def multihead_self_attention_incremental(query_antecedent,
prev_k,
prev_v,
step_num,
name="multihead_attention"):
"""Incremental self-attention (one decode step).
In order to use only one variable containing the four weight matrices
packed together, we insist that the query and memory antecedents have the
same dimensionality (io_channels) and that the keys and values have the
same dimensionality (kv_channels).
Args:
query_antecedent: a mtf.Tensor with shape [batch..., io_channels]
prev_k: mtf.Tensor with shape [batch..., heads, memory_length, kv_channels]
prev_v: mtf.Tensor with shape [batch..., heads, memory_length, kv_channels]
step_num: mtf Scalar with dtype tf.int32
name: an optional string.
Returns:
y: A mtf.Tensor with shape [batch..., io_channels]
new_k: mtf.Tensor with shape [batch..., heads, memory_length, kv_channels]
new_v: mtf.Tensor with shape [batch..., heads, memory_length, kv_channels]
Raises:
ValueError: if the dimensions do not match.
"""
batch_dims = query_antecedent.shape.dims[:-1]
io_channels = query_antecedent.shape.dims[-1]
heads, memory_length, kv_channels = prev_k.shape.dims[-3:]
with tf.variable_scope(name, default_name="multihead_attention"):
q_var, k_var, v_var, o_var = multihead_attention_vars(
query_antecedent.mesh, heads, io_channels, kv_channels,
query_antecedent.dtype)
memory_antecedent = query_antecedent
q = mtf.einsum(
[query_antecedent, q_var],
mtf.Shape(batch_dims + [heads, kv_channels]))
k = mtf.einsum(
[memory_antecedent, k_var],
mtf.Shape(batch_dims + [heads, kv_channels]))
v = mtf.einsum(
[memory_antecedent, v_var],
mtf.Shape(batch_dims + [heads, kv_channels]))
k = prev_k + mtf.multiply(
k, mtf.one_hot(step_num, memory_length), output_shape=prev_k.shape)
v = prev_v + mtf.multiply(
v, mtf.one_hot(step_num, memory_length), output_shape=prev_v.shape)
mask = mtf.to_float(mtf.greater(mtf.range(
query_antecedent.mesh, memory_length, dtype=tf.int32), step_num)
) * -1e9
o = dot_product_attention(q, k, v, mask)
y = mtf.einsum([o, o_var], query_antecedent.shape)
return y, k, v
def mnist_model(image, labels, mesh):
"""The model.
Args:
image: tf.Tensor with shape [batch, 28*28]
labels: a tf.Tensor with shape [batch] and dtype tf.int32
mesh: a mtf.Mesh
Returns:
logits: a tf.Tensor with shape [batch, 10]
loss: a mtf.Tensor with shape []
"""
batch_dim = mtf.Dimension("batch", FLAGS.batch_size)
rows_dim = mtf.Dimension("rows", 28)
cols_dim = mtf.Dimension("cols", 28)
classes_dim = mtf.Dimension("classes", 10)
hidden_dim1 = mtf.Dimension("hidden1", FLAGS.hidden_size)
hidden_dim2 = mtf.Dimension("hidden2", FLAGS.hidden_size)
x = mtf.import_tf_tensor(mesh, tf.reshape(image, [-1, 28, 28]),
mtf.Shape([batch_dim, rows_dim, cols_dim]))
h1 = mtf_layers.dense(
x, hidden_dim1, reduced_dims=[rows_dim, cols_dim],
activation=mtf.relu, name="hidden1")
h2 = mtf_layers.dense(
h1, hidden_dim2, activation=mtf.relu, name="hidden2")
logits = mtf_layers.dense(h2, classes_dim, name="logits")
if labels is None:
loss = None
else:
labels = mtf.import_tf_tensor(mesh, labels, mtf.Shape([batch_dim]))
loss = mtf_layers.softmax_cross_entropy_with_logits(
logits, mtf.one_hot(labels, classes_dim), classes_dim)
loss = mtf.reduce_mean(loss)
return logits, loss
def mnist_model(image, labels, mesh):
"""The model.
