * inf
return log_dot + zeros_to_minus_inf
@staticmethod
def log_dot_tensor(x, z):
inf = 1E12
log_dot = (x.dimshuffle(1, 'x', 0) * z).sum(axis=0).T
zeros_to_minus_inf = (z.max(axis=0) - 1) * inf
return log_dot + zeros_to_minus_inf.T
@classmethod
def log_path_probabs(cls, y, y_hat, y_mask, y_hat_mask, blank_symbol):
pred_y = cls.class_batch_to_labeling_batch(y, y_hat, y_hat_mask)
r2, r3 = cls.recurrence_relation(y, y_mask, blank_symbol)
def step(log_p_curr, log_p_prev):
p1 = log_p_prev
p2 = cls.log_dot_matrix(p1, r2)
p3 = cls.log_dot_tensor(p1, r3)
p123 = cls.log_add(p3, cls.log_add(p1, p2))
return (log_p_curr.T +
p123 +
cls._epslog(y_mask.T))
log_probabilities, _ = theano.scan(
step,
sequences=[cls._epslog(pred_y)],
outputs_info=[cls._epslog(tensor.eye(y.shape[0])[0] *
tensor.ones(y.T.shape))])
return log_probabilities
@classmethod
def log_cost(cls, y, y_hat, y_mask, y_hat_mask, blank_symbol):
y_hat_mask_len = tensor.sum(y_hat_mask, axis=0, dtype='int32')
y_mask_len = tensor.sum(y_mask, axis=0, dtype='int32')
log_probabs = cls.log_path_probabs(y, y_hat,
y_mask, y_hat_mask,
blank_symbol)
batch_size = log_probabs.shape[1]
labels_probab = cls.log_add(
log_probabs[y_hat_mask_len - 1,
tensor.arange(batch_size),
y_mask_len - 1],
log_probabs[y_hat_mask_len - 1,
tensor.arange(batch_size),
y_mask_len - 2])
avg_cost = tensor.mean(-labels_probab)
return avg_cost
@classmethod
def apply(cls, y, y_hat, y_mask, y_hat_mask, scale='log_scale'):
y_hat = y_hat.dimshuffle(0, 2, 1)
num_classes = y_hat.shape[1] - 1
blanked_y, blanked_y_mask = cls.add_blanks(
y=y,
blank_symbol=num_classes.astype(floatX),
y_mask=y_mask)
if scale == 'log_scale':
final_cost = cls.log_cost(blanked_y, y_hat,
blanked_y_mask, y_hat_mask,
num_classes)
else:
final_cost, sth = cls.cost(blanked_y, y_hat,
blanked_y_mask, y_hat_mask,
num_classes)
return final_cost