def beam_search(
symbols_to_logits_fn,
initial_ids,
beam_size,
decode_length,
vocab_size,
alpha,
eos_id,
states=None,
stop_early=True,
):
r"""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.
Variables used within this function follow the naming pattern:
`(alive|finished)_topk_(seq,scores)`.
Variables marked `alive` represent the new beam sequences that will be
processed in the next step. Variables marked `finished` represent
the completed beam sequences, which may be padded with 0 if no beams
finished.
Variables marked `seq` store the full beam sequence for the time step.
Variables 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.
Args:
symbols_to_logits_fn: Interface to the model, to provide logits.
Should take `[batch_size, decoded_ids]` and return
`[batch_size, vocab_size]`.
initial_ids: LongTensor of shape `[batch_size]`. IDs to start off the
decoding, this will be the first thing handed to
:attr:`symbols_to_logits_fn` (after expanding to beam size).
beam_size: Size of the beam.
decode_length: Number of steps to decode for.
vocab_size: Size of the vocab, must equal the size of the logits
returned by :attr:`symbols_to_logits_fn`.
alpha: alpha for length penalty.
eos_id: ID for end of sentence.
states: (possibly nested structure of) decoding states.
stop_early: a boolean - stop once best sequence is provably
determined.
Returns:
Tuple of
- decoded beams (shape: `[batch_size, beam_size, decode_length]`)
- decoding probabilities (shape: `[batch_size, beam_size]`)
"""
batch_size = initial_ids.size()[0]
# Assume initial_ids are prob 1.0
initial_log_probs = torch.Tensor([[0.0] + [-float("inf")] * (beam_size - 1)
]) # [1, beam_size]
initial_log_probs = initial_log_probs.to(device=initial_ids.device)
# Expand to beam_size (batch_size, beam_size)
alive_log_probs = initial_log_probs.repeat((batch_size, 1))
# Expand each batch and state to beam_size
alive_seq = _expand_to_beam_size(initial_ids, beam_size)
alive_seq = torch.unsqueeze(alive_seq, dim=2)
# (batch_size, beam_size, 1)
if states is not None:
states = map_structure(
lambda state: _expand_to_beam_size(state, beam_size), states)
# 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 = torch.zeros(alive_seq.size(), dtype=torch.long)
# Setting the scores of the initial to negative infinity.
finished_scores = torch.full((batch_size, beam_size), -INF)
finished_flags = torch.zeros((batch_size, beam_size), dtype=torch_bool)
finished_seq = finished_seq.to(device=initial_ids.device)
finished_scores = finished_scores.to(device=initial_ids.device)
finished_flags = finished_flags.to(device=initial_ids.device)
def grow_finished(
finished_seq: torch.LongTensor,
finished_scores: torch.Tensor,
finished_flags: torch.ByteTensor,
curr_seq: torch.LongTensor,
curr_scores: torch.Tensor,
curr_finished: torch.ByteTensor,
) -> Tuple[torch.LongTensor, torch.Tensor, torch.ByteTensor]:
r"""Given sequences and scores, will gather the top-k (`k = beam`) size
sequences.
Args:
finished_seq: Finished sequences.
Shape: `[batch_size, beam_size, current_decoded_length]`.
finished_scores: Scores for each finished sequences.
Shape: `[batch_size, beam_size]`.
finished_flags: Finished flags for each of these sequences.
Shape: `[batch_size, beam_size]`
curr_seq: Top-k sequences that has been grown by one
position.
Shape: `[batch_size, beam_size, current_decoded_length]`.
curr_scores: Scores for each of the top-k sequences.
Shape: `[batch_size, beam_size]`.
curr_finished: Finished flags for each of the top-k sequences.
Shape: `[batch_size, beam_size]`.
Returns:
Tuple of
- Top-k sequences based on scores.
- Log-probabilities of these sequences.
- Finished flags of these sequences.