Args:
image: tf.Tensor with shape [batch, 28*28]
labels: a tf.Tensor with shape [batch] and dtype tf.int32
mesh: a mtf.Mesh
Returns:
logits: a tf.Tensor with shape [batch, 10]
loss: a mtf.Tensor with shape []
"""
batch_dim = mtf.Dimension("batch", FLAGS.batch_size)
rows_dim = mtf.Dimension("rows", 28)
cols_dim = mtf.Dimension("cols", 28)
classes_dim = mtf.Dimension("classes", 10)
one_channel_dim = mtf.Dimension("one_channel", 1)
x = mtf.import_tf_tensor(mesh, tf.reshape(image, [-1, 28, 28]),
mtf.Shape([batch_dim, rows_dim, cols_dim]))
x = mtf.reshape(x, [batch_dim, rows_dim, cols_dim, one_channel_dim])
# add some convolutional layers to demonstrate that convolution works.
# TODO(noam): get spatially-partitioned convolution working.
fh_dim = mtf.Dimension("fh", 3)
fw_dim = mtf.Dimension("fw", 3)
filters1_dim = mtf.Dimension("filters1", 32)
filters2_dim = mtf.Dimension("filters2", 32)
kernel1 = mtf.get_variable(mesh, "kernel1",
[fh_dim, fw_dim, one_channel_dim, filters1_dim])
kernel2 = mtf.get_variable(mesh, "kernel2",
[fh_dim, fw_dim, filters1_dim, filters2_dim])
f1 = mtf.relu(mtf.conv2d(x, kernel1))
f2 = mtf.relu(mtf.conv2d(f1, kernel2))
x = mtf.reduce_mean(f2, reduced_dim=filters2_dim)
# add some fully-connected dense layers.
hidden_dim1 = mtf.Dimension("hidden1", FLAGS.hidden_size)
hidden_dim2 = mtf.Dimension("hidden2", FLAGS.hidden_size)
h1 = mtf_layers.dense(x,
hidden_dim1,
reduced_dims=[rows_dim, cols_dim],
activation=mtf.relu,
name="hidden1")
h2 = mtf_layers.dense(h1, hidden_dim2, activation=mtf.relu, name="hidden2")
logits = mtf_layers.dense(h2, classes_dim, name="logits")
if labels is None:
loss = None
else:
labels = mtf.import_tf_tensor(mesh, labels, mtf.Shape([batch_dim]))
loss = mtf_layers.softmax_cross_entropy_with_logits(
logits, mtf.one_hot(labels, classes_dim), classes_dim)
loss = mtf.reduce_mean(loss)
return logits, loss
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 _mtf_model_fn(self, features, mesh):
features = copy.copy(features)
hparams = self._hparams
targets = tf.to_int32(features["targets"])
if len(targets.get_shape()) > 2:
tf.logging.info("targets = %s" % targets)
targets = tf.squeeze(targets, [2, 3])
# pad targets to max_length
def pad_to_max_length(x):
extra_length = hparams.max_length - tf.shape(x)[1]
x = tf.pad(x, [[0, 0], [0, extra_length]])
x = tf.reshape(x, [hparams.batch_size, hparams.max_length])
return x
targets = pad_to_max_length(targets)
for key in ["targets_segmentation", "targets_position",
"inputs_segmentation", "inputs_position"]:
if key in features:
features[key] = pad_to_max_length(features[key])
shifted_targets = common_layers.shift_right_2d(targets)
targets = self._import_to_batch_by_length(targets, "targets", mesh, hparams)
shifted_targets = self._import_to_batch_by_length(
shifted_targets, "shifted_targets", mesh, hparams)
if "targets_segmentation" in features:
