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 attention_mask_ignore_padding(inputs, dtype=tf.float32):
"""Bias for encoder-decoder attention.
Args:
inputs: a mtf.Tensor with shape [..., length_dim]
dtype: a tf.dtype
Returns:
a mtf.Tensor with shape [..., memory_length_dim]
"""
inputs = rename_length_to_memory_length(inputs)
return mtf.cast(mtf.equal(inputs, 0), dtype) * -1e9
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
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.to_float(i + 1)) / 6.), alpha)
curr_scores = log_probs / length_penalty
# scores have shape [batch, beam, vocab]
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])
double_beam = mtf.Dimension("double_beam", beam_dim.size * 2)
# Flatten out (beam_size, vocab_size) probs in to a list of possibilities
flat_curr_scores = mtf.reshape(curr_scores, flat_shape)
top_ids, top_scores = mtf.top_k(flat_curr_scores,
reduced_dim=beam_and_vocab_dim,
new_dim=double_beam)
# Recovering the log probs because we will need to send them back
top_log_probs = top_scores * length_penalty
# 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
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)
if states:
states = [my_gather(state) for state in new_states]
# 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, states
def _top_2_gating(inputs,
outer_expert_dims,
experts_dim,
expert_capacity_dim,
hparams,
train,
importance=None):
"""Compute gating for mixture-of-experts in TensorFlow.
Note: until the algorithm and inferface solidify, we pass in a hyperparameters
dictionary in order not to complicate the interface in mtf_transformer.py .
Once this code moves out of "research", we should pass the hyperparameters
separately.
Hyperparameters used:
hparams.moe_use_second_place_loss: a boolean
hparams.moe_second_policy_train: a string
hparams.moe_second_policy_eval: a string
hparams.moe_second_threshold: a float
The returned forward assignment is a tensor used to map (via einsum) from the
inputs to the expert_inputs. Likewise, the returned combine_tensor is
used to map (via einsum) from the expert outputs to the outputs. Both the
forward and backward assignments are mostly zeros. The shapes of the tensors
are as follows.
inputs: [<batch_dims>, group_size_dim, input_dim]
importance: [<batch_dims>, group_size_dim]
dispatch_tensor:
[<batch_dims>, group_size_dim, experts_dim, expert_capacity_dim]
expert_inputs:
[<batch_dims>, experts_dim, expert_capacity_dim, input_dim]
expert_outputs: [<batch_dims>, experts_dim, expert_capacity_dim, output_dim]
combine_tensor:
[<batch_dims>, group_size_dim, experts_dim, expert_capacity_dim]
outputs: [<batch_dims>, group_size_dim, output_dim]
"importance" is an optional tensor with one floating-point value for each
input vector. If the importance of an input is 1.0, then we send it to
up to 2 experts. If 0.0 < importance < 1.0, then we send it to at most
one expert. If importance == 0.0, then we send it to no experts.
We use "importance" at the second-level gating function of a hierarchical
mixture of experts. Inputs to the first-choice expert-group get importance
1.0. Inputs to the second-choice expert group get importance 0.5.
Inputs that represent padding get importance 0.0.
Args:
inputs: a mtf.Tensor with shape [<batch_dims>, group_size_dim, input_dim]
outer_expert_dims: an optional list of dimensions. This is for the case
where we are at an inner level of a hierarchical MoE.
experts_dim: a Dimension (the number of experts)
expert_capacity_dim: a Dimension (number of examples per group per expert)
hparams: model hyperparameters.
train: a boolean
importance: an optional tensor with shape [<batch_dims>, group_size_dim]
Returns:
dispatch_tensor: a Tensor with shape
[<batch_dims>, group_size_dim, experts_dim, expert_capacity_dim]
combine_tensor: a Tensor with shape
[<batch_dims>, group_size_dim, experts_dim, expert_capacity_dim]
loss: a mtf scalar
Raises:
ValueError: on illegal hyperparameters
"""
group_size_dim, unused_input_dim = inputs.shape.dims[-2:]
raw_gates = mtf.softmax(
mtf_layers.dense(inputs,
experts_dim,
use_bias=False,
expert_dims=outer_expert_dims), experts_dim)
# The internals of this function run in float32.
# bfloat16 seems to reduce quality.
raw_gates = mtf.to_float(raw_gates)
expert_capacity_f = float(expert_capacity_dim.size)
# FIND TOP 2 EXPERTS PER POSITON
# Find the top expert for each position. shape=[batch, group]
index_1, gate_1 = mtf.top_1(raw_gates, experts_dim)
# [batch, group, experts]
mask_1 = mtf.one_hot(index_1, experts_dim, dtype=raw_gates.dtype)
density_1_proxy = raw_gates
if importance is not None:
mask_1 *= mtf.to_float(mtf.equal(importance, 1.0))
gate_1 *= mtf.to_float(mtf.equal(importance, 1.0))
density_1_proxy *= mtf.to_float(mtf.equal(importance, 1.0))
gates_without_top_1 = raw_gates * (1.0 - mask_1)
# [batch, group]
index_2, gate_2 = mtf.top_1(gates_without_top_1, experts_dim)
# [batch, group, experts]
mask_2 = mtf.one_hot(index_2, experts_dim, dtype=raw_gates.dtype)
if importance is not None:
mask_2 *= mtf.to_float(mtf.greater(importance, 0.0))
denom = gate_1 + gate_2 + 1e-9
gate_1 /= denom
gate_2 /= denom
# BALANCING LOSSES
# shape = [batch, experts]
# We want to equalize the fraction of the batch assigned to each expert
density_1 = mtf.reduce_mean(mask_1, reduced_dim=group_size_dim)