"""
# First append a column of 0'ids to finished to make the same
# length with finished scores
_appended = torch.zeros(batch_size, beam_size, 1, dtype=torch.long)
_appended = _appended.to(device=finished_seq.device)
finished_seq = torch.cat([finished_seq, _appended], dim=2)
# Set the scores of the unfinished seq in curr_seq to large
# negative values
curr_scores = curr_scores + (1.0 - curr_finished.float()) * -INF
# concatenating the sequences and scores along beam axis
curr_finished_seq = torch.cat([finished_seq, curr_seq], dim=1)
curr_finished_scores = torch.cat([finished_scores, curr_scores], dim=1)
curr_finished_flags = torch.cat([finished_flags, curr_finished], dim=1)
next_seq, next_scores, next_flags, _ = compute_topk_scores_and_seq(
curr_finished_seq,
curr_finished_scores,
curr_finished_scores,
curr_finished_flags,
beam_size,
batch_size,
)
return next_seq, next_scores, next_flags
def grow_alive(
curr_seq: torch.LongTensor, curr_scores: torch.Tensor,
curr_log_probs: torch.Tensor, curr_finished: torch.ByteTensor,
states: Optional[State]
) -> Tuple[torch.LongTensor, torch.Tensor, torch.ByteTensor,
Optional[State]]:
r"""Given sequences and scores, will gather the top k=beam size
sequences.
Args:
curr_seq: Current top-k sequences that has been grown by one
position.
Shape: `[batch_size, beam_size, i + 1]`.
curr_scores: Scores for each of these sequences.
Shape: `[batch_size, beam_size]`.
curr_log_probs: Log-probabilities for each of these sequences.
Shape: `[batch_size, beam_size]`.
curr_finished: Finished flags for each of these sequences.
Shape: `[batch_size, beam_size]`.
states: (possibly nested structure of) decoding states.
:returns: Tuple of:
- Top-k sequences based on scores.
- Log-probabilities of these sequences.
- Finished flags of these sequences.
- Decoding states for these sequences.
"""
# Set the scores of the finished seq in curr_seq to large negative
# values
curr_scores = curr_scores + curr_finished.float() * -INF
return compute_topk_scores_and_seq(
curr_seq,
curr_scores,
curr_log_probs,
curr_finished,
beam_size,
batch_size,
states,
)
def grow_topk(
i: int, alive_seq: torch.LongTensor, alive_log_probs: torch.Tensor,
states: Optional[State]
) -> Tuple[torch.LongTensor, torch.Tensor, torch.Tensor, torch.ByteTensor,
Optional[State]]:
r"""Inner beam search loop.
This function takes the current alive sequences, and grows them to
top-k 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 :math:`(5+len(decode)/6) ^ -\alpha`.
Please refer to https://arxiv.org/abs/1609.08144.
Args:
i: loop index
alive_seq: Top-k sequences decoded so far.
Shape: `[batch_size, beam_size, i + 1]`.
alive_log_probs: Log-probabilities of these sequences.
Shape: `[batch_size, beam_size]`
states: (possibly nested structure of) decoding states.
:returns: Tuple of:
- Top-k sequences extended by the next word.
- Log-probabilities of these sequences,
- The scores with length penalty of these sequences,
- Flags indicating which of these sequences have finished
decoding.
- Transformed decoding states with same structure as :attr:`state`.
"""
# Get the logits for all the possible next symbols
flat_ids = alive_seq.view(batch_size * beam_size, -1)
# (batch_size * beam_size, decoded_length)
if states is not None:
flat_states = map_structure(_merge_beam_dim, states)
flat_logits, flat_states = symbols_to_logits_fn(
flat_ids, flat_states)
states = map_structure(
lambda t: _unmerge_beam_dim(t, batch_size, beam_size),
flat_states,
)
else:
flat_logits = symbols_to_logits_fn(flat_ids)
logits = flat_logits.view(batch_size, beam_size, -1)
# Convert logits to normalized log-probs
candidate_log_probs = log_prob_from_logits(logits)
# 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.unsqueeze(dim=2)
length_penalty = ((5.0 + float(i + 1)) / 6.0)**alpha
curr_scores = log_probs / length_penalty
# Flatten out (beam_size, vocab_size) probs in to a list of
# possibilities
flat_curr_scores = curr_scores.view(-1, beam_size * vocab_size)
topk_scores, topk_ids = torch.topk(flat_curr_scores, k=beam_size * 2)
