def log_gaussian_pdf(x, mu, sigma): # pylint: disable=invalid-name
"""Compute log N(x | mu, sigma)."""
a = mu.shape[-1] * np.log(2 * np.pi)
_, b = np.linalg.slogdet(sigma)
y = np.linalg.solve(sigma, x - mu)
y = np.expand_dims(y, axis=-1)
xm = np.expand_dims(x - mu, axis=-2)
c = np.matmul(xm, y)
c = np.squeeze(np.squeeze(c, axis=-1), axis=-1)
return -0.5 * (a + b + c)
def log_gaussian_diag_pdf(x, mu, diag_sigma): # pylint: disable=invalid-name
"""Compute log N(x | mu, eye(diag_sigma))."""
a = mu.shape[-1] * np.log(2 * np.pi)
b = np.sum(np.log(diag_sigma), axis=-1)
y = x - mu / diag_sigma
y = np.expand_dims(y, axis=-1)
xm = np.expand_dims(x - mu, axis=-2)
c = np.matmul(xm, y)
c = np.squeeze(np.squeeze(c, axis=-1), axis=-1)
return -0.5 * (a + b + c)
def update(self, step, grads, params, slots, opt_params):
updates = []
learning_rate = opt_params["learning_rate"]
beta1 = opt_params["beta1"]
decay_rate = opt_params["decay_rate"]
clipping_threshold = opt_params["clipping_threshold"]
weight_decay_rate = opt_params["weight_decay_rate"]
epsilon1 = opt_params["epsilon1"]
epsilon2 = opt_params["epsilon2"]
decay_rate = self._decay_rate_pow(step, exponent=decay_rate)
update_scale = learning_rate
if self._multiply_by_parameter_scale:
update_scale *= np.maximum(np.sqrt(np.mean(params * params)),
epsilon2)
mixing_rate = 1.0 - decay_rate
grads_sqr = grads * grads + epsilon1
if self._factored and len(params.shape) >= 2:
v_row = slots.pop(0)
v_col = slots.pop(0)
new_v_row = decay_rate * v_row + mixing_rate * np.mean(grads_sqr,
axis=-1)
new_v_col = decay_rate * v_col + mixing_rate * np.mean(grads_sqr,
axis=-2)
updates.extend([new_v_row, new_v_col])
row_col_mean = np.mean(new_v_row, axis=-1, keepdims=True)
row_factor = (new_v_row / row_col_mean)**-0.5
col_factor = (new_v_col)**-0.5
y = (grads * np.expand_dims(row_factor, axis=-1) *
np.expand_dims(col_factor, axis=-2))
else:
v = slots.pop(0)
new_v = decay_rate * v + mixing_rate * grads_sqr
updates.append(new_v)
y = grads * (new_v)**-0.5
if self._do_clipping:
clipping_denom = (np.maximum(
1.0,
np.sqrt(np.mean(y * y)) / clipping_threshold))
y /= clipping_denom
subtrahend = update_scale * y
if self._do_momentum:
m = slots.pop(0)
new_m = beta1 * m + (1.0 - beta1) * subtrahend
subtrahend = new_m
updates.append(new_m)
new_params = (1 - weight_decay_rate) * params - subtrahend
# TODO(lukaszkaiser): why is the astype needed here? Check and correct.
return new_params.astype(params.dtype), updates
def make_target_mask(target, pad=0):
"""Create an attention mask to hide padding and future words."""
