def forward(self, x):
"""Executes this layer as part of a forward pass through the model.
Args:
x: Tensor of same shape and dtype as the input signature used to
initialize this layer.
Returns:
Tensor of same shape and dtype as the input.
"""
m1, m2, mb, w1, w2, b2 = self.weights
if self._mode != 'predict':
w1 = np.reshape(w1.T, (-1, self._d_ff))
w2 = np.reshape(w2, (self._d_ff, -1))
x_shape = x.shape
x = np.reshape(x,
[-1, x_shape[-1]]) # Easier to operate on flattened x.
# Q: should we add bias and/or put relu after the low-rank m1 dot?
mask_logits = np.dot(np.dot(x, m1), m2) + mb
mask_logits = np.reshape(mask_logits, [-1, self._d1, self._d2])
# Softmax.
mask_logsumexp = fastmath.logsumexp(mask_logits,
axis=-1,
keepdims=True)
log_mask = mask_logits - mask_logsumexp
mask = np.exp(log_mask)
# Gumbel-softmax with straight-through discretization.
rng1, rng2 = fastmath.random.split(self.rng, 2)
u = fastmath.random.uniform(rng1, mask.shape, np.float32, 1e-6,
1.0 - 1e-6)
g = -np.log(-np.log(u))
quant_mask = np.argmax(log_mask + g * self._temperature, axis=-1)
if self._mode == 'train':
# Tricks from Section 2.1 in https://arxiv.org/abs/1801.09797
quant_mask = metrics.one_hot(quant_mask, self._n_elements_in_block)
quant_mask = fastmath.stop_gradient(quant_mask)
quant_mask += mask - fastmath.stop_gradient(
mask) # straight-through
# We will sometimes (50% of the batches) use the soft-mask instead of
# the quantized mask to improve training stability (see the paper above).
# Q: is selecting 50% of batches the best? Other %? Mixed in-batch?
select = fastmath.random.uniform(rng2, (), np.float32, -1.0, 1.0)
quant_mask = np.where(select > 0.0, quant_mask, mask)
quant_mask = np.reshape(quant_mask, [-1, self._d_ff])
if self._mode == 'train':
# In training, run full matmul to get benefits from the above tricks.
mid = np.dot(x, w1) * quant_mask # [joint_batch, d_ff]
relu = np.where(mid <= 0, np.zeros_like(mid), mid)
res = np.dot(relu, w2) + b2
elif self._mode == 'predict':
# w1 = np.reshape(w1.T, (self._d1, self._d2, -1))
# w2 = np.reshape(w2, (self._d1, self._d2, -1))
# This implementation mimicks inference. It's not efficient for large
# size of joint_batch, but at inference that will be 1 most of the time.
# Shapes:
# quant_mask is [joint_batch, self._d1]
# w1 is [d_model, self._d1, self._d2]
# we'll index w1 with advanced numpy indexing, first range over
# self._d1 times the batch size, second range being quant_mask
batch_size = quant_mask.shape[0]
idx1 = np.array([np.arange(self._d1)] * batch_size)
# flatten indices and select from w1
idx1 = np.reshape(idx1, [-1])
idx2 = np.reshape(quant_mask, [-1])
w = w1[idx1,
idx2, :] # now we have per-element weights with batch dim
w = np.reshape(w, [batch_size, self._d1, -1])
mid = np.einsum('ai,aji->aj', x, w)
relu = np.where(mid <= 0, np.zeros_like(mid), mid)
# w2 is [self._d1, self._d2, d_model]
v = w2[idx1, idx2, :]
v = np.reshape(v, [batch_size, self._d1, -1])
res = np.einsum('ai,aij->aj', relu, v) + b2
else:
quant_mask = metrics.one_hot(quant_mask, self._n_elements_in_block)
quant_mask = np.reshape(quant_mask, [-1, self._d_ff])
mid = np.dot(x, w1) * quant_mask # [joint_batch, d_ff]
relu = np.where(mid <= 0, np.zeros_like(mid), mid)
res = np.dot(relu, w2) + b2
return np.reshape(res, x_shape) # un-flatten if needed
def forward(self, x):
"""Executes this layer as part of a forward pass through the model.
Args:
x: Tensor of same shape and dtype as the input signature used to
initialize this layer.
Returns:
Tensor of same shape and dtype as the input.