# Recovering the log-probs because we will need to send them back
topk_log_probs = topk_scores * length_penalty
# Work out what beam the top probabilities are in.
topk_beam_index = topk_ids // vocab_size
topk_ids %= vocab_size # Un-flatten the ids
# The next three steps are to create coordinates for torch.gather_nd
# to pull out the correct sequences from id's that we need to grow.
# We will also use the coordinates to gather the booleans of the
# beam items that survived.
batch_pos = compute_batch_indices(batch_size, beam_size * 2)
batch_pos = batch_pos.to(device=topk_beam_index.device)
# top beams will give us the actual coordinates to do the gather.
# stacking will create a tensor of dimension batch * beam * 2,
# where the last dimension contains the i,j gathering coordinates.
topk_coordinates = torch.stack([batch_pos, topk_beam_index], dim=2)
# [batch_size, beam_size, 2]
topk_seq = gather_nd(alive_seq, topk_coordinates)
if states is not None:
states = map_structure(
lambda state: gather_nd(state, topk_coordinates), states)
# Append the most probable alive
topk_seq = torch.cat([topk_seq, topk_ids.unsqueeze(dim=2)], dim=2)
topk_finished = topk_ids == eos_id
return topk_seq, topk_log_probs, topk_scores, topk_finished, states
def inner_loop(
i: int,
alive_seq: torch.LongTensor,
alive_log_probs: torch.Tensor,
finished_seq: torch.LongTensor,
finished_scores: torch.Tensor,
finished_flags: torch.ByteTensor,
states: Optional[State],
) -> Tuple[int, torch.LongTensor, torch.Tensor, torch.LongTensor,
torch.Tensor, torch.ByteTensor, Optional[State]]:
r"""Inner beam search loop.
There are three groups of tensors: `alive`, `finished`, and `top-k`.
- The `alive` group contains information about the current alive
sequences.
- The `top-k` group contains information about `alive + top_k`
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 not terminated (please refer to termination condition):
1. Grow the current `alive` to get `beam * 2` top-k sequences.
2. Among the `top-k`, move the top `beam_size` ones that haven't
reached `EOS` into `alive`.
3. Among the `top-k`, move 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 prevent that we add `-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
Shape: `[batch_size, beam_size, i + 1]`.
alive_log_probs: Log-probabilities of the beams.
Shape: `[batch_size, beam_size]`
finished_seq: Current finished sequences.
Shape: `[batch_size, beam_size, i+1]`.
finished_scores: Scores for each of these sequences.
Shape: `[batch_size, beam_size]`.
finished_flags: Finished flags for each of these sequences.
Shape: `[batch_size, beam_size]`
states: (possibly nested structure of) decoding states.
:returns: Tuple of:
- Incremented loop index.
- New `alive` sequences.
- Log-probabilities of the `alive` sequences.
- New `finished` sequences.
- Scores of the `finished` sequences.
- Flags indicating which sequences in `finished` has reached `EOS`.
- Final decoding states with same structure as :attr:`state`.
"""
# Each inner loop, we carry out three steps:
# 1. Get the current top-k items.
# 2. Extract the ones that have finished and haven't finished
# 3. Recompute the contents of finished based on scores.
topk_seq, topk_log_probs, topk_scores, topk_finished, \
states = grow_topk(i, alive_seq, alive_log_probs, states)
alive_seq, alive_log_probs, _, states = grow_alive(
topk_seq, topk_scores, topk_log_probs, topk_finished, states)
finished_seq, finished_scores, finished_flags = grow_finished(
finished_seq,
finished_scores,
finished_flags,
topk_seq,
topk_scores,
topk_finished,
)
return (
i + 1,
alive_seq,
alive_log_probs,
finished_seq,
finished_scores,
finished_flags,
states,
)
def _is_finished(i: int, alive_log_probs: torch.Tensor,
finished_scores: torch.Tensor) -> bool:
r"""Check 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 probable
item in alive divided by the max length penalty.
Args:
i: Loop index
alive_log_probs: Log-probabilities of the beams.
Shape: `[batch_size, beam_size]`.
finished_scores: Scores for each of these sequences.
Shape: `[batch_size, beam_size]`.
Returns:
Bool.
