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_mask=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_mask : L x B
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 = tensor.zeros((S, B))
l_blk = tensor.set_subtensor(l_blk[1::2,:],l)
# 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
def recursion(p, p_mask, prev_alpha, prev_c):
# TODO
return prev_alpha[-1], prev_c[-1]
# apply the recursion with scan
alpha, c = tensor.scan(fn=recursion,
sequences=[probs, probs_mask],
outputs_info=[alpha0, c0])
# return the probability of the labellings
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
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