def DotProductAttention(query, key, value, mask):
"""Dot product self-attention.
Args:
query (jax.interpreters.xla.DeviceArray): array of query representations with shape (L_q by d)
key (jax.interpreters.xla.DeviceArray): array of key representations with shape (L_k by d)
value (jax.interpreters.xla.DeviceArray): array of value representations with shape (L_k by d) where L_v = L_k
mask (jax.interpreters.xla.DeviceArray): attention-mask, gates attention with shape (L_q by L_k)
Returns:
jax.interpreters.xla.DeviceArray: Self-attention array for q, k, v arrays. (L_q by L_k)
"""
assert query.shape[-1] == key.shape[-1] == value.shape[
-1], "Embedding dimensions of q, k, v aren't all the same"
depth = query.shape[-1]
# Calculate scaled query key dot product according to formula above
dots = jnp.matmul(query, jnp.swapaxes(key, -1, -2)) / jnp.sqrt(depth)
if mask is not None: # The 'None' in this line does not need to be replaced
dots = jnp.where(mask, dots, jnp.full_like(dots, -1e9))
# Softmax formula implementation
logsumexp = trax.fastmath.logsumexp(dots, axis=-1, keepdims=True)
dots = jnp.exp(dots - logsumexp)
attention = jnp.matmul(dots, value)
return attention
def DotProductAttention(queries, keys, values, pos_emb, context_bias,
location_bias, mask, separate_cls, dropout, mode, rng):
"""Computes new activations via masked attention-weighted sum of values.
This function is the core of the attention mechanism. It:
- computes per-head attention weights from per-head `queries` and `keys`,
- applies `mask` to screen out positions that come from padding tokens,
- optionally applies dropout to attention weights, and
- uses attention weights to combine per-head `values` vectors.
Args:
queries: Per-head activations representing attention queries.
keys: Per-head activations representing attention keys.
values: Per-head activations to be combined by computed attention weights.
pos_emb: Per-head activations representing positional embeddings.
context_bias: Global context bias from Transformer XL's attention.
location_bias: Global location bias from Transformer XL's attention.
mask: Mask that distinguishes positions with real content vs. padding.
separate_cls: True/False if we separate_cls in calculations.
dropout: Probabilistic rate for dropout applied to attention strengths
(based on query-key pairs) before applying them to values.
mode: One of `'train'`, `'eval'`, or `'predict'`.
rng: Single-use random number generator (JAX PRNG key).
Returns:
Per-head activations resulting from masked per-head attention-weighted
sum of per-head values.
"""
d_feature = queries.shape[-1]
keys_len, queries_len = keys.shape[-2], queries.shape[-2]
funnel_factor, is_upsampling = calc_funnel_ratio(keys_len, queries_len)
ac = jnp.einsum('bnid,bnjd->bnij', queries + context_bias, keys)
bd = jnp.einsum('bnid,jnd->bnij', queries + location_bias, pos_emb)
if mode != 'predict':
bd = _fast_matrix_shift(bd, funnel_factor, is_upsampling)
if separate_cls:
# Masking out location part of attention for cls token
bd = bd.at[:, :, :, 0].set(0)
bd = bd.at[:, :, 0, :].set(0)
dots = (ac + bd) / jnp.sqrt(d_feature)
if mask is not None:
dots = jnp.where(mask, dots, jnp.full_like(dots, -1e9))
# Softmax.
dots = jnp.exp(dots - fastmath.logsumexp(dots, axis=-1, keepdims=True))
if dropout >= 1.0:
raise ValueError('Dropout rates must be lower than 1.')
if dropout is not None and dropout > 0.0 and mode == 'train':
keep = fastmath.random.bernoulli(rng, 1.0 - dropout, dots.shape)
dots = jnp.where(keep, dots / (1.0 - dropout), jnp.zeros_like(dots))
out = jnp.matmul(dots, values)
out = out.astype(jnp.float32)
dots = dots.astype(jnp.float32)
return out, dots
def _per_head_attention(queries, keys, values, mask, dropout, mode, rng):
"""Computes new per-head activations via scaled dot-product attention.
This function is the core of the attention mechanism. Given per-head
``queries`` (Q), ``keys`` (K), ``values`` (V), and ``mask``, it:
- computes the scaled dot product of each Q-K pair;
- applies ``mask`` to screen out positions that come from padding tokens
(indicated by 0 value);
- [in ``'train'`` mode] applies dropout to Q-K dot products;
- computes Q-K attention strengths using a per-query softmax of the Q-K dot
products; and
- for each query position, combines V vectors according to the Q-K
attention strengths.
