def entmax_forward(x, alpha=1.3, dim=None, n_iter=50):
assert alpha > 1 and alpha < 2, 'alpha must be between 1 and 2'
_gp = lambda x, alpha: x ** (alpha - 1)
_gp_inv = lambda x, alpha: mtf.pow(x, (1 / (alpha - 1)))
_p = lambda x, alpha: _gp_inv(mtf.relu(x), alpha)
dim = x.shape[-1] if dim is None else dim
d = dim.size
x = x * (alpha - 1)
max_val = mtf.reduce_max(x, reduced_dim=dim)
tau_lo = max_val - _gp(1, alpha)
tau_hi = max_val - _gp(1 / d, alpha)
f_lo = mtf.reduce_sum(_p(x - tau_lo, alpha), reduced_dim=dim) - 1
dm = tau_hi - tau_lo
for _ in range(n_iter):
dm = dm / 2
tau_m = tau_lo + dm
p_m = _p(x - tau_m, alpha)
f_m = mtf.reduce_sum(p_m, reduced_dim=dim) - 1
mask = mtf.greater_equal((f_m * f_lo), 0)
tau_lo = mtf.where(mask, tau_m, tau_lo)
p_m = p_m / mtf.reduce_sum(p_m, reduced_dim=dim)
return p_m
def cond_fn(position, ids, *unused_states):
"""Should we run another loop iteration?"""
past_end = mtf.greater_equal(position, length_dim.size)
if max_steps:
past_end = mtf.logical_or(
past_end, mtf.greater_equal(position - initial_position, max_steps))
is_done = past_end
if stop_at_token is not None:
eos_count = mtf.reduce_sum(
mtf.to_int32(mtf.equal(ids, stop_at_token)),
reduced_dim=length_dim)
has_additional_eos = mtf.greater(eos_count, partial_sequences_eos_count)
is_done = mtf.logical_or(is_done, has_additional_eos)
all_done = mtf.reduce_all(is_done)
return mtf.logical_not(all_done)
def ids_to_embedding(self, ids): """Ids to embeddings with ids not in cluster mapped to the zero vector.""" ids -= self._start_token_id # The mtf.gather in the embedding's ids_to_embedding implementation will # cause the one hot representations of tokens greater than cluster vocab # dimension size to be the zero vector. Thus the embeddings for those tokens # will be the zero vector. ids = mtf.where(mtf.greater_equal(ids, 0), ids, self._end_token_id) return self._embedding.ids_to_embedding(ids)
def cond_fn(position, ids, *unused_states):
"""Should we run another loop iteration."""
past_end = mtf.greater_equal(position, length_dim.size)
is_done = past_end
if stop_at_token is not None:
has_eos = mtf.reduce_any(
mtf.equal(ids, stop_at_token), reduced_dim=length_dim)
is_done = mtf.logical_or(is_done, has_eos)
all_done = mtf.reduce_all(is_done)
return mtf.logical_not(all_done)
def ids_to_embedding(self, ids, context):
"""Ids to embeddings with ids not in cluster mapped to the zero vector."""
ids -= self._start_token_id
# The mtf.gather in the embedding's ids_to_embedding implementation will
# cause the one hot representations of tokens greater than cluster vocab
# dimension size to be the zero vector. Thus the embeddings for those tokens
# will be the zero vector.
ids = mtf.where(mtf.greater_equal(ids, 0), ids, self._vocab_dim.size)
# Handle the case of the head cluster where we will have entries at the end
# corresponding to the tail clusters.
ids = mtf.where(
mtf.less(ids, self._end_token_id - self._start_token_id),
ids,
self._vocab_dim.size,
)
return self._embedding.ids_to_embedding(ids, context)
def call(self, context, x, losses=None):
"""Call the layer."""
