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 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 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 forward_with_state(self,
inputs,
weights=base.EMPTY_WEIGHTS,
state=base.EMPTY_STATE,
rng=None,
**kwargs):
if self._mode in ('train', 'eval'):
x = inputs
symbol_size = np.shape(x)[1]
px = weights[:, :symbol_size, :]
if self._dropout == 0:
return (x + px, state)
else:
noise_shape = list(px.shape)
for dim in self._dropout_broadcast_dims:
noise_shape[dim] = 1
keep_prob = 1.0 - self._dropout
if backend.get_name() == 'jax':
keep_prob = jax.lax.tie_in(
x, np.full((), keep_prob, dtype=x.dtype))
keep = backend.random.bernoulli(rng, keep_prob,
tuple(noise_shape))
multiplier = keep.astype(x.dtype) / keep_prob
return (x + px * multiplier, state)
else:
assert self._mode == 'predict'
assert self._dropout == 0
# State in this class is only used for fast inference. In that case,
# the model is called with consecutive elements position-by-position.
# This positional encoding layer needs to store the index of the current
# position then and increment it on each call -- that's how state is used
# and updated below.
return (inputs + np.expand_dims(weights[:, state, :], 1),
state + 1)