# "Packed" dataset - keep the examples from seeing each other.
targets_segmentation = self._import_to_batch_by_length(
features["targets_segmentation"], "targets_segmentation",
mesh, hparams)
targets_position = self._import_to_batch_by_length(
features["targets_position"], "targets_position",
mesh, hparams)
decoder_self_attention_mask = (
mtf_layers.attention_mask_autoregressive(
targets_position, dtype=self.activation_dtype) +
mtf_layers.attention_mask_same_segment(
targets_segmentation, dtype=self.activation_dtype))
else:
targets_position = mtf.range(mesh, self.length_dim, dtype=tf.int32)
decoder_self_attention_mask = mtf_layers.attention_mask_autoregressive(
targets_position, dtype=self.activation_dtype)
def layer_prepostprocess_dropout(x):
return mtf.dropout(
x, keep_prob=1.0 - hparams.layer_prepostprocess_dropout,
noise_shape=mtf.Shape([self.batch_dim, self.model_dim]))
extra_losses = []
(inputs_embedding_var,
targets_embedding_var,
softmax_var,
positional_embedding_var) = self._embedding_and_softmax_vars(mesh)
if self.has_input:
inputs = tf.squeeze(tf.to_int32(features["inputs"]), [2, 3])
inputs = pad_to_max_length(inputs)
inputs = self._import_to_batch_by_length(inputs, "inputs", mesh, hparams)
if "inputs_segmentation" in features:
# "Packed" dataset - keep the examples from seeing each other.
inputs_segmentation = self._import_to_batch_by_length(
features["inputs_segmentation"], "inputs_segmentation",
mesh, hparams)
inputs_position = self._import_to_batch_by_length(
features["inputs_position"], "inputs_position",
mesh, hparams)
encoder_self_attention_mask = (
mtf_layers.attention_mask_same_segment(
inputs_segmentation, dtype=self.activation_dtype))
encoder_decoder_attention_mask = (
mtf_layers.attention_mask_same_segment(
targets_segmentation, inputs_segmentation,
dtype=self.activation_dtype))
else:
inputs_position = mtf.range(mesh, self.length_dim, dtype=tf.int32)
encoder_self_attention_mask = (
mtf_layers.attention_mask_ignore_padding(
inputs, dtype=self.activation_dtype))
encoder_decoder_attention_mask = encoder_self_attention_mask
x = (mtf.gather(inputs_embedding_var, inputs, self.inputs_vocab_dim) +
mtf.gather(positional_embedding_var, inputs_position,
self.max_length_dim))
x = layer_prepostprocess_dropout(x)
with tf.variable_scope("encoder"):
x = self._layer_stack(x,
hparams.num_encoder_layers,
self_attention_mask=encoder_self_attention_mask,
losses=extra_losses)
encoder_output = mtf.rename_dimension(
x, self.length_dim.name, self.memory_length_dim.name)
else:
encoder_output = None
encoder_decoder_attention_mask = None
# DECODER
x = (mtf.gather(
targets_embedding_var, shifted_targets, self.targets_vocab_dim) +
mtf.gather(
positional_embedding_var, targets_position, self.max_length_dim))
x = layer_prepostprocess_dropout(x)
# Decoder
with tf.variable_scope("decoder"):
x = self._layer_stack(
x,
hparams.num_decoder_layers,
encoder_output=encoder_output,
self_attention_mask=decoder_self_attention_mask,
encdec_attention_mask=encoder_decoder_attention_mask,
losses=extra_losses)
logits = mtf.matmul(x, softmax_var)
off_value = hparams.label_smoothing / self._targets_vocab_size
on_value = 1.0 - hparams.label_smoothing + off_value
soft_targets = mtf.one_hot(
targets, self.targets_vocab_dim, on_value=on_value, off_value=off_value,
dtype=self.activation_dtype)
loss = mtf_layers.softmax_cross_entropy_with_logits(
logits, soft_targets, self.targets_vocab_dim)
weights = mtf_layers.weights_nonzero(
targets, dtype=self.activation_dtype)
loss = mtf.reduce_mean(loss * weights)
for l in extra_losses:
loss += l
return logits, loss
def _truncated_top_2_gating_mtf(
gates, group_dim, experts_dim, expert_capacity_dim):
"""Compute gating for mixture-of-experts in TensorFlow.
gates is usually the output of a softmax function.