# Something continuous that is correlated with what we want to equalize.
density_1_proxy = mtf.reduce_mean(density_1_proxy,
reduced_dim=group_size_dim)
density_1 = mtf.Print(
density_1, [mtf.reduce_mean(density_1, output_shape=[experts_dim])],
"density_1",
summarize=1000)
loss = (mtf.reduce_mean(density_1_proxy * density_1) *
float(experts_dim.size * experts_dim.size))
if hparams.moe_use_second_place_loss:
# Also add a loss to encourage all experts to be used equally also as the
# second-place expert. Experimentally, this seems to be a wash.
# We want to equalize the fraction of the batch assigned to each expert:
density_2 = mtf.reduce_mean(mask_2, reduced_dim=group_size_dim)
# As a proxy for density_2, we renormalize the raw gates after the top one
# has been removed.
normalized = gates_without_top_1 / (mtf.reduce_sum(
gates_without_top_1, reduced_dim=experts_dim) + 1e-9)
density_2_proxy = mtf.reduce_mean(normalized,
reduced_dim=group_size_dim)
loss_2 = (mtf.reduce_mean(density_2_proxy * density_2) *
float(experts_dim.size * experts_dim.size))
loss += loss_2 * 0.5
# Depending on the policy in the hparams, we may drop out some of the
# second-place experts.
policy = (hparams.moe_second_policy_train
if train else hparams.moe_second_policy_eval)
threshold = (hparams.moe_second_threshold_train
if train else hparams.moe_second_threshold_eval)
if policy == "all":
# Use second-place experts for all examples.
pass
elif policy == "none":
# Never use second-place experts for all examples.
mask_2 = mtf.zeros_like(mask_2)
elif policy == "threshold":
# Use second-place experts if gate_2 > threshold.
mask_2 *= mtf.to_float(mtf.greater(gate_2, threshold))
elif policy == "random":
# Use second-place experts with probablity min(1.0, gate_2 / threshold).
mask_2 *= mtf.to_float(
mtf.less(mtf.random_uniform(gate_2.mesh, gate_2.shape),
gate_2 / max(threshold, 1e-9)))
else:
raise ValueError("Unknown policy %s" % policy)
mask_2 = mtf.Print(mask_2,
[mtf.reduce_mean(mask_2, output_shape=[experts_dim])],
"density_2",
summarize=1000)
# COMPUTE ASSIGNMENT TO EXPERTS
# [batch, group, experts]
# This is the position within the expert's mini-batch for this sequence
position_in_expert_1 = mtf.cumsum(mask_1, group_size_dim,
exclusive=True) * mask_1
# Remove the elements that don't fit. [batch, group, experts]
mask_1 *= mtf.to_float(mtf.less(position_in_expert_1, expert_capacity_f))
# [batch, experts]
# How many examples in this sequence go to this expert
mask_1_count = mtf.reduce_sum(mask_1, reduced_dim=group_size_dim)
# [batch, group] - mostly ones, but zeros where something didn't fit
mask_1_flat = mtf.reduce_sum(mask_1, reduced_dim=experts_dim)
# [batch, group]
position_in_expert_1 = mtf.reduce_sum(position_in_expert_1,
reduced_dim=experts_dim)
# Weight assigned to first expert. [batch, group]
gate_1 *= mask_1_flat
# [batch, group, experts]
position_in_expert_2 = (
mtf.cumsum(mask_2, group_size_dim, exclusive=True) + mask_1_count)
position_in_expert_2 *= mask_2
mask_2 *= mtf.to_float(mtf.less(position_in_expert_2, expert_capacity_f))
# mask_2_count = mtf.reduce_sum(mask_2, reduced_dim=experts_dim)
mask_2_flat = mtf.reduce_sum(mask_2, reduced_dim=experts_dim)
gate_2 *= mask_2_flat
position_in_expert_2 = mtf.reduce_sum(position_in_expert_2,
reduced_dim=experts_dim)
# [batch, group, experts, expert_capacity]
combine_tensor = (
gate_1 * mask_1_flat * mtf.one_hot(index_1, experts_dim) *
mtf.one_hot(mtf.to_int32(position_in_expert_1), expert_capacity_dim) +
gate_2 * mask_2_flat * mtf.one_hot(index_2, experts_dim) *
mtf.one_hot(mtf.to_int32(position_in_expert_2), expert_capacity_dim))
combine_tensor = mtf.cast(combine_tensor, inputs.dtype)
loss = mtf.cast(loss, inputs.dtype)
dispatch_tensor = mtf.cast(mtf.cast(combine_tensor, tf.bool),
combine_tensor.dtype)
return dispatch_tensor, combine_tensor, loss