"""
max_length_penalty = ((5.0 + float(decode_length)) / 6.0)**alpha
# The best possible score of the most likely alive sequence
lower_bound_alive_scores = alive_log_probs[:, 0] / max_length_penalty
if not stop_early:
# by considering the min score (in the top N beams) we ensure that
# the decoder will keep decoding until there is at least one beam
# (in the top N) that can be improved (w.r.t. the alive beams).
# any unfinished beam will have score -INF - thus the min
# will always be -INF if there is at least one unfinished beam -
# which means the bound_is_met condition cannot be true in this
# case.
lowest_score_of_finished_in_finished = torch.min(finished_scores)
else:
# by taking the max score we only care about the first beam;
# as soon as this first beam cannot be beaten from the alive beams
# the beam decoder can stop.
# similarly to the above, if the top beam is not completed, its
# finished_score is -INF, thus it will not activate the
# bound_is_met condition. (i.e., decoder will keep going on).
# note we need to find the max for every sequence eparately - so,
# we need to keep the batch dimension (see axis=1)
lowest_score_of_finished_in_finished, _ = torch.max(
finished_scores, dim=1)
bound_is_met = ((lowest_score_of_finished_in_finished >
lower_bound_alive_scores).all().item())
ret = (i < decode_length) & (~bound_is_met)
return ret
step = 0
while _is_finished(step, alive_log_probs, finished_scores):
step, alive_seq, alive_log_probs, finished_seq, finished_scores, \
finished_flags, states = inner_loop(
step,
alive_seq,
alive_log_probs,
finished_seq,
finished_scores,
finished_flags,
states,
)
# 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.
ret_seq, ret_scores = [], []
for idx, flag_per_instance in enumerate(
finished_flags.any(dim=1).tolist()):
if flag_per_instance:
ret_seq.append(finished_seq[idx])
ret_scores.append(finished_scores[idx])
else:
ret_seq.append(alive_seq[idx])
ret_scores.append(alive_log_probs[idx])
ret_seq = torch.stack(ret_seq, dim=0)
ret_scores = torch.stack(ret_scores, dim=0)
return ret_seq, ret_scores
def grow_topk(
i: int, alive_seq: torch.LongTensor, alive_log_probs: torch.Tensor,
states: Optional[State]
) -> Tuple[torch.LongTensor, torch.Tensor, torch.Tensor, torch.ByteTensor,
Optional[State]]:
r"""Inner beam search loop.
This function takes the current alive sequences, and grows them to
top-k 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 :math:`(5+len(decode)/6) ^ -\alpha`.
Please refer to https://arxiv.org/abs/1609.08144.
Args:
i: loop index
alive_seq: Top-k sequences decoded so far.
Shape: `[batch_size, beam_size, i + 1]`.
alive_log_probs: Log-probabilities of these sequences.
Shape: `[batch_size, beam_size]`
states: (possibly nested structure of) decoding states.
:returns: Tuple of:
- Top-k sequences extended by the next word.
- Log-probabilities of these sequences,
- The scores with length penalty of these sequences,
- Flags indicating which of these sequences have finished
decoding.
- Transformed decoding states with same structure as :attr:`state`.
"""
# Get the logits for all the possible next symbols
flat_ids = alive_seq.view(batch_size * beam_size, -1)
# (batch_size * beam_size, decoded_length)
if states is not None:
flat_states = map_structure(_merge_beam_dim, states)
flat_logits, flat_states = symbols_to_logits_fn(
flat_ids, flat_states)
states = map_structure(
lambda t: _unmerge_beam_dim(t, batch_size, beam_size),
flat_states,
)
else:
flat_logits = symbols_to_logits_fn(flat_ids)
logits = flat_logits.view(batch_size, beam_size, -1)
# Convert logits to normalized log-probs
candidate_log_probs = log_prob_from_logits(logits)
# 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.unsqueeze(dim=2)
length_penalty = ((5.0 + float(i + 1)) / 6.0)**alpha
curr_scores = log_probs / length_penalty
# Flatten out (beam_size, vocab_size) probs in to a list of
# possibilities
flat_curr_scores = curr_scores.view(-1, beam_size * vocab_size)
topk_scores, topk_ids = torch.topk(flat_curr_scores, k=beam_size * 2)
