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rnnt_np.py
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rnnt_np.py
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import mxnet as mx
import numpy as np
def forward_pass(log_probs, labels, blank):
T, U, _ = log_probs.shape
alphas = np.zeros((T, U))
for t in range(1, T):
alphas[t, 0] = alphas[t-1, 0] + log_probs[t-1, 0, blank]
for u in range(1, U):
alphas[0, u] = alphas[0, u-1] + log_probs[0, u-1, labels[u-1]]
for t in range(1, T):
for u in range(1, U):
no_emit = alphas[t-1, u] + log_probs[t-1, u, blank]
emit = alphas[t, u-1] + log_probs[t, u-1, labels[u-1]]
alphas[t, u] = np.logaddexp(emit, no_emit)
loglike = alphas[T-1, U-1] + log_probs[T-1, U-1, blank]
return alphas, loglike
def backward_pass(log_probs, labels, blank):
T, U, _ = log_probs.shape
betas = np.zeros((T, U))
betas[T-1, U-1] = log_probs[T-1, U-1, blank]
for t in reversed(range(T-1)):
betas[t, U-1] = betas[t+1, U-1] + log_probs[t, U-1, blank]
for u in reversed(range(U-1)):
betas[T-1, u] = betas[T-1, u+1] + log_probs[T-1, u, labels[u]]
for t in reversed(range(T-1)):
for u in reversed(range(U-1)):
no_emit = betas[t+1, u] + log_probs[t, u, blank]
emit = betas[t, u+1] + log_probs[t, u, labels[u]]
betas[t, u] = np.logaddexp(emit, no_emit)
return betas, betas[0, 0]
def compute_gradient(log_probs, alphas, betas, labels, blank):
T, U, _ = log_probs.shape
grads = np.full(log_probs.shape, -float("inf"))
log_like = betas[0, 0]
grads[T-1, U-1, blank] = alphas[T-1, U-1]
grads[:T-1, :, blank] = alphas[:T-1, :] + betas[1:, :]
for u, l in enumerate(labels):
grads[:, u, l] = alphas[:, u] + betas[:, u+1]
grads = -np.exp(grads + log_probs - log_like)
return grads
def transduce(log_probs, labels, blank=0):
"""
Args:
log_probs: 3D array with shape
[input len, output len + 1, vocab size]
labels: 1D array with shape [output time steps]
Returns:
float: The negative log-likelihood
3D array: Gradients with respect to the
unnormalized input actications
"""
alphas, ll_forward = forward_pass(log_probs, labels, blank)
betas, ll_backward = backward_pass(log_probs, labels, blank)
grads = compute_gradient(log_probs, alphas, betas, labels, blank)
return -ll_forward, grads
def transduce_batch(log_probs, labels, flen, glen, blank=0):
grads = np.zeros_like(log_probs)
costs = []
# TODO parallel loop
for b in range(log_probs.shape[0]):
t = int(flen[b])
u = int(glen[b]) + 1
ll, g = transduce(log_probs[b, :t, :u, :], labels[b, :u-1], blank)
grads[b, :t, :u, :] = g
costs.append(ll)
return costs, grads
class RNNTransducer(mx.operator.CustomOp):
"""The implementation of RNN Transducer loss functions.
To make it usable for real-world cases, this class has two policies below.