The return value is a dense representation of the mapping between
the input positions in the positions in the batches sent to the experts.
TODO(noam): this function contains code factored out of
expert_utils.local_moe_tpu. Move this function to that file and
call it from both places.
Args:
gates: a Tensor
group_dim: one dimension of gates
experts_dim: one dimension of gates
expert_capacity_dim: a Dimension not in gates
Returns:
a Tensor with shape gates.shape + expert_capacity_dim
Raises:
ValueError: if group_dim has size >256
"""
gates = mtf.to_float(gates)
expert_capacity_f = float(expert_capacity_dim.size)
# Find the top expert for each position. shape=[batch, group]
index_1, gate_1 = mtf.top_1(gates, experts_dim)
# [batch, group, experts]
mask_1 = mtf.one_hot(index_1, experts_dim, dtype=gates.dtype)
if expert_capacity_dim.size > 256:
# using mtf.cumsum (implemented on TPU as bfloat16 matmul) to compute
# position in the mini-batch sent to the expert. This will cause
# very bad things to happen if expert_capacity_dim > 256.
raise ValueError(
"expert_capacity_dim.size must be <=256 to avoid roundoff errors in"
" indices - got %s" % (expert_capacity_dim,))
# [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_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_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
# Pick a second-place expert for each position.
# We first mask out the experts that we expect to be over-capacity
# [batch, experts]
space_remaining = expert_capacity_f - mask_1_count
use_rate = (mask_1_count + 1.0) / float(group_dim.size)
# At what point in the sequence do we expect the expert to be full.
# [batch, experts]
expected_exhaustion_pos = space_remaining / use_rate
# A Tensor with shape [batch, group, experts] representing a boolean
# - whether we expect that the expert will already be full.
expected_exhausted = mtf.to_float(mtf.greater(
mtf.range(gates.mesh, group_dim, tf.float32), expected_exhaustion_pos))
masked_gates = gates - mask_1 - expected_exhausted
# This section is similar to the section above.
# [batch, group]
index_2, gate_2 = mtf.top_1(masked_gates, experts_dim)
# [batch, group, experts]
mask_2 = mtf.one_hot(index_2, experts_dim, dtype=gates.dtype)
# [batch, group, experts]
position_in_expert_2 = (
mtf.cumsum(mask_2, group_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)
position_in_expert_2 = mtf.reduce_sum(
position_in_expert_2, reduced_dim=experts_dim)
gate_2 *= mask_2_flat
# renormalize the two gate values to add up to 1
denom = gate_1 + gate_2 + 1e-9
gate_1 /= denom
gate_2 /= denom
# [batch, group, experts, expert_capacity]
assignment = (
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))
return assignment
def mtf_model_fn(self, features, mesh):
features = copy.copy(features)
tf.logging.info("features = %s" % features)
hparams = self._hparams
activation_dtype = self.set_activation_type()
is_training = hparams.mode == tf.estimator.ModeKeys.TRAIN
# Declare all the dimensions
batch_dim = mtf.Dimension("batch", hparams.batch_size)
hidden_dim = mtf.Dimension("hidden", hparams.hidden_size)
filter_h_dim = mtf.Dimension("filter_height", 7)
