def SumLearnedPick(positions):
"""Get a pair (vec, pos) and pick new pos."""
succ_keys = positions[:-1, :]
succ_values = positions[1:, :]
subtract_1_keys = positions[1:, :]
subtract_1_values = positions[:-1, :]
l = int(positions.shape[0]) // 2
add_keys = np.array([
np.concatenate([positions[i, :], positions[j, :]]) for i in range(l)
for j in range(l)
])
add_values = np.array(
[positions[i + j, :] for i in range(l) for j in range(l)])
# TODO(lukaszkaiser): try this below: "for j in range(i) for i in range(2*l)"
sub_keys = np.array([
np.concatenate([positions[i, :], positions[j, :]]) for j in range(l)
for i in range(l)
])
sub_values = np.array(
[positions[max(i - j, 0), :] for j in range(l) for i in range(l)])
return tl.Serial(
tl.Dup(), tl.Dup(), tl.Dup(), tl.Dup(),
tl.Parallel(
LearnedQP(),
LearnedQP(keys=succ_keys, values=succ_values),
LearnedQP(keys=subtract_1_keys, values=subtract_1_values),
LearnedQP(keys=add_keys, values=add_values, binary=True),
LearnedQP(keys=sub_keys, values=sub_values, binary=True),
), Unnest(), SoftmaxBranches(n_branches=5))
def look_one_back(x):
# Output: pairs [ bin_i bin_{i-1} ] concatenated on the time axis.
if len(x.shape) == 2:
x_extra = np.concatenate([x[-1:, :], x[:-1, :]], axis=0)
return np.concatenate([x, x_extra], axis=1)
else:
assert len(x.shape) == 4
x_extra = np.concatenate([x[:, -1:, :, :], x[:, :-1, :, :]], axis=1)
return np.concatenate([x, x_extra], axis=2)
def hash_vectors(self, vecs, rng):
if self.bin_by_time:
# Instead of hashing, put chunks of consecutive items in the same bin.
# This exists as a sanity check for the other parts of this class.
return self.bin_vectors_by_time(vecs)
# See https://arxiv.org/pdf/1509.02897.pdf
# We sample a different random rotation for each batch element, head, and
# (crucially) each round of hashing. All of these are part of dimension 0
# of vecs. Applying multiple hashes to the same input is important because
# it increases the probability of being in the same bin as relevant items.
n_buckets = self.n_buckets_per_bin * self.n_bins
assert n_buckets % 2 == 0
rot_rng = rng
if self._one_rng:
rot_rng = jax.lax.tie_in(vecs, self._prng)
random_rotation = jax.random.normal(
rot_rng,
(vecs.shape[0], vecs.shape[-1], n_buckets // 2)).astype('float32')
# TODO(kitaev): making the vectors unit-length here is probably redundant.
# vecs = self.make_unit_length(vecs)
rng, subrng = backend.random.split(rng)
vecs = self.drop_for_hash(vecs, subrng)
rotated_vecs = np.matmul(vecs, random_rotation)
rotated_vecs = np.concatenate([rotated_vecs, -rotated_vecs], axis=-1)
bins = np.argmax(rotated_vecs, axis=-1)
return bins
def NewPositionalEncoding(x, positions=None, **kwargs):
"""Implements new positional encoding."""
del kwargs
x_length = np.shape(x)[1]
pos = np.array(positions)[np.newaxis, :x_length, :]
pos += np.zeros((np.shape(x)[0], 1, 1)) # Broadcast on batch.
res = np.concatenate([x, pos], axis=2)
return res
def ConcatenateN(xs, params, n=2, axis=-1, **kwargs):
"""Concatenate first N inputs (and output remainder as is if non-empty)."""
del params, kwargs
res = np.concatenate(xs[:n], axis)
rest = list(xs[n:])
if rest:
return tuple([res] + rest)
return res
def CopyHeadsPos(x, h=8, **unused_kwargs):
"""Mix x = (x, p) into x_h1, p_h1, x_h2, p_h2, ...."""
