def _is_finished(i, unused_alive_seq, alive_log_probs, unused_finished_seq,
finished_scores, finished_in_finished, *unused_states):
"""Checking termination condition.
We terminate when we decoded up to decode_length or the lowest scoring item
in finished has a greater score that the highest prob item in alive divided
by the max length penalty
Args:
i: loop index
alive_log_probs: probabilities of the beams. [batch_size, beam_size]
finished_scores: scores for each of these sequences.
[batch_size, beam_size]
finished_in_finished: finished bools for each of these sequences.
[batch_size, beam_size]
Returns:
Bool.
"""
# TODO(noam): support a different decode length...
# decode_length = mtf.constant(mesh, length_dim.size, dtype=tf.int32)
# del alive_log_probs, finished_scores, finished_in_finished
# return mtf.less(i, length_dim.size)
if not stop_early:
return mtf.less(i, decode_length)
max_length_penalty = mtf.pow(
((5. + mtf.cast(decode_length, finished_scores.dtype)) / 6.),
alpha)
# The best possible score of the most likely alive sequence.
lower_bound_alive_scores = mtf.gather(
alive_log_probs, mtf.constant(mesh, 0, dtype=tf.int32),
beam_dim) / max_length_penalty
# Now to compute the lowest score of a finished sequence in finished
# If the sequence isn't finished, we multiply it's score by 0. since
# scores are all -ve, taking the min will give us the score of the lowest
# finished item.
lowest_score_of_finished_in_finished = mtf.reduce_min(
finished_scores *
mtf.cast(finished_in_finished, finished_scores.dtype),
reduced_dim=beam_dim)
# If none of the sequences have finished, then the min will be 0 and
# we have to replace it by -ve INF if it is. The score of any seq in alive
# will be much higher than -ve INF and the termination condition will not
# be met.
lowest_score_of_finished_in_finished += ((1. - mtf.cast(
mtf.reduce_any(finished_in_finished, reduced_dim=beam_dim),
finished_scores.dtype)) * -INF)
bound_is_met = mtf.reduce_all(
mtf.greater(lowest_score_of_finished_in_finished,
lower_bound_alive_scores))
return mtf.logical_and(mtf.less(i, decode_length),
mtf.logical_not(bound_is_met))
def beam_search(logits_fn,
initial_ids,
alpha,
states=None,
eos_id=EOS_ID,
stop_early=True,
decode_length=None,
use_tpu=True,
dtype=tf.float32,
layout=None,
mesh_shape=None,
num_prefilter=2):
"""Beam search with length penalties.
Requires a function that can take the currently decoded symbols and return
the logits for the next symbol. The implementation is inspired by
https://arxiv.org/abs/1609.08144.
When running, the beam search steps can be visualized by using tfdbg to watch
the operations generating the output ids for each beam step. These operations
have the pattern:
(alive|finished)_topk_(seq,scores)
Operations marked `alive` represent the new beam sequences that will be
processed in the next step. Operations marked `finished` represent the
completed beam sequences, which may be padded with 0s if no beams finished.
Operations marked `seq` store the full beam sequence for the time step.
Operations marked `scores` store the sequence's final log scores.
The beam search steps will be processed sequentially in order, so when
capturing observed from these operations, tensors, clients can make
assumptions about which step is being recorded.
num_prefilter is a theoretically lossy shortcut around slow performance of
top_k on TPU on large Tensors and large k. This option should be removed once
better top_k implementations on TPU are avialable. If num_prefilter is set to
a nonzero value, then at each step we first compute the top num_prefilter
sequences per beam and then compute the top k sequences overall from among
those. Empirically, there seems to be no quality difference in setting
num_prefilter to 2.
Args:
logits_fn: Interface to the model, to provide logits.