filter_w_dim = mtf.Dimension("filter_width", 7)
filters = mtf.Dimension("filters", hparams.filter_sizes[0])
rows_dim = mtf.Dimension("rows_size", 32)
cols_dim = mtf.Dimension("cols_size", 96)
row_blocks_dim = mtf.Dimension("row_blocks", hparams.row_blocks)
col_blocks_dim = mtf.Dimension("col_blocks", hparams.col_blocks)
classes_dim = mtf.Dimension("classes", 10)
one_channel_dim = mtf.Dimension("one_channel", 1)
inputs = features["inputs"]
x = mtf.import_tf_tensor(
mesh,
tf.reshape(inputs, [
hparams.batch_size, hparams.row_blocks,
hparams.rows_size // hparams.row_blocks, hparams.col_blocks,
hparams.num_channels * hparams.cols_size // hparams.col_blocks,
1
]),
mtf.Shape([
batch_dim, row_blocks_dim, rows_dim, col_blocks_dim, cols_dim,
one_channel_dim
]))
x = mtf.transpose(x, [
batch_dim, row_blocks_dim, col_blocks_dim, rows_dim, cols_dim,
one_channel_dim
])
x = mtf.to_float(x)
initial_filters = mtf.get_variable(
mesh, "init_filters",
mtf.Shape([filter_h_dim, filter_w_dim, one_channel_dim, filters]))
x = mtf.conv2d_with_blocks(x,
initial_filters,
strides=[1, 1, 1, 1],
padding="SAME",
h_blocks_dim=None,
w_blocks_dim=col_blocks_dim)
x = batch_norm_relu(x, is_training)
# Conv blocks
# [ self attention - ffn - residual + dropout] x n
for layer in range(hparams.num_layers):
layer_name = "block_layer_%d" % layer
with tf.variable_scope(layer_name):
# Residual block layer
x = block_layer(inputs=x,
filters=hparams.filter_sizes[0],
blocks=hparams.layer_sizes[0],
strides=[1, 1, 1, 1],
is_training=is_training,
name="block_layer1",
row_blocks_dim=None,
col_blocks_dim=None)
x = block_layer(inputs=x,
filters=hparams.filter_sizes[1],
blocks=hparams.layer_sizes[1],
strides=[1, 2, 2, 1],
is_training=is_training,
name="block_layer2",
row_blocks_dim=None,
col_blocks_dim=None)
x = block_layer(inputs=x,
filters=hparams.filter_sizes[2],
blocks=hparams.layer_sizes[2],
strides=[1, 2, 2, 1],
is_training=is_training,
name="block_layer3",
row_blocks_dim=None,
col_blocks_dim=None)
# Calculate the logits and loss.
out = x
outputs = mtf_layers.dense(out,
hidden_dim,
reduced_dims=out.shape.dims[-5:],
activation=mtf.relu,
name="dense")
# We assume fixed vocab size for targets
labels = tf.squeeze(tf.to_int32(features["targets"]), [2, 3])
labels = mtf.import_tf_tensor(mesh,
tf.reshape(labels, [hparams.batch_size]),
mtf.Shape([batch_dim]))
logits = mtf_layers.dense(outputs, classes_dim, name="logits")
soft_targets = mtf.one_hot(labels, classes_dim, dtype=activation_dtype)
loss = mtf_layers.softmax_cross_entropy_with_logits(
logits, soft_targets, classes_dim)
# Reshape logits so it doesn't break inside t2t.
logits = mtf.reshape(
logits, mtf.Shape([batch_dim, one_channel_dim, classes_dim]))
loss = mtf.reduce_mean(loss)
return logits, loss
def mtf_model_fn(self, features, mesh):
features = copy.copy(features)
tf.logging.info("features = %s" % features)
hparams = self._hparams
activation_dtype = self.set_activation_type()
# We assume fixed vocab size for targets
targets_vocab_size = self._problem_hparams.target_modality._vocab_size # pylint: disable=protected-access
targets = tf.to_int32(features["targets"])
