def init(self, params):
shape = params.shape
slots = []
if self._factored and len(shape) >= 2:
v_row = np.zeros(shape[:-1], dtype=np.float32)
v_col = np.zeros(shape[:-2] + shape[-1:], dtype=np.float32)
slots.extend([v_row, v_col])
else:
v = np.zeros_like(params)
slots.append(v)
if self._do_momentum:
m = np.zeros_like(params)
slots.append(m)
return slots
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)
# JAX's `full_like` already ties in -1e9 to dots.
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 _update_diagonal(self, grads, params, m, v, opt_params):
learning_rate = opt_params['learning_rate']
momentum = opt_params['momentum']
v[0] += grads * grads
preconditioner = np.where(v[0] > 0, 1.0 / np.sqrt(v[0]),
np.zeros_like(v[0]))
preconditioned_grads = preconditioner * grads
m = (1 - momentum) * preconditioned_grads + momentum * m
params = params - (learning_rate * m).astype(params.dtype)
return params, (m, v)
def forward_and_backward(self,
inputs,
ct,
state=base.EMPTY_STATE,
new_state=base.EMPTY_STATE,
rng=None,
**kwargs):
del kwargs
output, _, (qk_ct,
v_ct) = self.batch_call_and_or_grad(inputs[0],
inputs[2],
ct=ct,
new_state=new_state,
rng=rng)
return output, (qk_ct, np.zeros_like(inputs[1]), v_ct)
def forward_with_state(self, x, weights=base.EMPTY_WEIGHTS,
state=base.EMPTY_STATE, rng=None, **kwargs):
"""Execute dropout."""
del kwargs
if self._mode != 'train':
return x, state
rate = self._initial_rate
if isinstance(state, dict) and self._name in state:
rate = state[self._name]
if rng is None:
msg = ('Dropout layer requires apply_fn to be called with a rng keyword '
'argument. That is, instead of `Dropout(weights, inputs)`, call '
'it like `Dropout(weights, inputs, rng=key)`.')
raise ValueError(msg)
keep = backend.random.bernoulli(rng, 1.0 - rate, x.shape)
return np.where(keep, x / (1.0 - rate), np.zeros_like(x)), state
def backward(self,
inputs,
output,
ct,
weights=base.EMPTY_WEIGHTS,
state=base.EMPTY_STATE,
new_state=base.EMPTY_STATE,
rng=None,
**kwargs):
del output, weights, state
_, _, (qk_ct, v_ct) = self.batch_call_and_or_grad(inputs[0],
inputs[2],
return_output=False,
ct=ct,
new_state=new_state,
rng=rng)
inputs_ct = (qk_ct, np.zeros_like(inputs[1]), v_ct)
return inputs_ct, ()
def _update_sketched(self, grads, params, m, v, opt_params):
"""Update for higher-rank parameters."""
learning_rate = opt_params['learning_rate']
momentum = opt_params['momentum']
shape = params.shape
rank = len(shape)
reshaped_accumulators = [np.reshape(v[i], self._expanded_shape(shape, i))
for i in range(rank)]
current_accumulator = self._minimum(reshaped_accumulators)
current_accumulator += grads * grads
accumulator_inv_sqrt = np.where(current_accumulator > 0.0,
1.0 / np.sqrt(current_accumulator),
np.zeros_like(current_accumulator))
preconditioned_gradient = grads * accumulator_inv_sqrt
m = (1.0 - momentum) * preconditioned_gradient + momentum * m
params = params - (learning_rate * m).astype(params.dtype)
for i in range(len(v)):
axes = list(range(int(i))) + list(range(int(i) + 1, rank))
dim_accumulator = np.amax(current_accumulator, axis=axes)
v[i] = dim_accumulator
return params, (m, v)
def forward_and_backward(self,
inputs,
ct,
state=base.EMPTY_STATE,
new_state=base.EMPTY_STATE,
rng=None,
**kwargs):
del state, new_state, kwargs
query, key, value = inputs
depth = np.shape(query)[-1]
do_backprop = ct is not None
# jax uses the term cotangent (ct) to refer to gradient signals, and
# vector-Jacobian product (vjp) for back-propagation through a layer.
def make_mask(N, M, k): # pylint: disable=invalid-name
"""Constructs a slice of the causal attention mask.
Args:
N: number of query positions
M: number of key positions
k: position of the initial query element
Returns:
N x M mask, where 1.0 indicates that attention is not allowed.
