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from theano import tensor, scan
from blocks.bricks import Brick
# T: INPUT_SEQUENCE_LENGTH
# B: BATCH_SIZE
# L: OUTPUT_SEQUENCE_LENGTH
# C: NUM_CLASSES
class CTC(Brick):
def apply(l, probs, l_len=None, probs_mask=None):
"""
Numeration:
Characters 0 to C-1 are true characters
Character C is the blank character
Inputs:
l : L x B : the sequence labelling
probs : T x B x C+1 : the probabilities output by the RNN
l_len : B : the length of each labelling sequence
probs_mask : T x B
Output: the B probabilities of the labelling sequences
Steps:
- Calculate y' the labelling sequence with blanks
- Calculate the recurrence relationship for the alphas
- Calculate the sequence of the alphas
- Return the probability found at the end of that sequence
"""
T = probs.shape[0]
C = probs.shape[2]-1
L = l.shape[0]
S = 2*L+1
B = l.shape[1]
# l_blk = l with interleaved blanks
l_blk = C * tensor.ones((S, B))
l_blk = tensor.set_subtensor(l_blk[1::2,:],l)
l_blk = l_blk.T # now l_blk is B x S
# dimension of alpha (corresponds to alpha hat in the paper) :
# T x B x S
# dimension of c :
# T x B
# first value of alpha (size B x S)
alpha0 = tensor.concatenate([
probs[0, :, C],
probs[0][tensor.arange(B), l[0]],
tensor.zeros((B, S-2))
], axis=1)
c0 = alpha0.sum(axis=1)
alpha0 = alpha0 / c0[:,None]
# recursion
l_blk_2 = tensor.concatenate([-tensor.ones((B,2)), l_blk[:,:-2]], axis=1)
l_case2 = tensor.ne(l_blk, numpy.float32(C)) * tensor.ne(l_blk, l_blk_2)
# l_case2 is B x S
def recursion(p, p_mask, prev_alpha, prev_c):
prev_alpha = prev_alpha[-1]
# p is B x C+1
# prev_alpha is B x S
prev_alpha_1 = tensor.concatenate([tensor.zeros((B,1)),prev_alpha[:,:-1]], axis=1)
prev_alpha_2 = tensor.concatenate([tensor.zeros((B,2)),prev_alpha[:,:-2]], axis=1)
alphabar = prev_alpha + prev_alpha1
alphabar = tensor.switch(l_case2, alphabar + prev_alpha2, alphabar)
next_alpha = alpha_bar * p[tensor.arange(B)[:,None].repeat(S,axis=1).flatten(), l_blk.flatten()].reshape((B,S))
next_alpha = tensor.switch(p_mask[:,None], next_alpha, prev_alpha]
next_c = next_alpha.sum(axis=1)
return next_alpha / next_c[:, None], next_c
# apply the recursion with scan
alpha, c = tensor.scan(fn=recursion,
sequences=[probs, probs_mask],
outputs_info=[alpha0, c0])
# return the log probability of the labellings
return tensor.log(c).sum(axis=0)
def best_path_decoding(y_hat, y_hat_mask=None):
# Easy one !
pass
def prefix_search(y_hat, y_hat_mask=None):
# Hard one...
pass
# vim: set sts=4 ts=4 sw=4 sw=4 tw=0 et:
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