# Image preprocessing, reshape into a 1D sequence and shift right.
length = hparams.img_len * hparams.img_len * hparams.num_channels
targets = tf.reshape(targets, [hparams.batch_size, length])
shifted_targets = common_layers.shift_right_2d(targets)
# Declare all the dimensions
model_dim = mtf.Dimension("d_model", hparams.hidden_size)
batch_dim = mtf.Dimension("batch", hparams.batch_size)
length_dim = mtf.Dimension("length", length)
max_length_dim = mtf.Dimension("max_length", hparams.max_length)
filter_dim = mtf.Dimension("d_ff", hparams.d_ff)
kv_channels = mtf.Dimension("kv_channels", hparams.d_kv)
heads = mtf.Dimension("heads", hparams.num_heads)
def import_to_batch_by_length(x, name):
return mtf.import_tf_tensor(mesh,
x,
mtf.Shape([batch_dim, length_dim]),
name=name)
def layer_prepostprocess_dropout(x):
return mtf.dropout(x,
keep_prob=1.0 -
hparams.layer_prepostprocess_dropout,
noise_shape=mtf.Shape([batch_dim, model_dim]))
targets = import_to_batch_by_length(targets, "targets")
shifted_targets = import_to_batch_by_length(shifted_targets,
"shifted_targets")
extra_losses = []
# Create targets content and position embeddings.
targets_vocab_size = 256 * hparams.num_channels
targets_vocab_dim = mtf.Dimension("vocab", targets_vocab_size)
outputs_vocab_dim = mtf.Dimension("output_vocab", 256)
# Create embedding var for targets and positions and do a gather.
targets_embedding_var = mtf.get_variable(
mesh,
"targets_embedding",
mtf.Shape([targets_vocab_dim, model_dim]),
initializer=tf.random_normal_initializer(),
activation_dtype=activation_dtype)
x = mtf.gather(targets_embedding_var, shifted_targets,
targets_vocab_dim)
# Add positional embeddings
x += mtf.reshape(
self.create_positional_emb_2d(targets, max_length_dim, model_dim),
[length_dim, model_dim])
# If conditional and input is given, add the input embedding to the target.
# TODO(nikip): Verify conditional.
if self.has_input and not hparams.unconditional:
vocab_size = hparams.num_classes
inputs_vocab_dim = mtf.Dimension("vocab", vocab_size)
inputs = tf.squeeze(tf.to_int32(features["inputs"]), [2, 3])
inputs = import_to_batch_by_length(inputs, "inputs")
# Input embeddings
inputs_embedding_var = mtf_layers.embedding(
mesh,
"input_embedding",
mtf.Shape([inputs_vocab_dim, model_dim]),
activation_dtype=activation_dtype)
inputs_emb = mtf.gather(inputs_embedding_var, inputs,
inputs_vocab_dim)
x += inputs_emb
# Image Transformer Decoder
# [ self attention - ffn - residual + dropout] x n
for layer in range(hparams.num_decoder_layers):
layer_name = "decoder_layer_%d" % layer
with tf.variable_scope(layer_name):
# Self attention layer
x += layer_prepostprocess_dropout(
mtf_layers.masked_local_attention_1d(
mtf_layers.layer_norm(x,
model_dim,
name="layer_norm_self_att"),
None,
kv_channels,
heads,
block_length=hparams.block_length,
name="self_att"))
# ffn layer
x += layer_prepostprocess_dropout(
mtf_layers.dense_relu_dense(
mtf_layers.layer_norm(x,
model_dim,
name="layer_norm_ffn"),
filter_dim,
hparams.dropout,
dropout_broadcast_dims=[length_dim]))
x = mtf_layers.layer_norm(x,
model_dim,
name="decoder_final_layer_norm")
# Calculate the logits and loss.
logits = mtf_layers.dense(x, outputs_vocab_dim, name="logits")
soft_targets = mtf.one_hot(targets,
outputs_vocab_dim,
dtype=activation_dtype)
loss = mtf_layers.softmax_cross_entropy_with_logits(
logits, soft_targets, outputs_vocab_dim)
loss = mtf.reduce_mean(loss)
for l in extra_losses:
loss += l
return logits, loss
def beam_search(logits_fn,
initial_ids,
alpha,
states=None,
eos_id=EOS_ID,
stop_early=True,
decode_length=None,
use_tpu=True):
"""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.