target_mask = (target != pad)[:, np.newaxis, :]
target_dtype = target_mask.dtype
target_mask = ((target_mask
& stax.causal_mask(target.shape[-1])).astype(target_dtype))
return np.expand_dims(target_mask, axis=1)
def update(self, step, grads, params, slots, opt_params):
updates = []
(learning_rate, beta1, decay_rate, clipping_threshold,
weight_decay_rate, epsilon1, epsilon2) = opt_params
decay_rate = self._decay_rate_pow(step, exponent=decay_rate)
update_scale = learning_rate
if self._multiply_by_parameter_scale:
update_scale *= np.maximum(np.sqrt(np.mean(params * params)),
epsilon2)
mixing_rate = 1.0 - decay_rate
grads_sqr = grads * grads + epsilon1
if self._factored and len(params.shape) >= 2:
v_row = slots.pop(0)
v_col = slots.pop(0)
new_v_row = decay_rate * v_row + mixing_rate * np.mean(grads_sqr,
axis=-1)
new_v_col = decay_rate * v_col + mixing_rate * np.mean(grads_sqr,
axis=-2)
updates.extend([new_v_row, new_v_col])
row_col_mean = np.mean(new_v_row, axis=-1, keepdims=True)
row_factor = (new_v_row / row_col_mean)**-0.5
col_factor = (new_v_col)**-0.5
y = (grads * np.expand_dims(row_factor, axis=-1) *
np.expand_dims(col_factor, axis=-2))
else:
v = slots.pop(0)
new_v = decay_rate * v + mixing_rate * grads_sqr
updates.append(new_v)
y = grads * (new_v)**-0.5
if self._do_clipping:
clipping_denom = (np.maximum(
1.0,
np.sqrt(np.mean(y * y)) / clipping_threshold))
y /= clipping_denom
subtrahend = update_scale * y
if self._do_momentum:
m = slots.pop(0)
new_m = beta1 * m + (1.0 - beta1) * subtrahend
subtrahend = new_m
updates.append(new_m)
new_params = (1 - weight_decay_rate) * params - subtrahend
return new_params, updates
def MakeTargetMask(target, pad=0):
"""Create an attention mask to hide padding and future words."""
target_mask = (target != pad)[:, np.newaxis, :]
target_dtype = target_mask.dtype
causal_mask = onp.tril(onp.ones((1, target.shape[-1], target.shape[-1]),
dtype=target_dtype),
k=0)
target_mask = target_mask & causal_mask
return np.expand_dims(target_mask, axis=1)
def forward(self, inputs, params=(), state=(), **kwargs):
if self._mode in ('train', 'eval'):
x = inputs
symbol_size = np.shape(x)[1]
return (x + params[:, :symbol_size, :], state)
else:
assert self._mode == 'predict'
# Fast inference: return consectutive elements of the encoding sequence,
# storing the index in state.
return (inputs + np.expand_dims(params[:, state, :], 1), state + 1)
def update(self, i, g, x, state):
updates = []
decay_rate = self._decay_rate(i)
update_scale = self._step_size(i)
if self._multiply_by_parameter_scale:
update_scale *= np.maximum(np.sqrt(np.mean(x * x)), self._epsilon2)
mixing_rate = 1.0 - decay_rate
g_sqr = g * g + self._epsilon1
if self._factored and len(x.shape) >= 2:
v_row = state.pop(0)
v_col = state.pop(0)
new_v_row = decay_rate * v_row + mixing_rate * np.mean(g_sqr, axis=-1)
new_v_col = decay_rate * v_col + mixing_rate * np.mean(g_sqr, axis=-2)
updates.extend([new_v_row, new_v_col])
row_col_mean = np.mean(new_v_row, axis=-1, keepdims=True)
row_factor = (new_v_row / row_col_mean)**-0.5
col_factor = (new_v_col)**-0.5
y = (
g * np.expand_dims(row_factor, axis=-1) *
np.expand_dims(col_factor, axis=-2))
else:
v = state.pop(0)
new_v = decay_rate * v + mixing_rate * g_sqr
updates.append(new_v)
y = g * (new_v)**-0.5
if self._clipping_threshold is not None:
clipping_denom = (
np.maximum(1.0,
np.sqrt(np.mean(y * y)) / self._clipping_threshold))
y /= clipping_denom
subtrahend = update_scale * y
if self._beta1:
m = state.pop(0)
new_m = self._beta1 * m + (1.0 - self._beta1) * subtrahend
subtrahend = new_m
updates.append(new_m)
new_x = x - subtrahend
return new_x, updates