Args:
queries: Per-head activations representing attention queries.
keys: Per-head activations representing attention keys.
values: Per-head activations to be combined by computed attention strengths.
mask: Mask that distinguishes positions with real content vs. padding.
dropout: Probababilistic rate for attention dropout, which overrides
(sets to zero) some attention strengths derived from query-key
matching. As a result, on a given forward pass, some value vectors
don't contribute to the output, analogous to how regular dropout can
cause some node activations to be ignored. Applies only in ``'train'``
mode.
mode: One of ``'train'``, ``'eval'``, or ``'predict'``.
rng: Single-use random number generator (JAX PRNG key).
Returns:
Tuple of (activations, attn_strengths), where activations are new per-head
activation vectors and attn_strengths is a matrix of per-head attention
strengths.
"""
if dropout >= 1.0:
raise ValueError(f'Dropout rate ({dropout}) must be lower than 1.')
d_feature = queries.shape[-1]
dots = jnp.matmul(queries, jnp.swapaxes(keys, -1, -2)) / jnp.sqrt(d_feature)
if mask is not None:
dots = jnp.where(mask,
dots,
jnp.full_like(dots, -1e9))
attn_strengths = (
jnp.exp(dots - fastmath.logsumexp(dots, axis=-1, keepdims=True)))
if dropout is not None and dropout > 0.0 and mode == 'train':
keep = fastmath.random.bernoulli(rng, 1.0 - dropout, attn_strengths.shape)
attn_strengths = jnp.where(keep,
attn_strengths / (1.0 - dropout),
jnp.zeros_like(attn_strengths))
activations = jnp.matmul(attn_strengths, values).astype(jnp.float32)
attn_strengths = attn_strengths.astype(jnp.float32)
return activations, attn_strengths
def DotProductAttention(queries, keys, values, mask, dropout, mode, rng):
"""Computes new activations via masked attention-weighted sum of values.
This function is the core of the attention mechanism. It:
- computes per-head attention weights from per-head `queries` and `keys`,
- applies `mask` to screen out positions that come from padding tokens,
- optionally applies dropout to attention weights, and
- uses attention weights to combine per-head `values` vectors.
Args:
queries: Per-head activations representing attention queries.
keys: Per-head activations representing attention keys.
values: Per-head activations to be combined by computed attention weights.
mask: Mask that distinguishes positions with real content vs. padding.
dropout: Probababilistic rate for dropout applied to attention strengths
(based on query-key pairs) before applying them to values.
mode: One of `'train'`, `'eval'`, or `'predict'`.
rng: Single-use random number generator (JAX PRNG key).
Returns:
Per-head activations resulting from masked per-head attention-weighted
sum of per-head values.
"""
d_feature = queries.shape[-1]
dots = jnp.matmul(queries, jnp.swapaxes(keys, -1, -2)) / jnp.sqrt(d_feature)
if mask is not None:
# TODO(kitaev): workaround for https://github.com/google/jax/issues/850
# We must ensure that both mask and the -1e9 constant have a data dependency
# on the input. Broadcasted copies of these use a lot of memory, so they
# should be computed at runtime (rather than being global constants).
if fastmath.is_backend(fastmath.Backend.JAX):
mask = jax.lax.tie_in(dots, mask)
# JAX's `full_like` already ties in -1e9 to dots.
dots = jnp.where(mask, dots, jnp.full_like(dots, -1e9))
# Softmax.
dots = jnp.exp(dots - fastmath.logsumexp(dots, axis=-1, keepdims=True))
if dropout >= 1.0:
raise ValueError('Dropout rates must be lower than 1.')
if dropout is not None and dropout > 0.0 and mode == 'train':
keep = fastmath.random.bernoulli(rng, 1.0 - dropout, dots.shape)
dots = jnp.where(keep, dots / (1.0 - dropout), jnp.zeros_like(dots))
out = jnp.matmul(dots, values)
out = out.astype(jnp.float32)
dots = dots.astype(jnp.float32)
return out, dots
def DotProductAttention(queries, keys, values, mask, dropout, mode, rng):
"""Computes new activations via masked attention-weighted sum of values.
This function is the core of the attention mechanism. It:
- computes per-head attention weights from per-head ``queries`` and
``keys``,
- applies ``mask`` to screen out positions that come from padding tokens,
- optionally applies dropout to attention weights, and
- uses attention weights to combine per-head ``values`` vectors.