WARNING: Assumes 2nd dimension of tensors in `states` and not invariant, this
means that the shape of the 2nd dimension of these tensors will not be
available (i.e. set to None) inside logits_fn.
Args:
logits_fn: Interface to the model, to provide logits.
Shoud take:
step_num - mtf Scalar
ids - mtf Tensor with shape [batch, beam, length]
Should return:
logits - [batch, beam, vocab_size]
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
Returns:
Tuple of
(decoded beams [batch, beam, length]
decoding probabilities [batch, beam_size])
"""
batch_dim, beam_dim, length_dim = initial_ids.shape.dims
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), 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)
# 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.to_float(curr_finished)) * -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",
states=None)
def grow_alive(curr_seq, curr_scores, curr_log_probs, curr_finished,
states):
"""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]
states: list of mtf.Tensor
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.to_float(curr_finished) * -INF
return compute_topk_scores_and_seq(curr_seq, curr_scores,
curr_log_probs, curr_finished,
beam_dim, "grow_alive", 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 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)
"""
# 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,
top2k_states) = grow_topk(i, alive_seq, alive_log_probs, states)
alive_seq, alive_log_probs, _, states = grow_alive(
top2k_seq, top2k_scores, top2k_log_probs, top2k_finished,
top2k_states)
finished_seq, finished_scores, finished_flags, _ = grow_finished(
finished_seq, finished_scores, finished_flags, top2k_seq,
top2k_scores, top2k_finished)
return (i + 1, alive_seq, alive_log_probs, finished_seq,
finished_scores, finished_flags) + tuple(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.to_float(decode_length)) / 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.to_float(finished_in_finished),
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.to_float(
mtf.reduce_any(finished_in_finished, reduced_dim=beam_dim))) *
-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)
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 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
def mnist_model(image, labels, mesh):
"""The model.
Args:
image: tf.Tensor with shape [batch, 28*28]
labels: a tf.Tensor with shape [batch] and dtype tf.int32
mesh: a mtf.Mesh
Returns:
logits: a tf.Tensor with shape [batch, 10]
loss: a mtf.Tensor with shape []
"""
batch_dim = mtf.Dimension("batch", FLAGS.batch_size)
row_blocks_dim = mtf.Dimension("row_blocks", 4)
col_blocks_dim = mtf.Dimension("col_blocks", 4)
rows_dim = mtf.Dimension("rows_size", 7)
cols_dim = mtf.Dimension("cols_size", 7)
classes_dim = mtf.Dimension("classes", 10)
one_channel_dim = mtf.Dimension("one_channel", 1)
x = mtf.import_tf_tensor(
mesh, tf.reshape(image, [FLAGS.batch_size, 4, 7, 4, 7, 1]),
mtf.Shape([
batch_dim, row_blocks_dim, rows_dim, col_blocks_dim, cols_dim,
one_channel_dim
]))
x = mtf.transpose(x, [
batch_dim, row_blocks_dim, col_blocks_dim, rows_dim, cols_dim,
one_channel_dim
])
# add some convolutional layers to demonstrate that convolution works.
fh_dim = mtf.Dimension("fh", 9)
fw_dim = mtf.Dimension("fw", 9)
filters1_dim = mtf.Dimension("filters1", 16)
filters2_dim = mtf.Dimension("filters2", 16)
kernel1 = mtf.get_variable(mesh, "kernel1",
[fh_dim, fw_dim, one_channel_dim, filters1_dim])
kernel2 = mtf.get_variable(mesh, "kernel2",
[fh_dim, fw_dim, filters1_dim, filters2_dim])
f1 = mtf.relu(
mtf.conv2d_with_blocks(x,
kernel1,
strides=[1, 1, 1, 1],
padding="SAME",
h_blocks_dim=row_blocks_dim,
w_blocks_dim=col_blocks_dim))
f2 = mtf.relu(
mtf.conv2d_with_blocks(f1,
kernel2,
strides=[1, 1, 1, 1],
padding="SAME",
h_blocks_dim=row_blocks_dim,
w_blocks_dim=col_blocks_dim))
x = mtf.reduce_mean(f2, reduced_dim=filters2_dim)