Should take:
step_num - mtf Scalar
ids - mtf Tensor with shape [batch, beam, length]
Should return:
logits - [batch, beam, vocab_size], dtype=dtype
initial_ids: a mtf.Tensor with shape [batch_dim, beam_dim, length_dim])
alpha: alpha for length penalty.
states: list of mtf.Tensor
eos_id: ID for end of sentence.
stop_early: a boolean - stop once best sequence is provably determined.
decode_length: a mtf Scalar of dtype tf.int32 - maximum length of decodes
use_tpu: a boolean
dtype: a tf.dtype
layout: an optional string
mesh_shape: an optional string
num_prefilter: an optional integer
Returns:
Tuple of
(decoded beams [batch, beam, length]
decoding probabilities [batch, beam_size])
"""
batch_dim, beam_dim, length_dim = initial_ids.shape.dims
batch_and_beam_dim = mtf.Dimension(batch_dim.name,
batch_dim.size * beam_dim.size)
mesh = initial_ids.mesh
batch_by_beam = mtf.Shape([batch_dim, beam_dim])
initial_log_probs = mtf.broadcast(
mtf.one_hot(mtf.constant(mesh, 0, dtype=tf.int32),
beam_dim,
on_value=0.0,
off_value=-INF,
dtype=dtype), batch_by_beam)
length_scalar = mtf.constant(mesh, length_dim.size, dtype=tf.int32)
if decode_length is None:
decode_length = length_scalar
else:
decode_length = mtf.minimum(decode_length, length_scalar)
alive_log_probs = initial_log_probs
alive_seq = initial_ids
# Finished will keep track of all the sequences that have finished so far
# Finished log probs will be negative infinity in the beginning
# finished_flags will keep track of booleans
finished_seq = initial_ids
finished_scores = mtf.constant(mesh, -INF, batch_by_beam, dtype=dtype)
# Setting the scores of the initial to negative infinity.
finished_flags = mtf.constant(mesh, False, batch_by_beam, tf.bool)
def grow_finished(finished_seq, finished_scores, finished_flags, curr_seq,
curr_scores, curr_finished):
"""Given sequences and scores, will gather the top k=beam size sequences.
Args:
finished_seq: Current finished sequences.
[batch, beam, length]
finished_scores: scores for each of these sequences.
[batch, beam]
finished_flags: finished bools for each of these sequences.
[batch, beam]
curr_seq: current topk sequence that has been grown by one position.
[batch, beam, length]
curr_scores: scores for each of these sequences. [batch, beam]
curr_finished: Finished flags for each of these sequences.
[batch, beam]
Returns:
Tuple of
(Topk sequences based on scores,
log probs of these sequences,
Finished flags of these sequences,
None (no states))
"""
# Set the scores of the unfinished seq in curr_seq to large negative
# values
curr_scores += (1. - mtf.cast(curr_finished, curr_scores.dtype)) * -INF
unused_batch_dim, beam_dim, unused_length_dim = finished_seq.shape.dims
# concatenating the sequences and scores along beam axis
def _my_concat(a, b):
a = mtf.rename_dimension(a, "beam", "triple_beam")
b = mtf.rename_dimension(b, "double_beam", "triple_beam")
return mtf.concat([a, b], "triple_beam")
curr_finished_seq = _my_concat(finished_seq, curr_seq)
curr_finished_scores = _my_concat(finished_scores, curr_scores)
curr_finished_flags = _my_concat(finished_flags, curr_finished)
return compute_topk_scores_and_seq(curr_finished_seq,
curr_finished_scores,
curr_finished_scores,
curr_finished_flags, beam_dim,
"grow_finished")
def grow_alive(curr_seq, curr_scores, curr_log_probs, curr_finished):
"""Given sequences and scores, will gather the top k=beam size sequences.
Args:
curr_seq: current topk sequence that has been grown by one position.
[batch, beam, length]
curr_scores: scores for each of these sequences. [batch_size, beam_size]
curr_log_probs: log probs for each of these sequences.
[batch, beam]
curr_finished: Finished flags for each of these sequences.
[batch, beam]
Returns:
Tuple of
(Topk sequences based on scores,
log probs of these sequences,
Finished flags of these sequences)
"""
# Set the scores of the finished seq in curr_seq to large negative
# values
curr_scores += mtf.cast(curr_finished, curr_scores.dtype) * -INF
return compute_topk_scores_and_seq(curr_seq, curr_scores,
curr_log_probs, curr_finished,
beam_dim, "grow_alive")
def grow_topk(i, alive_seq, alive_log_probs, states=None):
r"""Inner beam search loop.
