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"""Attention core modules for Flax."""
import functools
from typing import (Any, Callable, Optional, Tuple)
from flax.linen.dtypes import promote_dtype
from flax.linen.initializers import zeros
from flax.linen.linear import default_kernel_init
from flax.linen.linear import DenseGeneral
from flax.linen.linear import PrecisionLike
from flax.linen.module import compact
from flax.linen.module import merge_param
from flax.linen.module import Module
import jax
from jax import lax
from jax import random
import jax.numpy as jnp
PRNGKey = Any
Shape = Tuple[int, ...]
Dtype = Any
Array = Any
[docs]def dot_product_attention_weights(query: Array,
key: Array,
bias: Optional[Array] = None,
mask: Optional[Array] = None,
broadcast_dropout: bool = True,
dropout_rng: Optional[PRNGKey] = None,
dropout_rate: float = 0.,
deterministic: bool = False,
dtype: Optional[Dtype] = None,
precision: PrecisionLike = None):
"""Computes dot-product attention weights given query and key.
Used by :func:`dot_product_attention`, which is what you'll most likely use.
But if you want access to the attention weights for introspection, then
you can directly call this function and call einsum yourself.
Args:
query: queries for calculating attention with shape of
`[batch..., q_length, num_heads, qk_depth_per_head]`.
key: keys for calculating attention with shape of
`[batch..., kv_length, num_heads, qk_depth_per_head]`.
bias: bias for the attention weights. This should be broadcastable to the
shape `[batch..., num_heads, q_length, kv_length]`.
This can be used for incorporating causal masks, padding masks,
proximity bias, etc.
mask: mask for the attention weights. This should be broadcastable to the
shape `[batch..., num_heads, q_length, kv_length]`.
This can be used for incorporating causal masks.
Attention weights are masked out if their corresponding mask value
is `False`.
broadcast_dropout: bool: use a broadcasted dropout along batch dims.
dropout_rng: JAX PRNGKey: to be used for dropout
dropout_rate: dropout rate
deterministic: bool, deterministic or not (to apply dropout)
dtype: the dtype of the computation (default: infer from inputs and params)
precision: numerical precision of the computation see `jax.lax.Precision`
for details.
Returns:
Output of shape `[batch..., num_heads, q_length, kv_length]`.
"""
query, key = promote_dtype(query, key, dtype=dtype)
dtype = query.dtype
assert query.ndim == key.ndim, 'q, k must have same rank.'
assert query.shape[:-3] == key.shape[:-3], (
'q, k batch dims must match.')
assert query.shape[-2] == key.shape[-2], (
'q, k num_heads must match.')
assert query.shape[-1] == key.shape[-1], 'q, k depths must match.'
# calculate attention matrix
depth = query.shape[-1]
query = query / jnp.sqrt(depth).astype(dtype)
# attn weight shape is (batch..., num_heads, q_length, kv_length)
attn_weights = jnp.einsum('...qhd,...khd->...hqk', query, key,
precision=precision)
# apply attention bias: masking, dropout, proximity bias, etc.
if bias is not None:
attn_weights = attn_weights + bias
# apply attention mask
if mask is not None:
big_neg = jnp.finfo(dtype).min
attn_weights = jnp.where(mask, attn_weights, big_neg)
# normalize the attention weights
attn_weights = jax.nn.softmax(attn_weights).astype(dtype)
# apply attention dropout
if not deterministic and dropout_rate > 0.:
keep_prob = 1.0 - dropout_rate
if broadcast_dropout:
# dropout is broadcast across the batch + head dimensions
dropout_shape = tuple([1] * (key.ndim - 2)) + attn_weights.shape[-2:]
keep = random.bernoulli(dropout_rng, keep_prob, dropout_shape) # type: ignore
else:
keep = random.bernoulli(dropout_rng, keep_prob, attn_weights.shape) # type: ignore
multiplier = (keep.astype(dtype) /
jnp.asarray(keep_prob, dtype=dtype))
attn_weights = attn_weights * multiplier
return attn_weights
[docs]def dot_product_attention(query: Array,
key: Array,
value: Array,
bias: Optional[Array] = None,
mask: Optional[Array] = None,
broadcast_dropout: bool = True,
dropout_rng: Optional[PRNGKey] = None,
dropout_rate: float = 0.,
deterministic: bool = False,
dtype: Optional[Dtype] = None,
precision: PrecisionLike = None):
"""Computes dot-product attention given query, key, and value.