head_size = (x.shape[2] - h * POS_VECTOR_SIZE) // h
p = x[:, :, -h * POS_VECTOR_SIZE:]
res, idx = [], 0
for i in range(h):
res.append(x[:, :, idx:idx + head_size])
res.append(p[:, :, i * POS_VECTOR_SIZE:(i + 1) * POS_VECTOR_SIZE])
idx += head_size
return np.concatenate(res, axis=-1)
def MixHeadsPos(x, h=8, **unused_kwargs):
"""Mix x = (x0, p) into x0_h1, p, x0_h2, p, ...."""
head_size = (x.shape[2] - POS_VECTOR_SIZE) // h
p = x[:, :, -POS_VECTOR_SIZE:]
res, idx = [], 0
for _ in range(h):
res.append(x[:, :, idx:idx + head_size])
res.append(p)
idx += head_size
return np.concatenate(res, axis=-1)
def QueryPositionKV(x, keys=None, values=None, binary=False, **unused_kwargs):
"""Query a table with a position vector."""
if keys is None:
return x
k = np.array(keys)
v = np.array(values)
q = x
if binary:
q = np.concatenate([x, x], axis=-1)
return tl.DotProductAttention(q, k, v, None, None, None, None)
def ChunkedAttentionSelector(x, params, selector=None, **kwargs):
"""Select which chunks to attend to in chunked attention.
Args:
x: inputs, a list of elements of the form (q, k, v), mask for each chunk.
params: parameters (unused).
selector: a function from chunk_number -> list of chunk numbers that says
which other chunks should be appended to the given one (previous if None).
**kwargs: unused other arguments.
Returns:
a list of elements of the form (q, k', v', mask') where k', v' and mask' are
concatenations of k, v and identity-extended masks from selected chunks.
"""
del params, kwargs
selector = selector or (lambda x: [] if x < 1 else [x - 1])
triples, masks = zip(*x)
(queries, keys, values) = zip(*triples)
result = []
for i in range(len(x)):
selected = selector(i)
# Since keys and values are [batch, length, depth] we concatenate on axis=1.
# We also always include the current key or value at the end.
new_key_list = [keys[j] for j in selected]
new_key = np.concatenate(new_key_list + [keys[i]], axis=1)
new_value = np.concatenate([values[j] for j in selected] + [values[i]],
axis=1)
# Masks are (1, query-len, key-len) so we concatenate on axis=2.
new_mask_shapes = [(1, queries[i].shape[1], key.shape[1])
for key in new_key_list]
cur_mask = masks[i]
# Masks are all-1 for the added chunks (no masking).
new_mask_list = [
np.ones(s, dtype=cur_mask.dtype) for s in new_mask_shapes
]
# We still use the current (often causal) mask for the final chunk.
new_mask = np.concatenate(new_mask_list + [cur_mask], axis=2)
result.append((queries[i], new_key, new_value, new_mask))
return tuple(result)
def DiagonalGate(x, params, **kwargs):
"""Split channels in 3 parts. Shifts 1st and 3rd sections to left/right."""
del params
del kwargs
# x : [batch, 1, length, depth]
x = np.pad(
x, [(0, 0), (0, 0), (1, 1), (0, 0)], mode='constant', constant_values=0.0)
depth = x.shape[-1] // 3
assert 3 * depth == x.shape[-1], ('Depth must be divisible by 3', depth,
x.shape)
xs = [
x[:, :, :-2, :depth], x[:, :, 1:-1, depth:2 * depth],
x[:, :, 2:, 2 * depth:3 * depth]
]
return np.concatenate(xs, axis=3)
def hash_vectors(self, vecs, rng):
if self.bin_by_time:
# Instead of hashing, put chunks of consecutive items in the same bin.
# This exists as a sanity check for the other parts of this class.
return self.bin_vectors_by_time(vecs)
# See https://arxiv.org/pdf/1509.02897.pdf
assert self.n_bins % 2 == 0
random_rotation = jax.random.normal(
rng, (vecs.shape[-1], self.n_bins//2)).astype('float32')
# TODO(kitaev): making the vectors unit-length here is probably redundant.
vecs = self.make_unit_length(vecs)
rotated_vecs = np.matmul(vecs, random_rotation)
rotated_vecs = self.make_unit_length(rotated_vecs)
rotated_vecs = np.concatenate([rotated_vecs, -rotated_vecs], axis=-1)
bins = np.argmax(rotated_vecs, axis=-1)
return bins
def ShiftRight(x, **unused_kwargs):
"""Layer to shift the tensor to the right by padding on axis 1."""