"""
m1, w1, w2, b2 = self.weights
x_shape = x.shape
x = np.reshape(x,
[-1, x_shape[-1]]) # Easier to operate on flattened x.
# Q: check if we need bias and/or put relu after the m1 dot?
mask_logits = np.dot(x, m1)
# Softmax.
mask_logsumexp = fastmath.logsumexp(mask_logits,
axis=-1,
keepdims=True)
log_mask = mask_logits - mask_logsumexp
mask = np.exp(log_mask)
# Gumbel-softmax with straight-through discretization.
# TODO(lukaszkaiser, chowdhery): Extract this block and share
rng1, rng2 = fastmath.random.split(self.rng, 2)
u = fastmath.random.uniform(rng1, mask.shape, np.float32, 1e-6,
1.0 - 1e-6)
g = -np.log(-np.log(u))
selected_experts = np.argmax(log_mask + g * self._temperature, axis=-1)
if self._mode == 'train':
# Tricks from Section 2.1 in https://arxiv.org/abs/1801.09797
quant_mask = metrics.one_hot(selected_experts, self._num_experts)
quant_mask = fastmath.stop_gradient(quant_mask)
quant_mask += mask - fastmath.stop_gradient(
mask) # straight-through
# We will sometimes (50% of the batches) use the soft-mask instead of
# the quantized mask to improve training stability (see the paper above).
# Q: is selecting 50% of batches the best? Other %? Mixed in-batch?
select = fastmath.random.uniform(rng2, (), np.float32, -1.0, 1.0)
quant_mask = np.where(select > 0.0, quant_mask, mask)
else:
quant_mask = metrics.one_hot(selected_experts, self._num_experts)
quant_mask = np.reshape(quant_mask, [-1, self._num_experts, 1])
quant_mask_shape = quant_mask.shape
batch_size = quant_mask.shape[0]
if self._mode == 'predict' and batch_size == 1:
# This implementation mimicks inference for batch_size 1.
start_idx = selected_experts[0] * self._n_elements_in_block
# w1 is [d_model, d_ff], w is [d_model, n_elements_in_block]
w = jax.lax.dynamic_slice(w1, [0, start_idx],
[w1.shape[0], self._n_elements_in_block])
mid = np.dot(x, w)
relu = np.where(mid <= 0, np.zeros_like(mid), mid)
# w2 is [d_ff, d_model], v is [n_elements_in_block, d_model]
v = jax.lax.dynamic_slice(
w2, [start_idx, 0], [self._n_elements_in_block, w2.shape[-1]])
v = np.reshape(v, [self._n_elements_in_block, -1])
res = np.dot(relu, v) + b2
else:
expanded_mask = np.broadcast_to(
quant_mask, (quant_mask_shape[0], quant_mask.shape[1],
self._n_elements_in_block))
expanded_mask = np.reshape(expanded_mask, (-1, self._d_ff))
mid = np.dot(x, w1) * expanded_mask # [joint_batch, d_ff]
relu = np.where(mid <= 0, np.zeros_like(mid), mid)
res = np.dot(relu, w2) + b2
return np.reshape(res, x_shape) # un-flatten if needed
def entropy(self, inputs):
(_, std) = self._params(inputs)
return jnp.sum(jnp.exp(std) + .5 * jnp.log(2.0 * jnp.pi * jnp.e),
axis=-1)
def f(model_output, targets): # pylint: disable=invalid-name
probabilities = fastmath.expit(model_output)
binary_entropies = -(targets * jnp.log(probabilities) + (1 - targets) *
(jnp.log(1 - probabilities)))
return jnp.average(binary_entropies)
def Log():
"""Returns a layer that computes the element-wise logarithm of a tensor."""
return Fn('Log', lambda x: jnp.log(x)) # pylint: disable=unnecessary-lambda
def entropy(self, log_probs):
del log_probs # would be helpful if self._std was learnable
return jnp.exp(self._std) + .5 * jnp.log(2.0 * jnp.pi * jnp.e)
def gumbel_sample(log_probs, temperature=1.0):
"""Gumbel sampling from a categorical distribution."""
u = numpy.random.uniform(low=1e-6, high=1.0 - 1e-6, size=log_probs.shape)
g = -np.log(-np.log(u))
return np.argmax(log_probs + g * temperature, axis=-1)