1. This class computes forward and backward variables in the log domain.
2. This class do not apply the softmax function to inputs, since the gradient calculation will be easily overflow.
"""
def __init__(self, blank):
self.blank = blank
def forward(self, is_train, req, in_data, out_data, aux):
'''
`log_ytu`: am & pm joint probability, layout 'BTUV'
`y`: label sequence (blank, y1, ..., yU), layout 'BU'
`flen`: acoustic model outputs sequence true length <= T
`glen`: label sequence length <= U
'''
log_ytu, y, flen, glen = in_data
loss, grad = transduce_batch(log_ytu.asnumpy(), y.asnumpy().astype(np.int32), flen.asnumpy(), glen.asnumpy(), self.blank)
self.saved_tensors = mx.nd.array(grad, ctx=log_ytu.context),
self.assign(out_data[0], req[0], mx.nd.array(loss, ctx=log_ytu.context))
def backward(self, req, out_grad, in_data, out_data, in_grad, aux):
grad, = self.saved_tensors
self.assign(in_grad[0], req[0], grad)
@mx.operator.register('Transducer')
class RNNTransducerProp(mx.operator.CustomOpProp):
def __init__(self, blank=0):
super(RNNTransducerProp, self).__init__()
self.blank = int(blank)
def list_arguments(self):
return ['log_ytu', 'label', 'flen', 'glen']
def list_outputs(self):
return ['output']
def infer_shape(self, in_shapes):
return in_shapes, ((in_shapes[1][0],),), ()
def create_operator(self, ctx, shapes, dtypes):
return RNNTransducer(self.blank)
class RNNTLoss(mx.gluon.loss.Loss):
def __init__(self, blank=0, weight=None, **kwargs):
batch_axis = 0
self.blank = blank
super(RNNTLoss, self).__init__(weight, batch_axis, **kwargs)
def hybrid_forward(self, F, log_ytu, label, flen, glen):
loss = F.Custom(log_ytu, label, flen, glen, blank=self.blank, op_type='Transducer')
return loss
if __name__ == '__main__':
T = 400; U = 300; B = 8; V = 50
ctx = mx.cpu()
def joint_test():
log_ytu = mx.nd.log_softmax(mx.nd.random_uniform(-10, 10, shape=(B, T, U+1, V), ctx=ctx, dtype=np.float32), axis=3)
y = mx.nd.random_uniform(1, V, shape=(B, U), ctx=ctx).astype('i')
flen = mx.nd.full(B, T, ctx=ctx, dtype='i')
glen = mx.nd.full(B, U, ctx=ctx, dtype='i')
log_ytu.attach_grad()
with mx.autograd.record():
loss = mx.nd.Custom(log_ytu, y, flen, glen, op_type='Transducer')
loss.backward()
print(log_ytu.grad)
print(loss)
def seperate_test():
f = mx.nd.random_uniform(-10, 10, shape=(B, T, V), ctx=ctx, dtype=np.float32)
g = mx.nd.random_uniform(-10, 10, shape=(B, U+1, V), ctx=ctx, dtype=np.float32)
y = mx.nd.random_uniform(1, V, shape=(B, U), ctx=ctx).astype('i')
flen = mx.nd.full(B, T, ctx=ctx, dtype='i')
glen = mx.nd.full(B, U, ctx=ctx, dtype='i')
f.attach_grad()
g.attach_grad()
with mx.autograd.record():
f1 = mx.nd.expand_dims(f, axis=2)
g1 = mx.nd.expand_dims(g, axis=1)
log_ytu = mx.nd.log_softmax(f1 + g1, axis=3)
loss = mx.nd.Custom(log_ytu, y, flen, glen, op_type='Transducer', blank=0)
loss.backward()
print(f.grad)
print(g.grad)
print(loss)
def loss_test():
log_ytu = mx.nd.log_softmax(mx.nd.random_uniform(-10, 10, shape=(B, T, U+1, V), ctx=ctx, dtype=np.float32), axis=3)
y = mx.nd.random_uniform(1, V, shape=(B, U), ctx=ctx).astype('i')
flen = mx.nd.full(B, T, ctx=ctx, dtype='i')
glen = mx.nd.full(B, U, ctx=ctx, dtype='i')
log_ytu.attach_grad()
criterion = RNNTLoss()
with mx.autograd.record():
loss = criterion(log_ytu, y, flen, glen)
loss.backward()
print(log_ytu.grad)
print(loss)
# seperate_test()
loss_test()