"""
x = jax.lax.tie_in(k, np.arange(N, dtype=np.int32))
y = jax.lax.tie_in(k, np.arange(M, dtype=np.int32))
mask = jax.lax.lt((jax.lax.broadcast_in_dim(
x, shape=(N, M), broadcast_dimensions=(0, )) + k),
jax.lax.broadcast(y, [N]))
mask = jax.lax.convert_element_type(mask, np.float32)
return mask
def make_self_mask(N, M, k): # pylint: disable=invalid-name
"""Masks out elements attending to self.
Args:
N: number of query positions
M: number of key positions
k: position of the initial query element
Returns:
N x M mask, where 1.0 indicates that attention is not allowed.
"""
x = jax.lax.tie_in(k, np.arange(N, dtype=np.int32))
y = jax.lax.tie_in(k, np.arange(M, dtype=np.int32))
mask = jax.lax.eq((jax.lax.broadcast_in_dim(
x, shape=(N, M), broadcast_dimensions=(0, )) + k),
jax.lax.broadcast(y, [N]))
mask = jax.lax.convert_element_type(mask, np.float32)
return mask
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 forward_and_vjp_slice(query_slice, q_loop_idx, key, value,
ct_slice): # pylint: disable=invalid-name
# Capture q_loop_idx to avoid calculated gradients wrt. it.
def forward_slice_with_q_loop_idx(query_slice, key, value): # pylint: disable=invalid-name
return forward_slice(query_slice, q_loop_idx, key, value)
output_slice, vjpfun = jax.vjp(forward_slice_with_q_loop_idx,
query_slice, key, value)
return output_slice, vjpfun(ct_slice)
q_loop_idx = np.zeros((), dtype=np.int32)
q_loop_max = query.shape[-2]
q_loop_stride = self._loop_stride
if q_loop_max == 1: # For abstract runs with unknown shapes.
q_loop_stride = 1
assert q_loop_max % q_loop_stride == 0, (
'Stride must evenly divide the number of query elements.')
out_accum = np.zeros_like(query)
if do_backprop:
query_ct_accum = np.zeros_like(query)
key_ct_accum = np.zeros_like(key)
value_ct_accum = np.zeros_like(value)
init_vals = (q_loop_idx, out_accum, query_ct_accum, key_ct_accum,
value_ct_accum)
else:
init_vals = (q_loop_idx, out_accum)
def cond_fun(vals): # pylint: disable=invalid-name
q_loop_idx = vals[0]
return jax.lax.lt(q_loop_idx, q_loop_max)
def body_fun(vals): # pylint: disable=invalid-name
"""Compute a slice of the attention mechanism."""
if do_backprop:
(q_loop_idx, out_accum, query_ct_accum, key_ct_accum,
value_ct_accum) = vals
else:
q_loop_idx, out_accum = vals
query_slice = jax.lax.dynamic_slice_in_dim(query,
q_loop_idx,
q_loop_stride,
axis=-2)
if do_backprop:
ct_slice = jax.lax.dynamic_slice_in_dim(ct,
q_loop_idx,
q_loop_stride,
axis=-2)
out_slice, partial_ct = forward_and_vjp_slice(
query_slice, q_loop_idx, key, value, ct_slice)
query_ct_accum = jax.lax.dynamic_update_slice_in_dim(
query_ct_accum, partial_ct[0], q_loop_idx, axis=-2)
key_ct_accum = key_ct_accum + partial_ct[1]
value_ct_accum = value_ct_accum + partial_ct[2]
else:
out_slice = forward_slice(query_slice, q_loop_idx, key, value)
out_accum = jax.lax.dynamic_update_slice_in_dim(out_accum,
out_slice,
q_loop_idx,
axis=-2)
q_loop_idx = q_loop_idx + q_loop_stride
if do_backprop:
return (q_loop_idx, out_accum, query_ct_accum, key_ct_accum,
value_ct_accum)
else:
return (q_loop_idx, out_accum)
final_vals = jax.lax.while_loop(cond_fun, body_fun, init_vals)
if not do_backprop:
return final_vals[1], None
else:
return final_vals[1], final_vals[2:]
def drop_for_hash(self, x, rng):
rate = self._drop_for_hash_rate
if self._mode == 'train' and rate > 0.0:
keep = backend.random.bernoulli(rng, 1.0 - rate, x.shape)
return np.where(keep, x / (1.0 - rate), np.zeros_like(x))
return x
def batch_call_and_or_grad(self,
qk,
v,
ct=None,
return_output=True,
new_state=None,
return_state=False,
rng=None):
assert return_output or ct is not None, 'No work to perform!'