if not isinstance(x, (list, tuple)): # non-chunked inputs
pad_widths = [(0, 0), (1, 0)]
padded = np.pad(x, pad_widths, mode='constant')
return padded[:, :-1]
# Handling chunked inputs. Recall that the list of chunks represents a big
# sequence (the concatenation of the chunks). We want to shift that sequence,
# so we put a 0 in the beginning of the first chunk and the last element of
# that chunk is used as the new first element of the next chunk, and so on.
padded = []
last_value = np.zeros_like(x[0][:, -1])
for chunk in x:
padded_chunk = np.concatenate([last_value[:, np.newaxis], chunk],
axis=1)
last_value = chunk[:, -1]
padded.append(padded_chunk[:, :-1])
return padded
def binned_attn(sqk, sv): # pylint: disable=invalid-name
"""Performs attention on sorted queries/keys/values."""
# Split off a "bin" axis so that attention only occurs whithin chunks.
bq_t = bkv_t = chunk_scalars(sjoint_t)
bqk = chunk_vectors(sqk)
bv = chunk_vectors(sv)
# Hashing operates on unit-length vectors. Unnormalized query vectors are
# fine because they effectively provide a learnable temperature for the
# attention softmax, but normalizing keys is needed so that similarity for
# the purposes of attention correctly corresponds to hash locality.
bq = bqk
bk = self.make_unit_length(bqk)
# Allow each chunk to attend within itself, and also one chunk back. Chunk
# boundaries might occur in the middle of a sequence of items from the
# same bin, so this increases the chances of attending to relevant items.
# TODO(kitaev): benchmark whether XLA pad operation is noticeably faster.
bk_extra = np.concatenate([bk[:, -1:, :, :], bk[:, :-1, :, :]],
axis=1)
bk = np.concatenate([bk, bk_extra], axis=2)
bv_extra = np.concatenate([bv[:, -1:, :, :], bv[:, :-1, :, :]],
axis=1)
bv = np.concatenate([bv, bv_extra], axis=2)
bkv_t_extra = np.concatenate([bkv_t[:, -1:, :], bkv_t[:, :-1, :]],
axis=1)
bkv_t = np.concatenate([bkv_t, bkv_t_extra], axis=2)
# Dot-product attention.
dots = np.matmul(bq, np.swapaxes(bk, -1, -2)) / np.sqrt(
bq.shape[-1])
# Causal masking
mask = jax.lax.convert_element_type(
jax.lax.lt(bq_t[:, :, :, None], bkv_t[:, :, None, :]),
np.float32)
dots = dots - 1e9 * mask
# Mask out attention to self except when no other targets are available.
self_mask = jax.lax.broadcasted_eye(dots.dtype, dots.shape, (2, 3))
self_mask = jax.lax.tie_in(dots, self_mask)
dots = dots - 32 * self_mask
# Softmax.
dots = np.exp(dots -
backend.logsumexp(dots, axis=-1, keepdims=True))
bo = np.matmul(dots, bv)
so = unchunk_vectors(bo)
return so
def hash_vectors(self, vecs, rng):
# See https://arxiv.org/pdf/1509.02897.pdf
# We sample a different random rotation for each round of hashing to
# decrease the probability of hash misses.
assert self.n_buckets % 2 == 0
random_rotations_shape = (
vecs.shape[-1],
self.n_hashes if self._rehash_each_round else 1,
self.n_buckets // 2)
rng = jax.lax.tie_in(vecs, rng)
rng, subrng = backend.random.split(rng)
random_rotations = jax.random.normal(
rng, random_rotations_shape).astype('float32')