Args:
queries: Per-head activations representing attention queries.
keys: Per-head activations representing attention keys.
values: Per-head activations to be combined by computed attention weights.
mask: Mask that distinguishes positions with real content vs. padding.
dropout: Probababilistic rate for attention dropout, which overrides
(sets to zero) some attention strengths derived from query-key
matching. As a result, on a given forward pass, some value vectors
don't contribute to the output, analogous to how regular dropout can
cause some node activations to be ignored.
mode: One of ``'train'``, ``'eval'``, or ``'predict'``.
rng: Single-use random number generator (JAX PRNG key).
Returns:
Per-head activations resulting from masked per-head attention-weighted
sum of per-head values.
"""
d_feature = queries.shape[-1]
dots = jnp.matmul(queries, jnp.swapaxes(keys, -1,
-2)) / jnp.sqrt(d_feature)
if mask is not None:
dots = jnp.where(mask, dots, jnp.full_like(dots, -1e9))
# Softmax.
dots = jnp.exp(dots - fastmath.logsumexp(dots, axis=-1, keepdims=True))
if dropout >= 1.0:
raise ValueError('Dropout rates must be lower than 1.')
if dropout is not None and dropout > 0.0 and mode == 'train':
keep = fastmath.random.bernoulli(rng, 1.0 - dropout, dots.shape)
dots = jnp.where(keep, dots / (1.0 - dropout), jnp.zeros_like(dots))
out = jnp.matmul(dots, values)
out = out.astype(jnp.float32)
dots = dots.astype(jnp.float32)
return out, dots
def _calc_attn_scores(q, k):
ac = jnp.einsum('bnid,bnjd->bnij', q + context_bias, k)
bd = jnp.einsum('bnid,jnd->bnij', q + location_bias, pos_emb)
if mode != 'predict':
bd = _fast_matrix_shift(bd)
dots = (ac + bd) / jnp.sqrt(d_feature)
dots = jnp.where(mask, dots, jnp.full_like(dots, -1e9))
# Softmax.
dots = jnp.exp(dots - fastmath.logsumexp(dots, axis=-1, keepdims=True))
if dropout >= 1.0:
raise ValueError('Dropout rates must be lower than 1.')
if dropout is not None and dropout > 0.0 and mode == 'train':
keep = fastmath.random.bernoulli(rng, 1.0 - dropout, dots.shape)
dots = jnp.where(keep, dots / (1.0 - dropout), jnp.zeros_like(dots))
return dots
def DotProductAttention(query, key, value, mask):
assert query.shape[-1] == key.shape[-1] == value.shape[-1]
depth = query.shape[-1]
dots = jnp.matmul(query, jnp.swapaxes(key, -1, -2)) / jnp.sqrt(
depth) # Part of dot product formula
# Apply mask
if mask is not None:
dots = jnp.where(mask, dots, jnp.full_like(dots, -1e9))
# Rest of dot product attention formula
logsumexp = trax.fastmath.logsumexp(dots, axis=-1, keepdims=True)
dots = jnp.exp(dots - logsumexp)
attention = jnp.matmul(dots, value)
return attention
def DotProductAttention(query, key, value, mask):
"""Dot product self-attention.
Args:
query (jax.interpreters.xla.DeviceArray): array of query representations with shape (L_q by d)
key (jax.interpreters.xla.DeviceArray): array of key representations with shape (L_k by d)
value (jax.interpreters.xla.DeviceArray): array of value representations with shape (L_k by d) where L_v = L_k
mask (jax.interpreters.xla.DeviceArray): attention-mask, gates attention with shape (L_q by L_k)
Returns:
jax.interpreters.xla.DeviceArray: Self-attention array for q, k, v arrays. (L_q by L_k)
"""
assert query.shape[-1] == key.shape[-1] == value.shape[
-1], "Embedding dimensions of q, k, v aren't all the same"
# scaling down (Q. K) dot product with square root of depth
depth = query.shape[-1]
# Calculate scaled query key dot product according to formula above
dots = jnp.matmul(query, jnp.swapaxes(key, -1, -2)) / jnp.sqrt(depth)
# Apply the mask
if mask is not None:
dots = jnp.where(mask, dots, jnp.full_like(dots, -1e9))
# Softmax formula implementation
# Use trax.fastmath.logsumexp of dots to avoid underflow by division by large numbers
logsumexp = trax.fastmath.logsumexp(dots, axis=-1, keepdims=True)
# Note: softmax = e^(dots - logsumexp(dots)) = E^dots / sumexp(dots)
dots = jnp.exp(dots - logsumexp)
# Multiply dots by value to get self-attention
# Use jnp.matmul()
attention = jnp.matmul(dots, value)
return attention