This function takes the current alive sequences, and grows them to topk
sequences where k = 2*beam. We use 2*beam because, we could have beam_size
number of sequences that might hit <EOS> and there will be no alive
sequences to continue. With 2*beam_size, this will not happen. This relies
on the assumption the vocab size is > beam size. If this is true, we'll
have at least beam_size non <EOS> extensions if we extract the next top
2*beam words.
Length penalty is given by = (5+len(decode)/6) ^ -\alpha. Pls refer to
https://arxiv.org/abs/1609.08144.
Args:
i: loop index
alive_seq: Topk sequences decoded so far [batch, beam, length]
alive_log_probs: probabilities of these sequences. [batch, beam]
states: optional list of mtf.Tensor
Returns:
Tuple of
(Topk sequences extended by the next word,
The log probs of these sequences,
The scores with length penalty of these sequences,
Flags indicating which of these sequences have finished decoding,
list of transformed decoding states)
"""
logits, new_states = logits_fn(i, alive_seq, states)
batch_dim, beam_dim, vocab_dim = logits.shape.dims
# Convert logits to normalized log probs
candidate_log_probs = mtf.log_softmax(logits, vocab_dim)
# Multiply the probabilities by the current probabilities of the beam.
# (batch_size, beam_size, vocab_size) + (batch_size, beam_size, 1)
log_probs = candidate_log_probs + alive_log_probs
length_penalty = mtf.pow(((5. + mtf.cast(i + 1, logits.dtype)) / 6.),
alpha)
# scores have shape [batch, beam, vocab]
curr_scores = log_probs / length_penalty
# We find the top 2k sequences to make sure we get k alive sequences.
#
# TODO(noam): This is inefficient. We should separately compute the k
# finished sequences (previously alive sequences + EOS), and the top k new
# alive sequences.
double_beam = mtf.Dimension("double_beam", beam_dim.size * 2)
if use_tpu and layout is not None and mesh_shape is not None:
# Do some partial top-k-ing first locally to avoid communication.
# We reshape the logits from:
# [batch, beam, vocab] to
# [batch, beam, major_vocab, minor_vocab]
# We first reduce (locally) across the minor_vocab dimension. This makes
# the thing we need to broadcast smaller.
# This also enables our shortcut of only picking the top num_prefilter
# sequences per beam per major_vocab in the first pass.
major_vocab_size = mtf.tensor_dim_to_mesh_dim_size(
layout, mesh_shape, vocab_dim)
major_vocab = mtf.Dimension(vocab_dim.name, major_vocab_size)
minor_vocab = mtf.Dimension("minor_vocab",
vocab_dim.size // major_vocab_size)
curr_scores = mtf.reshape(
curr_scores, [batch_dim, beam_dim, major_vocab, minor_vocab])
prefilter = mtf.Dimension("prefilter", num_prefilter
or double_beam.size)
# shape = [batch_dim, beam_dim, major_vocab, prefilter]
top_scores, top_minor_vocab_ids = mtf.top_k(
curr_scores, reduced_dim=minor_vocab, k_dim=prefilter)
combined = mtf.Dimension(
"combined", beam_dim.size * major_vocab.size * prefilter.size)
top_scores = mtf.reshape(top_scores, [batch_dim, combined])
top_minor_vocab_ids = mtf.reshape(top_minor_vocab_ids,
[batch_dim, combined])
# shpae = [batch_dim, double_beam]
# ids are indices representing (beam, major_vocab, prefilter)
top_scores, top_combined_ids = mtf.top_k(top_scores,
reduced_dim=combined,
k_dim=double_beam)
top_minor_vocab_ids = mtf.gather(
top_minor_vocab_ids,
top_combined_ids,
combined,
output_shape=[batch_dim, double_beam])
top_beam_index = top_combined_ids // (major_vocab.size *
prefilter.size)
top_combined_ids -= top_beam_index * (major_vocab.size *
prefilter.size)
top_major_vocab_ids = top_combined_ids // prefilter.size
top_combined_ids -= top_major_vocab_ids * prefilter.size
top_ids = top_major_vocab_ids * minor_vocab.size + top_minor_vocab_ids
else:
beam_and_vocab_dim = mtf.Dimension("beam_and_vocab",
beam_dim.size * vocab_dim.size)
flat_shape = mtf.Shape([batch_dim, beam_and_vocab_dim])
# Flatten out (beam_size, vocab_size) probs into a list of possibilities
flat_curr_scores = mtf.reshape(curr_scores,
flat_shape,
name="flatten_scores")
top_scores, top_ids = mtf.top_k(flat_curr_scores,
reduced_dim=beam_and_vocab_dim,
k_dim=double_beam)