# TODO(lukaszkaiser): the dropout mask will be used for all rounds of
# hashing, so it's shared between them. Check if that's what we want.
dropped_vecs = self.drop_for_hash(vecs, subrng)
rotated_vecs = np.einsum('tf,fhb->htb', dropped_vecs, random_rotations)
rotated_vecs = np.concatenate([rotated_vecs, -rotated_vecs], axis=-1)
if self._rehash_each_round:
buckets = np.argmax(rotated_vecs, axis=-1)
# buckets is now (self.n_hashes, seqlen). Next we add offsets so that
# bucket numbers from different hashing rounds don't overlap.
offsets = jax.lax.tie_in(buckets, np.arange(self.n_hashes))
offsets = np.reshape(offsets * self.n_buckets, (-1, 1))
buckets = np.reshape(buckets + offsets, (-1,))
else:
# In this configuration, we map each item to the top self.n_hashes buckets
rotated_vecs = np.squeeze(rotated_vecs, 0)
bucket_range = jax.lax.tie_in(vecs, np.arange(rotated_vecs.shape[-1]))
bucket_range = np.reshape(bucket_range, (1, -1))
bucket_range = np.broadcast_to(bucket_range, rotated_vecs.shape)
_, buckets = jax.lax.sort_key_val(
rotated_vecs, bucket_range, dimension=-1)
buckets = buckets[:, -self.n_hashes:]
buckets = np.reshape(np.moveaxis(buckets, 0, -1), (-1,))
return buckets
def CombineHeadsPos(x, h=8, **unused_kwargs):
"""Mix x = (x0, p0, ..., xH, pH) into x0, ...., xH, p_combined.
The positions are added as vectors.
Args:
x: input vector, concatenated (x0, p0, ..., xH, pH).
h: number of heads.
Returns:
the vector with combined positions.
"""
head_size = int((x.shape[2] / h) - POS_VECTOR_SIZE)
res, positions, idx = [], [], 0
for _ in range(h):
res.append(x[:, :, idx:idx + head_size])
idx += head_size
positions.append(x[:, :, idx:idx + POS_VECTOR_SIZE])
idx += POS_VECTOR_SIZE
combined_position = sum(positions)
res.append(combined_position)
return np.concatenate(res, axis=-1)
def hash_vectors(self, vecs, rng):
if self.bin_by_time:
# Instead of hashing, put chunks of consecutive items in the same bin.
# This exists as a sanity check for the other parts of this class.
return self.bin_vectors_by_time(vecs)
# See https://arxiv.org/pdf/1509.02897.pdf
# It's not clear whether sampling a different random rotation for each head
# and batch element matters here, but see MergedMultiHashedCausalAttention.
assert self.n_bins % 2 == 0
rot_rng = rng
if self._one_rng:
rot_rng = jax.lax.tie_in(vecs, self._prng)
random_rotation = jax.random.normal(
rot_rng, (vecs.shape[0], vecs.shape[-1],
self.n_bins // 2)).astype('float32')
# TODO(kitaev): making the vectors unit-length here is probably redundant.
vecs = self.make_unit_length(vecs)
rotated_vecs = np.matmul(vecs, random_rotation)
rotated_vecs = self.make_unit_length(rotated_vecs)
rotated_vecs = np.concatenate([rotated_vecs, -rotated_vecs], axis=-1)
bins = np.argmax(rotated_vecs, axis=-1)
return bins
def call(self, inputs, params=(), state=(), rng=None, **kwargs):
del params, kwargs
# We use the same vector as both a query and a key. For now we haven't
# adjusted any of the surrounding code, so we still get a separate "key"
# input that we ignore.
qk, _, v = inputs
seqlen = qk.shape[-2]
# qk/v are n_hashes*n_batch*n_heads, seqlen, d_head
# TODO(kitaev): is it faster to fuse this tiling into gather/scatter ops?
qk = np.tile(qk, (self.n_hashes, 1, 1))
v = np.tile(v, (self.n_hashes, 1, 1))
