def DotProductAttention(query, key, value, mask, dropout, mode, rng):
"""Core dot product self-attention.
Args:
query: array of representations
key: array of representations
value: array of representations
mask: attention-mask, gates attention
dropout: float: dropout rate
mode: 'eval' or 'train': whether to use dropout
rng: JAX PRNGKey: subkey for disposable use
Returns:
Self attention for q, k, v arrays.
"""
depth = np.shape(query)[-1]
dots = np.matmul(query, np.swapaxes(key, -1, -2)) / np.sqrt(depth)
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 backend.get_name() == 'jax':
mask = jax.lax.tie_in(dots, mask)
dots = np.where(mask, dots, np.full_like(dots, -1e9))
# Softmax.
dots = np.exp(dots - backend.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 = backend.random.bernoulli(rng, 1.0 - dropout, dots.shape)
dots = np.where(keep, dots / (1.0 - dropout), np.zeros_like(dots))
out = np.matmul(dots, value)
return out
def SoftmaxBranches(x_list_in, n_branches=2, **unused_kwargs):
"""Softmax xs.
The input xs is a list of embeddings and weights of the form
w_1 e_1 .... w_n e_n (followed by optional rest that is preserved).
Args:
x_list_in: the input weights and embeddings.
n_branches: what part of the list to use.
Returns:
softmax(w) * e for the joint weights w and embeddings e.
"""
x_list, x_list_rest = x_list_in[:2 * n_branches], x_list_in[2 *
n_branches:]
softmax_activations = [x_list[2 * i] for i in range(n_branches)]
max_sa = softmax_activations[0]
for x in softmax_activations:
max_sa = np.maximum(max_sa, x)
softmax_activations = [x - max_sa for x in softmax_activations]
softmax_activations = [np.exp(x) for x in softmax_activations]
sum_sa = sum(softmax_activations)
softmax_activations = [x / sum_sa for x in softmax_activations]
res = sum([
x_list[2 * i + 1] * softmax_activations[i] for i in range(n_branches)
])
return tuple([res] + list(x_list_rest))
def forward_slice(query_slice, q_loop_idx, key, value): # pylint: disable=invalid-name
"""Forward pass for a subset of the query vectors."""
dots = np.matmul(query_slice, np.swapaxes(key, -1,
-2)) / np.sqrt(depth)
# Causal masking
mask = make_mask(dots.shape[-2], dots.shape[-1], q_loop_idx)
dots = dots - 1e9 * mask
# Softmax.
dots = np.exp(dots -
backend.logsumexp(dots, axis=-1, keepdims=True))
if self.dropout is not None and self.dropout > 0.0:
# Dropout is broadcast across the batch+head dimension
dropout_shape = (1, dots.shape[-2], dots.shape[-1])
slice_rng = jax.random.fold_in(rng, q_loop_idx)
keep_prob = jax.lax.tie_in(dots, 1.0 - self.dropout)
keep = backend.random.bernoulli(slice_rng, keep_prob,
dropout_shape)
multiplier = keep.astype(dots.dtype) / jax.lax.tie_in(
keep, keep_prob)
dots = dots * multiplier
out_slice = np.matmul(dots, value)
return out_slice
def DotProductAttention(query, key, value, mask, dropout, mode, rng):
"""Core dot product self-attention.
Args:
query: array of representations
key: array of representations
value: array of representations
mask: attention-mask, gates attention
dropout: float: dropout rate
mode: 'eval' or 'train': whether to use dropout
rng: JAX PRNGKey: subkey for disposable use
Returns:
Self attention for q, k, v arrays.
"""
depth = np.shape(query)[-1]
dots = np.matmul(query, np.swapaxes(key, -1, -2)) / np.sqrt(depth)
if mask is not None:
dots = np.where(mask, dots, -1e9)
# Softmax.
dots = np.exp(dots - backend.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 = backend.random.bernoulli(rng, 1.0 - dropout, dots.shape)
dots = np.where(keep, dots / (1.0 - dropout), 0)
out = np.matmul(dots, value)
return out
def binned_attn(sq, sk, sv):
"""Performs attention on sorted queries/keys/values."""
# Split off a "bin" axis so that attention only occurs whithin chunks.
bq_t = chunk_rank3(sq_t)
bkv_t = chunk_rank3(skv_t)
bq = chunk_rank4(sq)
bk = chunk_rank4(sk)
bv = chunk_rank4(sv)
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
# Softmax.
dots = np.exp(dots - dots.max(axis=-1, keepdims=True))
dots = dots / dots.sum(axis=-1, keepdims=True)
bo = np.matmul(dots, bv)
so = unchunk_rank4(bo)
return so
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 forward_slice(query_slice, q_loop_idx, key, value):
"""Forward pass for a subset of the query vectors."""
