def build_odeint(ofunc, rtol=1.4e-8, atol=1.4e-8): """Return `f(y0, t, args) = odeint(ofunc(y, t, *args), y0, t, args)`. Given the function ofunc(y, t, *args), return the jitted function `f(y0, t, args) = odeint(ofunc(y, t, *args), y0, t, args)` with the VJP of `f` defined using `vjp_odeint`, where: `y0` is the initial condition of the ODE integration, `t` is the time course of the integration, and `*args` are all other arguments to `ofunc`. Args: ofunc: The function to be wrapped into an ODE integration. rtol: relative local error tolerance for solver. atol: absolute local error tolerance for solver. Returns: `f(y0, t, args) = odeint(ofunc(y, t, *args), y0, t, args)` """ ct_odeint = jax.custom_transforms( lambda y0, t, *args: odeint(ofunc, y0, t, *args, rtol=rtol, atol=atol)) v = lambda y0, t, *args: vjp_odeint( ofunc, y0, t, *args, rtol=rtol, atol=atol) jax.defvjp_all(ct_odeint, v) return jax.jit(ct_odeint)
def permute_via_sort(val, keys, inverse_keys, axis=0): """Permutation helper for LSH attention.""" # It is *not* safe to use jax.custom_vjp here (see permute_via_gather). keys = jax.lax.stop_gradient(keys) inverse_keys = jax.lax.stop_gradient(inverse_keys) def permute_impl(val): # On TPU, sorting scalars by key is faster than a gather. _, permuted = jax.lax.sort_key_val(keys, val, dimension=axis) return permuted def permute_vjp(val): permuted = permute_impl(jax.lax.stop_gradient(val)) def vjpfun(permuted_grad): _, val_grad = jax.lax.sort_key_val(inverse_keys, permuted_grad, dimension=axis) return (val_grad, ) return permuted, vjpfun permute = jax.custom_transforms(permute_impl) jax.defvjp_all(permute, permute_vjp) return permute(val)
def permute_via_gather(val, permutation, inverse_permutation, axis=0): """Permutation helper for LSH attention.""" # It is *not* safe to use jax.custom_vjp here. The most likely cause is that # it can't close over values: https://github.com/google/jax/issues/2676 # The error only occurs in some configurations (e.g. use_python_loop = True, # num_parallel_heads = 1) but not others. permutation = jax.lax.stop_gradient(permutation) inverse_permutation = jax.lax.stop_gradient(inverse_permutation) def permute_impl(val): return jnp.take(val, permutation, axis=axis) def permute_vjp(val): permuted = permute_impl(jax.lax.stop_gradient(val)) def vjpfun(permuted_grad): # JAX autodiff would synthesize a scatter operation because it doesn't # know that the indices are a permutatation. However on TPU, gathers are # faster than scatters (at least in the regime the LSH attention uses). return (jnp.take(permuted_grad, inverse_permutation, axis=axis), ) return permuted, vjpfun permute = jax.custom_transforms(permute_impl) jax.defvjp_all(permute, permute_vjp) return permute(val)
def test_odeint_2_linearize(): def odeint2(y0, ts, fargs): return odeint(f, y0, ts, fargs, atol=1e-8, rtol=1e-8) odeint2_prim = custom_transforms(odeint2).primitive def odeint2_jvp((y0, ts, fargs), (tan_y, tan_ts, tan_fargs)): return jvp_odeint(f, (y0, ts, fargs), (tan_y, tan_ts, tan_fargs))
def permute_via_gather(val, permutation, inverse_permutation, axis=0): """Permutation helper for LSH attention.""" def permute_impl(val): return np.take(val, permutation, axis=axis) def permute_vjp(val): permuted = permute_impl(jax.lax.stop_gradient(val)) def vjpfun(permuted_grad): # JAX autodiff would synthesize a scatter operation because it doesn't # know that the indices are a permutatation. However on TPU, gathers are # faster than scatters (at least in the regime the LSH attention uses). return (np.take(permuted_grad, inverse_permutation, axis=axis),) return permuted, vjpfun permute = jax.custom_transforms(permute_impl) jax.defvjp_all(permute, permute_vjp) return permute(val)
def _custom_grad(f_vjp, f_original): f_ = jax.custom_transforms(f_original) jax.defvjp_all(f_, f_vjp) return f_
def forward_unbatched(self, x, *, weights, state, update_state): w_q, w_v, w_o = weights q = np.matmul(x, w_q) v = np.matmul(x, w_v) if update_state: _, old_rng = state rng = jax.random.fold_in(old_rng, 0) hash_rng = jax.random.fold_in(rng, 1) buckets = self.hash_vectors(q, hash_rng) state = (buckets, rng) else: buckets, rng = state rng = jax.random.fold_in(rng, 2) seqlen = x.shape[0] assert int(buckets.shape[0]) == self.n_hashes * seqlen ticker = jax.lax.tie_in(x, 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) sq = np.take(q, st, axis=0) sv = np.take(v, st, axis=0) mask_fn = functools.partial(mask_self_attention, causal=self.causal, exclude_self=True) q_info = st so, slogits = attend( sq, k=None, v=sv, q_chunk_len=self.chunk_len, n_chunks_before=self.n_chunks_before, n_chunks_after=self.n_chunks_after, mask_fn=mask_fn, q_info=q_info, dropout=self.attention_dropout, rng=rng, ) 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: o = np.reshape(o, (self.n_hashes, seqlen, o.shape[-1])) logits = np.reshape(logits, (self.n_hashes, seqlen, 1)) probs = np.exp(logits - logsumexp(logits, axis=0, keepdims=True)) o = np.sum(o * probs, axis=0) assert o.shape == (seqlen, w_v.shape[-1]) out = np.matmul(o, w_o) return out, state
def single_call(self, qk, v, buckets, 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) if self._dropout > 0.0: # Dropout is broadcast across the bin dimension dropout_shape = (1, 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 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