if new_state is not None and new_state is not base.EMPTY_STATE:
buckets = new_state
else:
buckets = None
# The approach here is to perform attention for one batch element and head
# at a time. Note that there is absolutely no interaction across examples or
# heads: this layer has no parameters, and hashing patterns are also
# different across examples/heads. As a result, batching doesn't give any
# performance gains except in the case of accelerator under-utilization. We
# assume that hash-based attention will be applied primarily to long
# sequences, where unbatched attention for a single head has sufficient
# computation to fill up the accelerator.
batch_loop_idx = np.zeros((), dtype=np.int32)
batch_loop_max = qk.shape[0]
init_vals = (batch_loop_idx, )
if return_output:
out_accum = np.zeros_like(qk)
init_vals = init_vals + (out_accum, )
if return_state:
buckets_accum = np.zeros(
[qk.shape[0], self.n_hashes * qk.shape[1]], dtype=np.int32)
init_vals = init_vals + (buckets_accum, )
if ct is not None:
qk_ct_accum = np.zeros_like(qk)
v_ct_accum = np.zeros_like(v)
init_vals = init_vals + (qk_ct_accum, v_ct_accum)
def cond_fun(vals):
batch_loop_idx = vals[0]
return jax.lax.lt(batch_loop_idx, batch_loop_max)
def body_fun(vals):
"""Performs attention for a single batch element and head."""
batch_loop_idx = vals[0]
if self._prng is None:
hash_slice_rng = jax.random.fold_in(rng, batch_loop_idx)
hash_rng, slice_rng = backend.random.split(hash_slice_rng)
else:
# TODO(kitaev): Maybe use the same RNG across examples (but not heads)?
hash_rng = jax.random.fold_in(self._prng, batch_loop_idx)
slice_rng = jax.random.fold_in(rng, batch_loop_idx)
qk_slice = jax.lax.dynamic_index_in_dim(qk,
batch_loop_idx,
axis=0,
keepdims=False)
v_slice = jax.lax.dynamic_index_in_dim(v,
batch_loop_idx,
axis=0,
keepdims=False)
if buckets is None:
buckets_slice = self.hash_vectors(qk_slice, rng=hash_rng)
else:
buckets_slice = jax.lax.dynamic_index_in_dim(buckets,
batch_loop_idx,
axis=0,
keepdims=False)
if ct is None:
out_slice = self.single_call(qk_slice,
v_slice,
buckets_slice,
rng=slice_rng)
else:
def _do_single_call(qk_slice, v_slice):
return self.single_call(qk_slice,
v_slice,
buckets_slice,
rng=slice_rng)
ct_slice = jax.lax.dynamic_index_in_dim(ct,
batch_loop_idx,
axis=0,
keepdims=False)
out_slice, vjpfun = jax.vjp(_do_single_call, qk_slice, v_slice)
qk_ct_slice, v_ct_slice = vjpfun(ct_slice)
new_vals = (batch_loop_idx + 1, )
if return_output:
out_accum = vals[1]
out_accum = jax.lax.dynamic_update_index_in_dim(out_accum,
out_slice,
batch_loop_idx,
axis=0)
new_vals = new_vals + (out_accum, )
if return_state:
buckets_accum = vals[2]
buckets_accum = jax.lax.dynamic_update_index_in_dim(
buckets_accum, buckets_slice, batch_loop_idx, axis=0)
new_vals = new_vals + (buckets_accum, )
if ct is not None:
qk_ct_accum, v_ct_accum = vals[-2:]
qk_ct_accum = jax.lax.dynamic_update_index_in_dim(
qk_ct_accum, qk_ct_slice, batch_loop_idx, axis=0)
v_ct_accum = jax.lax.dynamic_update_index_in_dim(
v_ct_accum, v_ct_slice, batch_loop_idx, axis=0)
new_vals = new_vals + (qk_ct_accum, v_ct_accum)
return new_vals
final_vals = jax.lax.while_loop(cond_fun, body_fun, init_vals)
if return_output:
out = final_vals[1]
else:
out = None
if return_state:
state = final_vals[2]
else:
state = None
if ct is not None:
input_ct = final_vals[-2:]
else:
input_ct = None
return out, state, input_ct
def ParametricRelu(x, a=1., **unused_kwargs): return np.maximum(a * x, np.zeros_like(x))
def Relu(x, **unused_kwargs): return np.maximum(x, np.zeros_like(x))
def init(self, params):
vs = [np.zeros(sz, dtype=params.dtype) for sz in params.shape]
return (np.zeros_like(params), vs)
def init(self, params):
m = np.zeros_like(params)
v = np.zeros_like(params)
return m, v
def init(self, params):
return np.zeros_like(params)