# Work out what beam the top probs are in.
top_beam_index = top_ids // vocab_dim.size
top_ids %= vocab_dim.size # Unflatten the ids
# Recovering the log probs because we will need to send them back
top_log_probs = top_scores * length_penalty
selector = mtf.one_hot(top_beam_index, beam_dim, dtype=tf.float32)
def my_gather(tensor):
return mtf.gather(tensor,
top_beam_index,
beam_dim,
output_shape=mtf.Shape([
double_beam if d == beam_dim else d
for d in tensor.shape.dims
]))
# Gather up the most probable 2*beams both for the ids and finished_in_alive
# bools
top_seq = my_gather(alive_seq)
# Append the most probable alive
top_seq += top_ids * mtf.one_hot(i, length_dim, dtype=tf.int32)
top_finished = mtf.equal(top_ids, eos_id)
return (top_seq, top_log_probs, top_scores, top_finished, new_states,
selector)
def inner_loop(i, alive_seq, alive_log_probs, finished_seq,
finished_scores, finished_flags, *states):
"""Inner beam search loop.
There are three groups of tensors, alive, finished, and topk.
The alive group contains information about the current alive sequences
The topk group contains information about alive + topk current decoded words
the finished group contains information about finished sentences, that is,
the ones that have decoded to <EOS>. These are what we return.
The general beam search algorithm is as follows:
While we haven't terminated (pls look at termination condition)
1. Grow the current alive to get beam*2 topk sequences
2. Among the topk, keep the top beam_size ones that haven't reached EOS
into alive
3. Among the topk, keep the top beam_size ones have reached EOS into
finished
Repeat
To make things simple with using fixed size tensors, we will end
up inserting unfinished sequences into finished in the beginning. To stop
that we add -ve INF to the score of the unfinished sequence so that when a
true finished sequence does appear, it will have a higher score than all the
unfinished ones.
Args:
i: loop index
alive_seq: Topk sequences decoded so far [batch_size, beam_size, i+1]
alive_log_probs: probabilities of the beams. [batch_size, beam_size]
finished_seq: Current finished sequences.
[batch_size, beam_size, i+1]
finished_scores: scores for each of these sequences.
[batch_size, beam_size]
finished_flags: finished bools for each of these sequences.
[batch_size, beam_size]
*states: mtf Tensors
Returns:
Tuple of
(Incremented loop index
New alive sequences,
Log probs of the alive sequences,
New finished sequences,
Scores of the new finished sequences,
Flags indicating which sequence in finished as reached EOS,
dict of final decoding states)
"""
states = [
mtf.replace_dimensions(state, batch_and_beam_dim,
[batch_dim, beam_dim]) for state in states
]
# Each inner loop, we carry out three steps:
# 1. Get the current topk items.
# 2. Extract the ones that have finished and haven't finished
# 3. Recompute the contents of finished based on scores.
(top2k_seq, top2k_log_probs, top2k_scores, top2k_finished, new_states,
first_selector) = grow_topk(i, alive_seq, alive_log_probs, states)
with tf.variable_scope("grow_alive"):
alive_seq, alive_log_probs, _, second_selector = grow_alive(
top2k_seq, top2k_scores, top2k_log_probs, top2k_finished)
with tf.variable_scope("grow_finished"):
finished_seq, finished_scores, finished_flags, _ = grow_finished(
finished_seq, finished_scores, finished_flags, top2k_seq,
top2k_scores, top2k_finished)
old_beam_dim = mtf.Dimension("old_beam", beam_dim.size)
selector = mtf.einsum([
mtf.rename_dimension(first_selector, beam_dim.name,
old_beam_dim.name), second_selector
],
output_shape=[batch_dim, old_beam_dim, beam_dim])
gathered_states = []
if use_tpu and layout is not None and mesh_shape is not None:
# This hack combines the beam dimension with some of the batch dimension.
# It makes gathering faster on TPU.
#
# Instead of multiplying by a [beam, beam] selector matrix, we instead
# multiply by a [minor_batch*beam, minor_batch*beam] selector matrix.
# This is theoretically more FLOPs, but it brings the matrix size closer
# to the magic optimal value of 128.
#
# TODO(noam): file a bug with the XLA team to do this automatically
major_batch_size = mtf.tensor_dim_to_mesh_dim_size(
layout, mesh_shape, batch_dim)
major_batch = mtf.Dimension(batch_dim.name, major_batch_size)
minor_batch = mtf.Dimension("minor_batch",
batch_dim.size // major_batch.size)
old_minor_batch = mtf.Dimension("old_minor_batch",
minor_batch.size)
old_combined = mtf.Dimension("old_combined",
minor_batch.size * beam_dim.size)
combined = mtf.Dimension("new_combined", old_combined.size)
same_minor_batch = mtf.to_float(
mtf.equal(mtf.range(mesh, old_minor_batch, tf.float32),
mtf.range(mesh, minor_batch, tf.float32)))
selector = mtf.reshape(
selector, [major_batch, minor_batch, old_beam_dim, beam_dim])
selector = mtf.einsum([selector, same_minor_batch],
output_shape=[
major_batch, old_minor_batch,
old_beam_dim, minor_batch, beam_dim
],
reduced_dims=[])
selector = mtf.reshape(selector,
[major_batch, old_combined, combined])
for state in new_states:
s = mtf.replace_dimensions(state, [batch_dim, beam_dim],
[major_batch, old_combined])
s = mtf.einsum([s, mtf.cast(selector, state.dtype)],
reduced_dims=[old_combined],
output_shape=mtf.replace_dimensions(
state.shape, [batch_dim, beam_dim],
[major_batch, combined]))
gathered_states.append(
mtf.replace_dimensions(s, [major_batch, combined],
batch_and_beam_dim))
else:
for state in new_states:
state = mtf.einsum([
mtf.rename_dimension(state, beam_dim.name,
old_beam_dim.name),
mtf.cast(selector, state.dtype)
],
reduced_dims=[old_beam_dim],
output_shape=state.shape)
state = mtf.replace_dimensions(state, [batch_dim, beam_dim],
batch_and_beam_dim)
gathered_states.append(state)
return (i + 1, alive_seq, alive_log_probs, finished_seq,
finished_scores, finished_flags) + tuple(gathered_states)
def _is_finished(i, unused_alive_seq, alive_log_probs, unused_finished_seq,
finished_scores, finished_in_finished, *unused_states):
"""Checking termination condition.
We terminate when we decoded up to decode_length or the lowest scoring item
in finished has a greater score that the highest prob item in alive divided
by the max length penalty
Args:
i: loop index
alive_log_probs: probabilities of the beams. [batch_size, beam_size]
finished_scores: scores for each of these sequences.
[batch_size, beam_size]
finished_in_finished: finished bools for each of these sequences.
[batch_size, beam_size]
Returns:
Bool.
"""
# TODO(noam): support a different decode length...
# decode_length = mtf.constant(mesh, length_dim.size, dtype=tf.int32)
# del alive_log_probs, finished_scores, finished_in_finished
# return mtf.less(i, length_dim.size)
if not stop_early:
return mtf.less(i, decode_length)
max_length_penalty = mtf.pow(
((5. + mtf.cast(decode_length, finished_scores.dtype)) / 6.),
alpha)
# The best possible score of the most likely alive sequence.
lower_bound_alive_scores = mtf.gather(
alive_log_probs, mtf.constant(mesh, 0, dtype=tf.int32),
beam_dim) / max_length_penalty
# Now to compute the lowest score of a finished sequence in finished
# If the sequence isn't finished, we multiply it's score by 0. since
# scores are all -ve, taking the min will give us the score of the lowest
# finished item.
lowest_score_of_finished_in_finished = mtf.reduce_min(
finished_scores *
mtf.cast(finished_in_finished, finished_scores.dtype),
reduced_dim=beam_dim)