# Recovering the log-probs because we will need to send them back
topk_log_probs = topk_scores * length_penalty
# Work out what beam the top probabilities are in.
topk_beam_index = topk_ids // vocab_size
topk_ids %= vocab_size # Un-flatten the ids
# The next three steps are to create coordinates for torch.gather_nd
# to pull out the correct sequences from id's that we need to grow.
# We will also use the coordinates to gather the booleans of the
# beam items that survived.
batch_pos = compute_batch_indices(batch_size, beam_size * 2)
batch_pos = batch_pos.to(device=topk_beam_index.device)
# top beams will give us the actual coordinates to do the gather.
# stacking will create a tensor of dimension batch * beam * 2,
# where the last dimension contains the i,j gathering coordinates.
topk_coordinates = torch.stack([batch_pos, topk_beam_index], dim=2)
# [batch_size, beam_size, 2]
topk_seq = gather_nd(alive_seq, topk_coordinates)
if states is not None:
states = map_structure(
lambda state: gather_nd(state, topk_coordinates), states)
# Append the most probable alive
topk_seq = torch.cat([topk_seq, topk_ids.unsqueeze(dim=2)], dim=2)
topk_finished = topk_ids == eos_id
return topk_seq, topk_log_probs, topk_scores, topk_finished, states
def compute_topk_scores_and_seq(
sequences: torch.LongTensor,
scores: torch.Tensor,
scores_to_gather: torch.Tensor,
flags: torch.ByteTensor,
beam_size: int,
batch_size: int,
states_to_gather: Optional[State] = None,
) -> Tuple[torch.LongTensor, torch.Tensor, torch.ByteTensor, Optional[State]]:
r"""Given sequences and scores, will gather the top-k (`k = beam`) size
sequences.
This function is used to grow alive, and finished. It takes sequences,
scores, and flags, and returns the top k from sequence
:attr:`scores_to_gather`, and flags based on the values in scores.
Args:
sequences: Tensor of sequences that we need to gather from.
Shape: `[batch_size, beam_size, seq_length]`.
scores: Tensor of scores for each sequence in sequences. We will use
these to compute the top-k. Shape: `[batch_size, beam_size]`.
scores_to_gather: Tensor of scores for each sequence in sequences.
Shape: `[batch_size, beam_size]`.
We will return the gathered scores from here.
Scores to gather is different from scores because for
grow_alive, we will need to return log-probabilities, while for
grow_finished, we will need to return the length penalized
scores.
flags: Tensor of booleans for sequences that say whether a sequence
has reached `EOS`.
beam_size: int
batch_size: int
states_to_gather: (possibly nested structure of) decoding states.
:returns: Tuple of:
- `topk_seq`: `[batch_size, beam_size, decode_length]`.
- `topk_gathered_scores`: `[batch_size, beam_size]`.
- `topk_finished_flags`: `[batch_size, beam_size]`.
"""
# by default top-k is for the last dimension
_, topk_indexes = torch.topk(scores, k=beam_size)
# The next three steps are to create coordinates for torch.gather_nd to
# pull out the top-k sequences from sequences based on scores.
# batch pos is a tensor like [[0,0,0,0,],[1,1,1,1],..]. It says which
# batch the beam item is in. This will create the i of the i,j
# coordinate needed for the gather
batch_pos = compute_batch_indices(batch_size, beam_size)
batch_pos = batch_pos.to(device=topk_indexes.device)
# top coordinates will give us the actual coordinates to do the gather.
# stacking will create a tensor of dimension batch * beam * 2, where
# the last dimension contains the i,j gathering coordinates.
top_coordinates = torch.stack([batch_pos, topk_indexes], dim=2)
# Gather up the highest scoring sequences.
topk_seq = gather_nd(sequences, top_coordinates)
topk_flags = gather_nd(flags, top_coordinates)
topk_gathered_scores = gather_nd(scores_to_gather, top_coordinates)
if states_to_gather is not None:
topk_gathered_states = map_structure(
lambda state: gather_nd(state, top_coordinates), states_to_gather)
else:
topk_gathered_states = states_to_gather
return topk_seq, topk_gathered_scores, topk_flags, topk_gathered_states