params = mtf.layers.multihead_attention_params(context.mesh,
self.heads_dim,
context.model_dim,
self.kv_dim,
context.variable_dtype)
if context.mode == "incremental":
prev_k, prev_v = context.get_states(2)
y, new_k, new_v = mtf.layers.masked_local_attention_1d_incremental(
x, prev_k, prev_v, context.position, params=params)
context.record_new_states([new_k, new_v])
return y
else:
kv = []
y = mtf.layers.masked_local_attention_1d(x,
self.kv_dim,
self.heads_dim,
self.window_size,
params=params,
return_kv=kv)
if context.mode == "first_part":
k = kv[0]
v = kv[1]
window_dim = mtf.Dimension("window", self.window_size)
mesh = k.mesh
window_pos = mtf.range(mesh, window_dim, tf.int32)
pos = mtf.range(mesh, context.length_dim, tf.int32)
select_recent = mtf.cast(
mtf.equal(window_pos, mtf.mod(pos, self.window_size)),
k.dtype)
select_recent *= mtf.cast(
mtf.less(pos, context.initial_position), k.dtype)
select_recent *= mtf.cast(
mtf.greater_equal(
pos, context.initial_position - self.window_size),
k.dtype)
state_shape = k.shape.dims[:-2] + [window_dim, self.kv_dim]
k_state = mtf.einsum([k, select_recent],
output_shape=state_shape,
reduced_dims=[context.length_dim])
v_state = mtf.einsum([v, select_recent],
output_shape=state_shape,
reduced_dims=[context.length_dim])
context.new_states.extend([k_state, v_state])
return y
def get_cluster_mask(self, targets):
"""Computes mask over the targets masking out tokens not in the cluster."""
return mtf.logical_and(
mtf.greater_equal(targets, self._start_token_id),
mtf.less(targets, self._end_token_id))
def call(self, context, x, losses=None):
"""Call the layer."""
params = self.make_params(context)
q = params.compute_q(x)
if self.shared_kv:
kv = params.compute_kv(x)
k = kv
v = kv
else:
k = params.compute_k(x)
v = params.compute_v(x)
if context.mode == "incremental":
if self.shared_kv:
prev_kv, = context.get_states(1)
else:
prev_k, prev_v = context.get_states(2)
current_position = mtf.equal(
mtf.range(context.mesh, self.window_dim, dtype=tf.int32),
mtf.mod(context.position, self.radius))
if self.shared_kv:
kv = mtf.where(current_position,
kv,
prev_kv,
output_shape=prev_kv.shape)
k = kv
v = kv
context.record_new_states([kv])
else:
k = mtf.where(current_position,
params.compute_k(x),
prev_k,
output_shape=prev_k.shape)
v = mtf.where(current_position,
params.compute_v(x),
prev_v,
output_shape=prev_v.shape)
context.record_new_states([k, v])
window_pos = mtf.range(context.mesh, self.window_dim, tf.int32)
visible = mtf.greater_equal(context.position, window_pos)
bias = attention.visibility_mask_to_attention_bias(
visible, context.activation_dtype)
o = attention.attention(
q, k, v, self.window_dim, self.kv_dim, self.kv_dim, bias,
**self.attention_kwargs_from_context(context))
elif context.length_dim.size <= max(256, self.radius * 4):
# nothing fancy - just do full attention and mask
memory_length = self.rename_length_to_memory_length(
context.position, context)
o = attention.attention(
q, self.rename_length_to_memory_length(k, context),
self.rename_length_to_memory_length(v, context),
self.memory_length(context), self.kv_dim, self.kv_dim,
self.compute_bias(context, memory_length, x),
**self.attention_kwargs_from_context(context))
else:
# fancy local attention algorithm
o = attention.local_attention_1d(
q=q,
k=k,
v=None if self.shared_kv else v,
length_dim=context.length_dim,
key_dim=self.kv_dim,
value_dim=self.kv_dim,
length_dim_num_splits=1, # TODO(noam): look at the layout
autoregressive=context.model.fully_autoregressive,
radius=self.radius,
sequence_id=context.sequence_id,
write_priority=context.write_priority,
read_priority=context.read_priority,
attention_kwargs=self.attention_kwargs_from_context(context))
if context.mode == "first_part":
window_pos = mtf.range(context.mesh, self.window_dim, tf.int32)
pos = mtf.range(context.mesh, context.length_dim, tf.int32)
select_recent = mtf.cast(
mtf.equal(mtf.mod(pos, self.radius), window_pos), x.dtype)
select_recent *= mtf.cast(mtf.less(pos, context.initial_position),
x.dtype)
select_recent *= mtf.cast(
mtf.greater_equal(pos, context.initial_position - self.radius),
x.dtype)
state_shape = (k.shape - [context.length_dim, self.kv_dim] +
[self.window_dim, self.kv_dim])
k_state = mtf.einsum([k, select_recent],
output_shape=state_shape,
reduced_dims=[context.length_dim])
context.new_states.append(k_state)
if not self.shared_kv:
v_state = mtf.einsum([v, select_recent],
output_shape=state_shape,
reduced_dims=[context.length_dim])
context.new_states.append(v_state)
return params.compute_output(o, output_shape=x.shape)
def compute_bias(self, context, memory_position, x):
"""Compute attention bias.