# bins are n_hashes*n_batch*n_heads, seqlen
# They specify which hash bucket the query/key/value vectors fall in.
bins = self.hash_vectors(qk, rng=rng)
# joint_t is n_hashes*n_batch*n_heads, seqlen
joint_t = jax.lax.tie_in(qk, np.arange(seqlen))
joint_t = np.reshape(joint_t, (1, seqlen))
joint_t = np.broadcast_to(joint_t, qk.shape[:-1])
assert int(
(self.n_buckets_per_bin * self.n_bins + 1) * seqlen
) < 2**31, (
'Potential 32-bit integer overflow; please double-check the code.')
joint_bins_and_t = seqlen * bins + joint_t
def chunk_scalars(x): # pylint: disable=invalid-name
return np.reshape(x, (x.shape[0], self.n_bins, -1))
def chunk_vectors(x): # pylint: disable=invalid-name
return np.reshape(x, (x.shape[0], self.n_bins, -1, x.shape[-1]))
def unchunk_vectors(x): # pylint: disable=invalid-name
return np.reshape(x, (x.shape[0], -1, x.shape[-1]))
# Sort everything by bin number, with a secondary sort by time
# (variables starting with "s" are sorted)
_, sjoint_t = jax.lax.sort_key_val(joint_bins_and_t,
joint_t,
dimension=-1)
_, undo_sort = jax.lax.sort_key_val(sjoint_t, joint_t, dimension=-1)
# TODO(kitaev): why does jax flag integer indices as differentiable?
# If we don't call stop_gradient here, custom gradients below won't work
# because the primitive functions close over "differentiable" variables.
sjoint_t = jax.lax.stop_gradient(sjoint_t)
undo_sort = jax.lax.stop_gradient(undo_sort)
# The backward pass of gather is in general a scatter operation, but we know
# we're dealing with permutations so we use gather for the backward pass
# too. This custom gradient should be about 2x faster than having jax infer
# one that uses scatter ops instead.
def permute_impl(vecs):
assert len(vecs.shape) == 3
return np.take_along_axis(vecs, sjoint_t[:, :, None], axis=-2)
def unpermute_impl(vecs):
assert len(vecs.shape) == 3
return np.take_along_axis(vecs, undo_sort[:, :, None], axis=-2)
@jax.custom_transforms
def permute(vecs):
return permute_impl(vecs)
def permute_vjp(vecs):
out_vecs = permute_impl(vecs)
def vjpfun(grad):
return (unpermute_impl(grad), )
return out_vecs, vjpfun
@jax.custom_transforms
def unpermute(vecs):
return unpermute_impl(vecs)
def unpermute_vjp(vecs):
out_vecs = unpermute_impl(vecs)
def vjpfun(grad):
return (permute_impl(grad), )
return out_vecs, vjpfun
jax.defvjp_all(permute, permute_vjp)
jax.defvjp_all(unpermute, unpermute_vjp)
sqk = permute(qk)
sv = permute(v)
# Split off a "bin" axis so that attention only occurs within chunks.
bq_t = bkv_t = chunk_scalars(sjoint_t)
bqk = chunk_vectors(sqk)
bv = chunk_vectors(sv)
# Hashing operates on unit-length vectors. Unnormalized query vectors are
# fine because they effectively provide a learnable temperature for the
# attention softmax, but normalizing keys is needed so that similarity for
# the purposes of attention correctly corresponds to hash locality.
bq = bqk
bk = self.make_unit_length(bqk)