# add some fully-connected dense layers.
hidden_dim1 = mtf.Dimension("hidden1", FLAGS.hidden_size)
hidden_dim2 = mtf.Dimension("hidden2", FLAGS.hidden_size)
h1 = mtf_layers.dense(x,
hidden_dim1,
reduced_dims=x.shape.dims[-4:],
activation=mtf.relu,
name="hidden1")
h2 = mtf_layers.dense(h1, hidden_dim2, activation=mtf.relu, name="hidden2")
logits = mtf_layers.dense(h2, classes_dim, name="logits")
if labels is None:
loss = None
else:
labels = mtf.import_tf_tensor(mesh,
tf.reshape(labels, [FLAGS.batch_size]),
mtf.Shape([batch_dim]))
loss = mtf_layers.softmax_cross_entropy_with_logits(
logits, mtf.one_hot(labels, classes_dim), classes_dim)
loss = mtf.reduce_mean(loss)
return logits, loss
def _top_2_gating(inputs, experts_dim, expert_capacity_dim, max_experts,
hparams, train):
"""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
max_experts is an float tensor with shape [batch_dim, group_dim]
indicating at most how many experts to use per example. This can be
used to prevent padding from going to experts.
The returned forward assignment is a tensor used to map (via einsum) from the
inputs to the expert_inputs. Likewise, the returned backward_assignment 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 all of these
are as follows.
inputs: [batch_dim, group_dim, input_dim]
forward_assignment: [batch_dim, group_dim, experts_dim, expert_capacity_dim]
expert_inputs: [batch_dim, experts_dim, expert_capacity_dim, input_dim]
expert_outputs: [batch_dim, experts_dim, expert_capacity_dim, output_dim]
backward_assignment: [batch_dim, group_dim, experts_dim, expert_capacity_dim]
outputs: [batch_dim, group_dim, output_dim]
Args:
inputs: a mtf.Tensor with shape [batch_dim, group_dim, input_dim]
experts_dim: a Dimension (the number of experts)
expert_capacity_dim: a Dimension (number of examples per group per expert)
max_experts: optional mtf.Tensor with shape [batch_dim, group_dim]
hparams: model hyperparameters.
train: a boolean
Returns:
forward_assignment: a Tensor with shape
[batch_dim, group_dim, experts_dim, expert_capacity_dim]
backward_assignment: a Tensor with shape
[batch_dim, group_dim, experts_dim, expert_capacity_dim]
loss: a mtf scalar
Raises:
ValueError: on illegal hyperparameters
"""
unused_batch_dim, group_dim, unused_input_dim = inputs.shape.dims
raw_gates = mtf.softmax(
mtf_layers.dense(inputs, experts_dim, use_bias=False), experts_dim)
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)
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 max_experts is not None:
geq1 = mtf.to_float(mtf.greater_equal(max_experts, 1.0))
geq2 = mtf.to_float(mtf.greater_equal(max_experts, 2.0))
mask_1 *= geq1
mask_2 *= geq2
raw_gates *= geq1
gates_without_top_1 *= geq2
# 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_dim)
# Something continuous that is correlated with what we want to equalize.
density_1_proxy = mtf.reduce_mean(raw_gates, reduced_dim=group_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_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_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_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_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_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)
# renormalize the two gate values to add up to 1
denom = gate_1 + gate_2 + 1e-9
gate_1 /= denom
gate_2 /= denom
# [batch, group, experts, expert_capacity]
backward_assignment = (
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))
forward_assignment = mtf.cast(mtf.cast(backward_assignment, tf.bool),
backward_assignment.dtype)
return forward_assignment, backward_assignment, loss