Args:
context: a transformer.Context
memory_position: an int32 tensor containing memory_length dimension.
x: a Tensor - the query antecedent - required for relative attention
Returns:
a Tensor or None
"""
min_relative_position = self.min_relative_position(context)
max_relative_position = self.max_relative_position(context)
# we can often cache the result of this function between similar layers
can_cache = (self.relative_attention_type is None
or self.relative_attention_type == "bias_shared")
if can_cache:
cache_key = ("self_attention_mask", min_relative_position,
max_relative_position, self.relative_attention_type,
self.num_heads)
if cache_key in context.cache:
return context.cache[cache_key]
biases = []
relative_position = memory_position - context.position
if min_relative_position is not None:
visible = mtf.greater_equal(relative_position,
min_relative_position)
biases.append(
attention.visibility_mask_to_attention_bias(
visible, context.activation_dtype))
if max_relative_position is not None:
visible = mtf.less_equal(relative_position, max_relative_position)
biases.append(
attention.visibility_mask_to_attention_bias(
visible, context.activation_dtype))
if context.read_priority is not None:
visible = mtf.greater_equal(
context.read_priority,
mtf.layers.rename_length_to_memory_length(
context.write_priority))
biases.append(
attention.visibility_mask_to_attention_bias(
visible, context.activation_dtype))
sequence_id = None
# Subsequence id should only be set if we are in the decoder and have
# multiple targets per input. This will allow each sub-target to only attend
# to itself.
if isinstance(context.subsequence_id, mtf.Tensor):
sequence_id = context.subsequence_id
elif isinstance(context.sequence_id, mtf.Tensor):
sequence_id = context.sequence_id
if (sequence_id is not None
and context.length_dim in sequence_id.shape):
visible = mtf.equal(
sequence_id,
self.rename_length_to_memory_length(sequence_id, context))
biases.append(
attention.visibility_mask_to_attention_bias(
visible, context.activation_dtype))
if self.relative_attention_type is not None:
buckets_dim = mtf.Dimension("buckets",
self.relative_attention_num_buckets)
heads_dim = mtf.Dimension("heads", self.num_heads)
bidirectional = not context.model.fully_autoregressive
rp_bucket = _relative_position_bucket(relative_position,
bidirectional=bidirectional,
num_buckets=buckets_dim.size)
if (self.relative_attention_type == "bias"
or self.relative_attention_type == "bias_shared"):
values = mtf.get_variable(context.mesh,
"relative_attention_bias",
[heads_dim, buckets_dim],
dtype=context.variable_dtype)
elif self.relative_attention_type == "contextual":
values = layers.dense(x, [buckets_dim, heads_dim],
variable_dtype=context.variable_dtype,
name="relative_attention_contextual")
else:
raise ValueError(
"unrecognized relative_attention_type \"%s\"" %
self.relative_attention_type)
biases.append(mtf.gather(values, rp_bucket, buckets_dim))
ret = mtf.add_n(biases) if biases else None
if can_cache:
context.cache[cache_key] = ret
return ret
def local_attention_1d(q,
k,
v,
length_dim,
key_dim,
value_dim,
fully_autoregressive=True,
length_dim_num_splits=1,
radius=128,
sequence_id=1,
write_priority=None,
read_priority=None,
attention_kwargs=None):
"""Attention to the a neighborood around the source.