# Allow each chunk to attend within itself, and also one chunk back. Chunk
# boundaries might occur in the middle of a sequence of items from the
# same bin, so this increases the chances of attending to relevant items.
# TODO(kitaev): benchmark whether XLA pad operation is noticeably faster.
bk_extra = np.concatenate([bk[:, -1:, :, :], bk[:, :-1, :, :]], axis=1)
bk = np.concatenate([bk, bk_extra], axis=2)
bv_extra = np.concatenate([bv[:, -1:, :, :], bv[:, :-1, :, :]], axis=1)
bv = np.concatenate([bv, bv_extra], axis=2)
bkv_t_extra = np.concatenate([bkv_t[:, -1:, :], bkv_t[:, :-1, :]],
axis=1)
bkv_t = np.concatenate([bkv_t, bkv_t_extra], axis=2)
# Dot-product attention.
dots = np.matmul(bq, np.swapaxes(bk, -1, -2)) / np.sqrt(bq.shape[-1])
# Causal masking
mask = jax.lax.convert_element_type(
jax.lax.lt(bq_t[:, :, :, None], bkv_t[:, :, None, :]), np.float32)
dots = dots - 1e9 * mask
# Mask out attention to self except when no other targets are available.
self_mask = jax.lax.broadcasted_eye(dots.dtype, dots.shape, (2, 3))
self_mask = jax.lax.tie_in(dots, self_mask)
dots = dots - 32 * self_mask
# Softmax.
dots_logsumexp = backend.logsumexp(dots, axis=-1, keepdims=True)
dots = np.exp(dots - dots_logsumexp)
if self._hard_k > 0:
top_k = np.sort(dots)[...,
-self._hard_k] # Get the top-kth weight.
top_k = jax.lax.stop_gradient(top_k)
dots -= top_k[..., np.newaxis] # Subtract (be 0 for lower ones).
dots = np.maximum(dots, 0)
dots_sum = np.sum(dots, axis=-1,
keepdims=True) # Sum to re-normalize.
dots_logsumexp += np.log(dots_sum) # Add it to the weight.
dots /= dots_sum # Re-normalize.
bo = np.matmul(dots, bv)
so = unchunk_vectors(bo)
slogits = unchunk_vectors(dots_logsumexp)
o = unpermute(so)
logits = unpermute(slogits)
o = np.reshape(o, (self.n_hashes, -1, seqlen, o.shape[-1]))
logits = np.reshape(logits, (self.n_hashes, -1, seqlen, 1))
probs = np.exp(logits -
backend.logsumexp(logits, axis=0, keepdims=True))
out = np.sum(o * probs, axis=0)
assert out.shape == inputs[2].shape
return out, state
def look_one_back(x):
if len(x.shape) == 2:
x_extra = np.concatenate([x[-1:, :], x[:-1, :]], axis=0)
else:
x_extra = np.concatenate([x[-1:, :, :], x[:-1, :, :]], axis=0)
return np.concatenate([x, x_extra], axis=1)
def apply_fun(params, inputs, **kwargs):
return np.concatenate(inputs, axis)
def single_call(self, qk, v, buckets, hash_rng=None):
# We use the same vector as both a query and a key.
seqlen = qk.shape[-2]
assert int(buckets.shape[0]) == self.n_hashes * seqlen
ticker = jax.lax.tie_in(qk, np.arange(self.n_hashes * seqlen))
buckets_and_t = seqlen * buckets + (ticker % seqlen)
buckets_and_t = jax.lax.stop_gradient(buckets_and_t)
# Hash-based sort ("s" at the start of variable names means "sorted")
sbuckets_and_t, sticker = jax.lax.sort_key_val(
buckets_and_t, ticker, dimension=-1)
_, undo_sort = jax.lax.sort_key_val(sticker, ticker, dimension=-1)
sbuckets_and_t = jax.lax.stop_gradient(sbuckets_and_t)
sticker = jax.lax.stop_gradient(sticker)
undo_sort = jax.lax.stop_gradient(undo_sort)
st = (sticker % seqlen)
sqk = np.take(qk, st, axis=0)
sv = np.take(v, st, axis=0)
# Split off a "bin" axis so that attention only occurs within chunks.
bq_t = bkv_t = np.reshape(st, (self.n_hashes * self.n_bins, -1))
bqk = np.reshape(sqk, (self.n_hashes * self.n_bins, -1, sqk.shape[-1]))
bv = np.reshape(sv, (self.n_hashes * self.n_bins, -1, sv.shape[-1]))
bq_buckets = bkv_buckets = np.reshape(
sbuckets_and_t // seqlen, (self.n_hashes * self.n_bins, -1))
# Hashing operates on unit-length vectors. Unnormalized query vectors are
# fine because they effectively provide a learnable temperature for the
# attention softmax, but normalizing keys is needed so that similarity for
# the purposes of attention correctly corresponds to hash locality.
bq = bqk
bk = self.make_unit_length(bqk)