dots = np.matmul(query_slice, np.swapaxes(key, -1,
-2)) / np.sqrt(depth)
# Causal masking
mask = make_mask(dots.shape[-2], dots.shape[-1], q_loop_idx)
dots = dots - 1e9 * mask
# Softmax.
dots = np.exp(dots - dots.max(axis=-1, keepdims=True))
dots = dots / dots.sum(axis=-1, keepdims=True)
out_slice = np.matmul(dots, value)
return out_slice
def forward_slice(query_slice, q_loop_idx, key, value): # pylint: disable=invalid-name
"""Forward pass for a subset of the query vectors."""
if self._share_qk:
key = self.make_unit_length(key)
dots = np.matmul(
query_slice, np.swapaxes(key, -1, -2)) / np.sqrt(depth)
# Causal masking
mask = make_mask(dots.shape[-2], dots.shape[-1], q_loop_idx)
dots = dots - 1e9 * mask
# Mask out attention to self except when no other targets are available.
if self._share_qk:
self_mask = make_self_mask(dots.shape[-2], dots.shape[-1], q_loop_idx)
dots = dots - 1e5 * self_mask
# Softmax.
dots = np.exp(dots - backend.logsumexp(dots, axis=-1, keepdims=True))
if self.dropout is not None and self.dropout > 0.0:
# Dropout is broadcast across the batch+head dimension
dropout_shape = (1, dots.shape[-2], dots.shape[-1])
slice_rng = jax.random.fold_in(rng, q_loop_idx)
keep_prob = jax.lax.tie_in(dots, 1.0 - self.dropout)
keep = backend.random.bernoulli(slice_rng, keep_prob, dropout_shape)
multiplier = keep.astype(dots.dtype) / jax.lax.tie_in(keep, keep_prob)
dots = dots * multiplier
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) # Re-normalize.
dots /= dots_sum # Re-normalize.
out_slice = np.matmul(dots, value)
return out_slice
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 Sigmoid(x, **unused_kwargs):
return 1. / (1. + np.exp(-x))
def Softmax(x, params, axis=-1, **kwargs):
"""Apply softmax to x: exponentiate and normalize along the given axis."""
del params, kwargs
return np.exp(x - backend.logsumexp(x, axis, keepdims=True))
def Exp(x, **unused_kwargs):
return np.exp(x)
def Exp(params, x, **kwargs):
del params, kwargs
return np.exp(x)
def softmax(x, axis=-1):
"""Apply softmax to an array of logits, exponentiating and normalizing along an axis."""
unnormalized = np.exp(x - x.max(axis, keepdims=True))
return unnormalized / unnormalized.sum(axis, keepdims=True)
def _forward_train_eval(self, inputs, rng):
(inputs, original_len, n_bins) = self._pad_inputs(inputs)
q, k, v = inputs
seqlen = q.shape[-2]
# q/k/v are n_batch*n_heads, seqlen, d_head
# Time indices for causal masking.
t = jax.lax.tie_in(q, np.arange(seqlen))
# Split off a "bin" axis for chunks of consecutive items.
bq_t = np.reshape(t, (n_bins, -1))
bq = np.reshape(q, (q.shape[0], n_bins, -1, q.shape[-1]))
if self._share_qk:
bk = self.make_unit_length(bq)
else:
bk = np.reshape(k, (k.shape[0], n_bins, -1, k.shape[-1]))
bv = np.reshape(v, (v.shape[0], n_bins, -1, v.shape[-1]))
# Allow each chunk to attend within itself, and also one chunk back.
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)
bkv_t = look_one_back(bq_t)
bk = look_one_back(bk)
bv = look_one_back(bv)
# Dot-product attention.
dots = np.matmul(bq, np.swapaxes(bk, -1, -2)) / np.sqrt(bq.shape[-1])
# Causal masking based on the time indices.
mask = jax.lax.convert_element_type(
jax.lax.lt(bq_t[None, :, :, None], bkv_t[None, :, None, :]),
np.float32)
dots = dots - 1e9 * mask
# Mask out attention to self except when no other targets are available.
if self._share_qk:
self_mask = jax.lax.broadcasted_eye(dots.dtype, dots.shape, (2, 3))
self_mask = jax.lax.tie_in(dots, self_mask)
dots = dots - 1e5 * self_mask
if self.dropout > 0.0:
# Dropout is broadcast across the batch+head dimension
dropout_shape = (1, dots.shape[-3], dots.shape[-2], dots.shape[-1])
keep_prob = jax.lax.tie_in(dots, 1.0 - self.dropout)
keep = backend.random.bernoulli(rng, keep_prob, dropout_shape)
multiplier = keep.astype(dots.dtype) / jax.lax.tie_in(keep, keep_prob)
dots = dots * multiplier
# Softmax.
dots = np.exp(dots - backend.logsumexp(dots, axis=-1, keepdims=True))
bo = np.matmul(dots, bv)
output = np.reshape(bo, (bo.shape[0], -1, bo.shape[-1]))
assert output.shape == v.shape
return output[..., :original_len, :]
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