This is the core function for applying attention based on
https://arxiv.org/abs/1706.03762. It calculates the attention weights given
query and key and combines the values using the attention weights.
Note: query, key, value needn't have any batch dimensions.
Args:
query: queries for calculating attention with shape of
`[batch..., q_length, num_heads, qk_depth_per_head]`.
key: keys for calculating attention with shape of
`[batch..., kv_length, num_heads, qk_depth_per_head]`.
value: values to be used in attention with shape of
`[batch..., kv_length, num_heads, v_depth_per_head]`.
bias: bias for the attention weights. This should be broadcastable to the
shape `[batch..., num_heads, q_length, kv_length]`.
This can be used for incorporating causal masks, padding masks,
proximity bias, etc.
mask: mask for the attention weights. This should be broadcastable to the
shape `[batch..., num_heads, q_length, kv_length]`.
This can be used for incorporating causal masks.
Attention weights are masked out if their corresponding mask value
is `False`.
broadcast_dropout: bool: use a broadcasted dropout along batch dims.
dropout_rng: JAX PRNGKey: to be used for dropout
dropout_rate: dropout rate
deterministic: bool, deterministic or not (to apply dropout)
dtype: the dtype of the computation (default: infer from inputs)
precision: numerical precision of the computation see `jax.lax.Precision`
for details.
Returns:
Output of shape `[batch..., q_length, num_heads, v_depth_per_head]`.
"""
query, key, value = promote_dtype(query, key, value, dtype=dtype)
dtype = query.dtype
assert key.ndim == query.ndim == value.ndim, 'q, k, v must have same rank.'
assert query.shape[:-3] == key.shape[:-3] == value.shape[:-3], (
'q, k, v batch dims must match.')
assert query.shape[-2] == key.shape[-2] == value.shape[-2], (
'q, k, v num_heads must match.')
assert key.shape[-3] == value.shape[-3], 'k, v lengths must match.'
# compute attention weights
attn_weights = dot_product_attention_weights(
query, key, bias, mask, broadcast_dropout, dropout_rng, dropout_rate,
deterministic, dtype, precision)
# return weighted sum over values for each query position
return jnp.einsum('...hqk,...khd->...qhd', attn_weights, value,
precision=precision)
[docs]class MultiHeadDotProductAttention(Module):
"""Multi-head dot-product attention.
Attributes:
num_heads: number of attention heads. Features (i.e. inputs_q.shape[-1])
should be divisible by the number of heads.
dtype: the dtype of the computation
(default: infer from inputs and params)
param_dtype: the dtype passed to parameter initializers (default: float32)
qkv_features: dimension of the key, query, and value.
out_features: dimension of the last projection
broadcast_dropout: bool: use a broadcasted dropout along batch dims.
dropout_rate: dropout rate
deterministic: if false, the attention weight is masked randomly
using dropout, whereas if true, the attention weights
are deterministic.
precision: numerical precision of the computation see `jax.lax.Precision`
for details.
kernel_init: initializer for the kernel of the Dense layers.
bias_init: initializer for the bias of the Dense layers.
use_bias: bool: whether pointwise QKVO dense transforms use bias.
attention_fn: dot_product_attention or compatible function. Accepts
query, key, value, and returns output of shape
`[bs, dim1, dim2, ..., dimN,, num_heads, value_channels]``
decode: whether to prepare and use an autoregressive cache.
