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)
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 call(self, x, params, **kwargs):
del kwargs
return np.take(params, x, axis=0)
def call(self, params, inputs, **kwargs):
del kwargs
return np.take(params, inputs, axis=0)
def forward(self, x, params=(), state=(), **kwargs):
del kwargs
return np.take(params, x, axis=0), state
def apply_fun(params, inputs, **kwargs):
del kwargs
dense_embedding = params
return np.take(dense_embedding, inputs, axis=0)
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