# Allow each chunk to attend within itself, and also one chunk back. Chunk
# boundaries might occur in the middle of a sequence of items from the
# same bucket, so this increases the chances of attending to relevant items.
# TODO(kitaev): benchmark whether XLA pad operation is noticeably faster.
def look_one_back(x):
if len(x.shape) == 2:
x_extra = np.concatenate([x[-1:, :], x[:-1, :]], axis=0)
else:
x_extra = np.concatenate([x[-1:, :, :], x[:-1, :, :]], axis=0)
return np.concatenate([x, x_extra], axis=1)
bk = look_one_back(bk)
bv = look_one_back(bv)
bkv_t = look_one_back(bkv_t)
bkv_buckets = look_one_back(bkv_buckets)
# Dot-product attention.
dots = np.matmul(bq, np.swapaxes(bk, -1, -2)) / np.sqrt(bq.shape[-1])
# Causal masking
mask = jax.lax.convert_element_type(
jax.lax.lt(bq_t[:, :, None], bkv_t[:, None, :]),
np.float32)
dots = dots - 1e9 * mask
# Mask out attention to self except when no other targets are available.
self_mask = jax.lax.convert_element_type(
jax.lax.eq(bq_t[:, :, None], bkv_t[:, None, :]),
np.float32)
dots = dots - 1e5 * self_mask
# Mask out attention to other hash buckets.
if not self._attend_across_buckets:
bucket_mask = jax.lax.convert_element_type(
jax.lax.ne(bq_buckets[:, :, None], bkv_buckets[:, None, :]),
np.float32)
dots = dots - 1e7 * bucket_mask
# Don't double-count query-key pairs across multiple rounds of hashing.
# There are two possible strategies here. (1) The default is to count how
# many times a query-key pair is repeated, and to lower its log-prob
# correspondingly at each repetition. (2) When hard_k is set, the code
# instead masks all but the first occurence of each query-key pair.
# TODO(kitaev): is one strategy faster or more numerically stable?
if not self._allow_duplicate_attention:
locs1 = undo_sort // bq_t.shape[-1]
locs2 = (locs1 + 1) % (self.n_hashes * self.n_bins)
if not self._attend_across_buckets:
locs1 = buckets * (self.n_hashes * self.n_bins) + locs1
locs2 = buckets * (self.n_hashes * self.n_bins) + locs2
locs = np.moveaxis(np.concatenate([
np.reshape(locs1, (self.n_hashes, seqlen)),
np.reshape(locs2, (self.n_hashes, seqlen)),
], 0), 0, -1) # produces shape (seqlen, 2 * self.n_hashes)
slocs = np.take(locs, st, axis=0)
b_locs = np.reshape(
slocs, (self.n_hashes * self.n_bins, -1, 2 * self.n_hashes))
# Queries always use the primary location (based on locs1).
b_locs1 = b_locs[:, :, None, :self.n_hashes]
if self._hard_k > 0:
range_n_hashes = jax.lax.tie_in(b_locs, np.arange(self.n_hashes))
nouse_locs = (range_n_hashes[:, None] > range_n_hashes[None, :])
nouse_locs = 2 * nouse_locs - 1 # 1 = use, -1 = don't use
nouse_locs = np.reshape(
np.broadcast_to(nouse_locs[:, None, :],
(self.n_hashes, self.n_bins, self.n_hashes)),
(self.n_hashes * self.n_bins, 1, 1, self.n_hashes))
b_locs1 = b_locs1 * nouse_locs
bq_locs = np.broadcast_to(
b_locs1,
b_locs.shape[:2] + (2, self.n_hashes))
bq_locs = np.reshape(bq_locs, b_locs.shape)
bkv_locs = look_one_back(b_locs)
dup_counts = np.sum(
jax.lax.convert_element_type(
jax.lax.eq(bq_locs[:, :, None, :], bkv_locs[:, None, :, :]),
np.float32),
axis=-1)
assert dup_counts.shape == dots.shape
if self._hard_k > 0:
dots = dots - 1e7 * jax.lax.stop_gradient(dup_counts)
else:
dots = dots - jax.lax.stop_gradient(np.log(dup_counts + 1e-9))