# If none of the sequences have finished, then the min will be 0 and
# we have to replace it by -ve INF if it is. The score of any seq in alive
# will be much higher than -ve INF and the termination condition will not
# be met.
lowest_score_of_finished_in_finished += ((1. - mtf.cast(
mtf.reduce_any(finished_in_finished, reduced_dim=beam_dim),
finished_scores.dtype)) * -INF)
bound_is_met = mtf.reduce_all(
mtf.greater(lowest_score_of_finished_in_finished,
lower_bound_alive_scores))
return mtf.logical_and(mtf.less(i, decode_length),
mtf.logical_not(bound_is_met))
initial_step_num = mtf.constant(mesh, 0, dtype=tf.int32)
states = [
mtf.replace_dimensions(state, [batch_dim, beam_dim],
batch_and_beam_dim) for state in states
]
while_loop_inputs = [
initial_step_num, alive_seq, alive_log_probs, finished_seq,
finished_scores, finished_flags
] + states
(_, alive_seq, alive_log_probs, finished_seq, finished_scores,
finished_flags) = mtf.while_loop(_is_finished,
inner_loop,
while_loop_inputs,
num_loop_vars=None if use_tpu else 6)[:6]
# Accounting for corner case: It's possible that no sequence in alive for a
# particular batch item ever reached EOS. In that case, we should just copy
# the contents of alive for that batch item. tf.reduce_any(finished_flags, 1)
# if 0, means that no sequence for that batch index had reached EOS. We need
# to do the same for the scores as well.
finished_seq = mtf.where(
mtf.reduce_any(finished_flags, reduced_dim=beam_dim), finished_seq,
alive_seq)
finished_scores = mtf.where(
mtf.reduce_any(finished_flags, reduced_dim=beam_dim), finished_scores,
alive_log_probs)
return finished_seq, finished_scores
def greedy_decode(logits_fn,
initial_ids,
temperature=0.0,
initial_states=None,
eos_id=EOS_ID,
forced_ids=None,
use_tpu=True):
"""Greedy decoding.
Args:
logits_fn: Interface to the model, to provide logits.
Shoud take:
step_num - mtf Scalar
ids - mtf Tensor with shape [..., length]
states - list of mtf.Tensor
Should return:
logits - [batch, vocab_size]
new_states - list of mtf.Tensor
initial_ids: mtf.Tensor with shape [..., length], containing zeros.
temperature: a float between 0.0 (argmax) and 1.0 (random)
initial_states: list of mtf.Tensor
eos_id: ID for end of sentence.
forced_ids: optional mtf.Tensor with shape [..., length]
use_tpu: a boolean
Returns:
Tensor with shape [..., length]
"""
length_dim = initial_ids.shape.dims[-1]
mesh = initial_ids.mesh
num_steps = mtf.constant(mesh, length_dim.size, dtype=tf.int32)
def cond_fn(step_num, prev_ids, *unused_states):
"""Should we run another loop iteration."""
overflow = mtf.equal(step_num, num_steps)
has_eos = mtf.reduce_any(mtf.equal(prev_ids, eos_id),
reduced_dim=length_dim)
all_has_eos = mtf.reduce_all(has_eos)
return mtf.logical_not(mtf.logical_or(overflow, all_has_eos))
def body_fn(step_num, ids, *states):
"""Body function for greedy decoding.
Args:
step_num: a mtf.Tensor
ids: a mtf.Tensor
*states: additional mtf.Tensors
Returns:
new_step_num, new_ids, *new_states
"""
logits, new_states = logits_fn(step_num, ids, states)
vocab_dim = logits.shape.dims[-1]
new_ids = mtf.sample_with_temperature(logits, vocab_dim, temperature)
if forced_ids is not None:
# force the new ids to equal the partial targets where specified
# (positions where partial_targets contain nonzero values)
forced = mtf.gather(forced_ids, step_num, length_dim)
new_ids = forced + new_ids * mtf.to_int32(mtf.equal(forced, 0))
ids += new_ids * mtf.one_hot(step_num, length_dim, dtype=tf.int32)
new_step_num = step_num + 1
return [new_step_num, ids] + new_states
initial_step_num = mtf.constant(mesh, 0, dtype=tf.int32)
while_loop_inputs = [initial_step_num, initial_ids] + initial_states
final_step_num, mtf_samples = mtf.while_loop(
cond_fn,
body_fn,
while_loop_inputs,
num_loop_vars=None if use_tpu else 2)[:2]
mtf_samples = mtf.Print(mtf_samples, [final_step_num], "output_length")
return mtf_samples