"""
num_heads: int
dtype: Optional[Dtype] = None
param_dtype: Dtype = jnp.float32
qkv_features: Optional[int] = None
out_features: Optional[int] = None
broadcast_dropout: bool = True
dropout_rate: float = 0.
deterministic: Optional[bool] = None
precision: PrecisionLike = None
kernel_init: Callable[[PRNGKey, Shape, Dtype], Array] = default_kernel_init
bias_init: Callable[[PRNGKey, Shape, Dtype], Array] = zeros
use_bias: bool = True
attention_fn: Callable[..., Array] = dot_product_attention
decode: bool = False
[docs] @compact
def __call__(self,
inputs_q: Array,
inputs_kv: Array,
mask: Optional[Array] = None,
deterministic: Optional[bool] = None):
"""Applies multi-head dot product attention on the input data.
Projects the inputs into multi-headed query, key, and value vectors,
applies dot-product attention and project the results to an output vector.
Args:
inputs_q: input queries of shape
`[batch_sizes..., length, features]`.
inputs_kv: key/values of shape
`[batch_sizes..., length, features]`.
mask: attention mask of shape
`[batch_sizes..., num_heads, query_length, key/value_length]`.
Attention weights are masked out if their corresponding mask value
is `False`.
deterministic: if false, the attention weight is masked randomly
using dropout, whereas if true, the attention weights
are deterministic.
Returns:
output of shape `[batch_sizes..., length, features]`.
"""
features = self.out_features or inputs_q.shape[-1]
qkv_features = self.qkv_features or inputs_q.shape[-1]
assert qkv_features % self.num_heads == 0, (
'Memory dimension must be divisible by number of heads.')
head_dim = qkv_features // self.num_heads
dense = functools.partial(DenseGeneral,
axis=-1,
dtype=self.dtype,
param_dtype=self.param_dtype,
features=(self.num_heads, head_dim),
kernel_init=self.kernel_init,
bias_init=self.bias_init,
use_bias=self.use_bias,
precision=self.precision)
# project inputs_q to multi-headed q/k/v
# dimensions are then [batch..., length, n_heads, n_features_per_head]
query, key, value = (dense(name='query')(inputs_q),
dense(name='key')(inputs_kv),
dense(name='value')(inputs_kv))
# During fast autoregressive decoding, we feed one position at a time,
# and cache the keys and values step by step.
if self.decode:
# detect if we're initializing by absence of existing cache data.
is_initialized = self.has_variable('cache', 'cached_key')
cached_key = self.variable('cache', 'cached_key',
jnp.zeros, key.shape, key.dtype)
cached_value = self.variable('cache', 'cached_value',
jnp.zeros, value.shape, value.dtype)
cache_index = self.variable('cache', 'cache_index',
lambda: jnp.array(0, dtype=jnp.int32))
if is_initialized:
*batch_dims, max_length, num_heads, depth_per_head = (
cached_key.value.shape)
# shape check of cached keys against query input
expected_shape = tuple(batch_dims) + (1, num_heads, depth_per_head)
if expected_shape != query.shape:
raise ValueError('Autoregressive cache shape error, '
'expected query shape %s instead got %s.' %
(expected_shape, query.shape))
# update key, value caches with our new 1d spatial slices
cur_index = cache_index.value
indices = (0,) * len(batch_dims) + (cur_index, 0, 0)
key = lax.dynamic_update_slice(cached_key.value, key, indices)
value = lax.dynamic_update_slice(cached_value.value, value, indices)
cached_key.value = key
cached_value.value = value
cache_index.value = cache_index.value + 1
# causal mask for cached decoder self-attention:
# our single query position should only attend to those key
# positions that have already been generated and cached,
# not the remaining zero elements.
mask = combine_masks(
mask,
jnp.broadcast_to(jnp.arange(max_length) <= cur_index,
tuple(batch_dims) + (1, 1, max_length)))
dropout_rng = None
if self.dropout_rate > 0.: # Require `deterministic` only if using dropout.
m_deterministic = merge_param('deterministic', self.deterministic,
deterministic)
if not m_deterministic:
dropout_rng = self.make_rng('dropout')
else:
m_deterministic = True
# apply attention
x = self.attention_fn(
query,
key,
value,
mask=mask,
dropout_rng=dropout_rng,
dropout_rate=self.dropout_rate,
broadcast_dropout=self.broadcast_dropout,
deterministic=m_deterministic,
dtype=self.dtype,
precision=self.precision) # pytype: disable=wrong-keyword-args
# back to the original inputs dimensions
out = DenseGeneral(features=features,
axis=(-2, -1),
kernel_init=self.kernel_init,
bias_init=self.bias_init,
use_bias=self.use_bias,
dtype=self.dtype,
param_dtype=self.param_dtype,
precision=self.precision,
name='out')(x)
return out
[docs]class SelfAttention(MultiHeadDotProductAttention):
"""Self-attention special case of multi-head dot-product attention."""