If fully_autoregressive, then query position p can only see memory positions
in the range (p - radius, p].
If not fully_autoregressive, then query position p can only see memory
positions in the range (p - window_size, p + radius].
In addition, if write_priority and read_priority are provided, then attention
is limited to position pairs where
read_priority[query position] >= write_priority[memory position]
Args:
q: a Tensor containing length_dim
k: a Tensor containing length_dim
v: an optional Tensor containing length_dim. If none then uses v=k.
length_dim: a Dimension
key_dim: a Dimension (the channels dimension of q and k)
value_dim: a Dimension (the channels dimension of v)
fully_autoregressive: a boolean
length_dim_num_splits: an optional integer indicating how many ways the
length dimension is split
radius: an integer
sequence_id: a Tensor or an integer
write_priority: an optional Tensor containing length_dim
read_priority: an optional Tensor containing length_dim
attention_kwargs: optional keyword arguments for attention()
Returns:
a Tensor with the shape x.shape - key_dim + value_dim
Raises:
ValueError: if channels or depth don't match.
"""
# Choose a suitable block size.
# We choose the greatest divisor of length_per_split less than or equal
# to max(window_size, 128)
length_per_split = length_dim.size // length_dim_num_splits
block_length = max(radius, 128)
while length_per_split % block_length != 0:
block_length -= 1
query_block_length = mtf.Dimension("query_block_length", block_length)
memory_block_length = mtf.Dimension("memory_block_length", block_length)
# The num_blocks dimension gets the same name as the length dimension,
# so it will be split in the same way.
num_blocks = mtf.Dimension(length_dim.name, length_dim.size // block_length)
def _reshape_query(x):
return mtf.replace_dimensions(
x, length_dim, [num_blocks, query_block_length])
def _reshape_memory(x):
x = mtf.replace_dimensions(
x, length_dim, [num_blocks, memory_block_length])
return (mtf.left_halo_exchange if fully_autoregressive
else mtf.halo_exchange)(
x, num_blocks, memory_block_length, radius)
q = _reshape_query(q)
k = _reshape_memory(k)
if v:
v = _reshape_memory(v)
else:
v = k
if sequence_id is None:
sequence_id = 1
if (not isinstance(sequence_id, mtf.Tensor) or
length_dim not in sequence_id.shape.dims):
sequence_id += mtf.zeros(q.mesh, [length_dim], tf.int32)
q_sequence_id = _reshape_query(sequence_id)
m_sequence_id = _reshape_memory(sequence_id)
pos = mtf.range(q.mesh, length_dim, dtype=tf.int32)
q_pos = _reshape_query(pos)
m_pos = _reshape_memory(pos)
padded_memory_block_length = mtf.Dimension(
"memory_block_length",
(1 if fully_autoregressive else 2) * radius + block_length)
relative_position = m_pos - q_pos
visible = mtf.equal(q_sequence_id, m_sequence_id)
visible = mtf.logical_and(visible, mtf.greater(relative_position, -radius))
visible = mtf.logical_and(visible, mtf.less_equal(
relative_position, 0 if fully_autoregressive else radius))
if read_priority is not None:
write_priority = _reshape_memory(write_priority)
read_priority = _reshape_query(read_priority)
visible = mtf.logical_and(
visible, mtf.greater_equal(read_priority, write_priority))
bias = visibility_mask_to_attention_bias(visible, q.dtype)
o = attention(q, k, v, padded_memory_block_length,
key_dim, value_dim, bias, **attention_kwargs)
return mtf.replace_dimensions(o, [num_blocks, query_block_length], length_dim)