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"""
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
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