# Each query only attends to the top k most relevant keys.
if self._hard_k > 0:
b_top_dots = np.sort(dots)[..., -self._hard_k:] # Get the top k dots.
b_top_dots = jax.lax.stop_gradient(b_top_dots)
s_top_dots = np.reshape(b_top_dots, (-1, self._hard_k))
top_dots = np.take(s_top_dots, undo_sort, axis=0)
merged_top_dots = np.moveaxis(
np.reshape(top_dots, (self.n_hashes, seqlen, self._hard_k)), 0, -1)
merged_top_dots = np.reshape(merged_top_dots, (seqlen, -1))
dots_thresh = np.sort(merged_top_dots)[:, -self._hard_k]
# It's possible to compute the partition function at this point, but right
# now this codepath isn't set up for backprop, and there might also be
# issues computing it this way if two dot-products are exactly equal.
sdots_thresh = dots_thresh[st]
bdots_thresh = np.reshape(sdots_thresh, (self.n_hashes * self.n_bins, -1))
bdots_thresh = jax.lax.stop_gradient(bdots_thresh)
top_k_mask = jax.lax.convert_element_type(
dots < bdots_thresh[..., None], np.float32)
dots = dots - 1e7 * jax.lax.stop_gradient(top_k_mask)
# Softmax.
dots_logsumexp = backend.logsumexp(dots, axis=-1, keepdims=True)
dots = np.exp(dots - dots_logsumexp)
bo = np.matmul(dots, bv)
so = np.reshape(bo, (-1, bo.shape[-1]))
slogits = np.reshape(dots_logsumexp, (-1,))
def unsort_for_output_impl(so, slogits):
o = np.take(so, undo_sort, axis=0)
# Sorting is considerably faster than gather, but first we need to get the
# XLA compiler to abandon the idea of fusing this sort with the input sort
# (which introduces a computation cycle and leads to a crash).
# TODO(kitaev): remove "sticker_" variable if XLA is fixed.
sticker_ = sticker + jax.lax.convert_element_type(
slogits[0] > 0, sticker.dtype)
_, logits = jax.lax.sort_key_val(sticker_, slogits, dimension=-1)
return o, logits
def unsort_for_output_vjp(so, slogits):
"""Custom gradient for unsort_for_output."""
so = jax.lax.stop_gradient(so)
slogits = jax.lax.stop_gradient(slogits)
o, logits = unsort_for_output_impl(so, slogits)
def vjpfun(o_logits_grads):
so_grad = np.take(o_logits_grads[0], sticker, axis=0)
# TODO(kitaev): this exists to match the forward pass, but I'm not sure
# if it's actually required.
buckets_and_t_ = buckets_and_t + jax.lax.convert_element_type(
o_logits_grads[1][0] > 0, buckets_and_t.dtype)
_, slogits_grad = jax.lax.sort_key_val(
buckets_and_t_, o_logits_grads[1], dimension=-1)
return (so_grad, slogits_grad)
return (o, logits), vjpfun
unsort_for_output = jax.custom_transforms(unsort_for_output_impl)
jax.defvjp_all(unsort_for_output, unsort_for_output_vjp)
o, logits = unsort_for_output_impl(so, slogits)
if self.n_hashes == 1:
out = o
else:
o = np.reshape(o, (self.n_hashes, seqlen, o.shape[-1]))
logits = np.reshape(logits, (self.n_hashes, seqlen, 1))
probs = np.exp(logits - backend.logsumexp(logits, axis=0, keepdims=True))
out = np.sum(o * probs, axis=0)
assert out.shape == v.shape
return out