[docs] @compact
def __call__(self, inputs_q: Array, mask: Optional[Array] = None, # type: ignore
deterministic: Optional[bool] = None):
"""Applies multi-head dot product self-attention on the input data.
Projects the inputs into multi-headed query, key, and value vectors,
applies dot-product attention and project the results to an output vector.
Args:
inputs_q: input queries of shape
`[batch_sizes..., length, features]`.
mask: attention mask of shape
`[batch_sizes..., num_heads, query_length, key/value_length]`.
Attention weights are masked out if their corresponding mask value
is `False`.
deterministic: if false, the attention weight is masked randomly
using dropout, whereas if true, the attention weights
are deterministic.
Returns:
output of shape `[batch_sizes..., length, features]`.
"""
return super().__call__(inputs_q, inputs_q, mask,
deterministic=deterministic)
# mask-making utility functions
[docs]def make_attention_mask(query_input: Array,
key_input: Array,
pairwise_fn: Callable[..., Any] = jnp.multiply,
extra_batch_dims: int = 0,
dtype: Dtype = jnp.float32):
"""Mask-making helper for attention weights.
In case of 1d inputs (i.e., `[batch..., len_q]`, `[batch..., len_kv]`, the
attention weights will be `[batch..., heads, len_q, len_kv]` and this
function will produce `[batch..., 1, len_q, len_kv]`.
Args:
query_input: a batched, flat input of query_length size
key_input: a batched, flat input of key_length size
pairwise_fn: broadcasting elementwise comparison function
extra_batch_dims: number of extra batch dims to add singleton
axes for, none by default
dtype: mask return dtype
Returns:
A `[batch..., 1, len_q, len_kv]` shaped mask for 1d attention.
"""
mask = pairwise_fn(jnp.expand_dims(query_input, axis=-1),
jnp.expand_dims(key_input, axis=-2))
mask = jnp.expand_dims(mask, axis=-3)
mask = jnp.expand_dims(mask, axis=tuple(range(extra_batch_dims)))
return mask.astype(dtype)
[docs]def make_causal_mask(x: Array,
extra_batch_dims: int = 0,
dtype: Dtype = jnp.float32) -> Array:
"""Make a causal mask for self-attention.
In case of 1d inputs (i.e., `[batch..., len]`, the self-attention weights
will be `[batch..., heads, len, len]` and this function will produce a
causal mask of shape `[batch..., 1, len, len]`.
Args:
x: input array of shape `[batch..., len]`
extra_batch_dims: number of batch dims to add singleton axes for,
none by default
dtype: mask return dtype
Returns:
A `[batch..., 1, len, len]` shaped causal mask for 1d attention.
"""
idxs = jnp.broadcast_to(jnp.arange(x.shape[-1], dtype=jnp.int32), x.shape)
return make_attention_mask(idxs, idxs, jnp.greater_equal,
extra_batch_dims=extra_batch_dims, dtype=dtype)
def combine_masks(*masks: Optional[Array],
dtype: Dtype = jnp.float32) -> Array:
"""Combine attention masks.
Args:
*masks: set of attention mask arguments to combine, some can be None.
dtype: dtype for the returned mask.
Returns:
Combined mask, reduced by logical and, returns None if no masks given.
"""
masks_list = [m for m in masks if m is not None]
if not masks_list:
return None
assert all(map(lambda x: x.ndim == masks_list[0].ndim, masks_list)), (
f'masks must have same rank: {tuple(map(lambda x: x.ndim, masks_list))}')
mask, *other_masks = masks_list
for other_mask in other_masks:
mask = jnp.logical_and(mask, other_mask)
return mask.astype(dtype)
