File size: 5,563 Bytes
9b2107c |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 |
import math
import numpy as np
import torch
import torch.nn.functional as F
from torch.distributions.normal import Normal
def gaussian_loss(y_hat, y, log_std_min=-7.0):
assert y_hat.dim() == 3
assert y_hat.size(2) == 2
mean = y_hat[:, :, :1]
log_std = torch.clamp(y_hat[:, :, 1:], min=log_std_min)
# TODO: replace with pytorch dist
log_probs = -0.5 * (-math.log(2.0 * math.pi) - 2.0 * log_std - torch.pow(y - mean, 2) * torch.exp((-2.0 * log_std)))
return log_probs.squeeze().mean()
def sample_from_gaussian(y_hat, log_std_min=-7.0, scale_factor=1.0):
assert y_hat.size(2) == 2
mean = y_hat[:, :, :1]
log_std = torch.clamp(y_hat[:, :, 1:], min=log_std_min)
dist = Normal(
mean,
torch.exp(log_std),
)
sample = dist.sample()
sample = torch.clamp(torch.clamp(sample, min=-scale_factor), max=scale_factor)
del dist
return sample
def log_sum_exp(x):
"""numerically stable log_sum_exp implementation that prevents overflow"""
# TF ordering
axis = len(x.size()) - 1
m, _ = torch.max(x, dim=axis)
m2, _ = torch.max(x, dim=axis, keepdim=True)
return m + torch.log(torch.sum(torch.exp(x - m2), dim=axis))
# It is adapted from https://github.com/r9y9/wavenet_vocoder/blob/master/wavenet_vocoder/mixture.py
def discretized_mix_logistic_loss(y_hat, y, num_classes=65536, log_scale_min=None, reduce=True):
if log_scale_min is None:
log_scale_min = float(np.log(1e-14))
y_hat = y_hat.permute(0, 2, 1)
assert y_hat.dim() == 3
assert y_hat.size(1) % 3 == 0
nr_mix = y_hat.size(1) // 3
# (B x T x C)
y_hat = y_hat.transpose(1, 2)
# unpack parameters. (B, T, num_mixtures) x 3
logit_probs = y_hat[:, :, :nr_mix]
means = y_hat[:, :, nr_mix : 2 * nr_mix]
log_scales = torch.clamp(y_hat[:, :, 2 * nr_mix : 3 * nr_mix], min=log_scale_min)
# B x T x 1 -> B x T x num_mixtures
y = y.expand_as(means)
centered_y = y - means
inv_stdv = torch.exp(-log_scales)
plus_in = inv_stdv * (centered_y + 1.0 / (num_classes - 1))
cdf_plus = torch.sigmoid(plus_in)
min_in = inv_stdv * (centered_y - 1.0 / (num_classes - 1))
cdf_min = torch.sigmoid(min_in)
# log probability for edge case of 0 (before scaling)
# equivalent: torch.log(F.sigmoid(plus_in))
log_cdf_plus = plus_in - F.softplus(plus_in)
# log probability for edge case of 255 (before scaling)
# equivalent: (1 - F.sigmoid(min_in)).log()
log_one_minus_cdf_min = -F.softplus(min_in)
# probability for all other cases
cdf_delta = cdf_plus - cdf_min
mid_in = inv_stdv * centered_y
# log probability in the center of the bin, to be used in extreme cases
# (not actually used in our code)
log_pdf_mid = mid_in - log_scales - 2.0 * F.softplus(mid_in)
# tf equivalent
# log_probs = tf.where(x < -0.999, log_cdf_plus,
# tf.where(x > 0.999, log_one_minus_cdf_min,
# tf.where(cdf_delta > 1e-5,
# tf.log(tf.maximum(cdf_delta, 1e-12)),
# log_pdf_mid - np.log(127.5))))
# TODO: cdf_delta <= 1e-5 actually can happen. How can we choose the value
# for num_classes=65536 case? 1e-7? not sure..
inner_inner_cond = (cdf_delta > 1e-5).float()
inner_inner_out = inner_inner_cond * torch.log(torch.clamp(cdf_delta, min=1e-12)) + (1.0 - inner_inner_cond) * (
log_pdf_mid - np.log((num_classes - 1) / 2)
)
inner_cond = (y > 0.999).float()
inner_out = inner_cond * log_one_minus_cdf_min + (1.0 - inner_cond) * inner_inner_out
cond = (y < -0.999).float()
log_probs = cond * log_cdf_plus + (1.0 - cond) * inner_out
log_probs = log_probs + F.log_softmax(logit_probs, -1)
if reduce:
return -torch.mean(log_sum_exp(log_probs))
return -log_sum_exp(log_probs).unsqueeze(-1)
def sample_from_discretized_mix_logistic(y, log_scale_min=None):
"""
Sample from discretized mixture of logistic distributions
Args:
y (Tensor): :math:`[B, C, T]`
log_scale_min (float): Log scale minimum value
Returns:
Tensor: sample in range of [-1, 1].
"""
if log_scale_min is None:
log_scale_min = float(np.log(1e-14))
assert y.size(1) % 3 == 0
nr_mix = y.size(1) // 3
# B x T x C
y = y.transpose(1, 2)
logit_probs = y[:, :, :nr_mix]
# sample mixture indicator from softmax
temp = logit_probs.data.new(logit_probs.size()).uniform_(1e-5, 1.0 - 1e-5)
temp = logit_probs.data - torch.log(-torch.log(temp))
_, argmax = temp.max(dim=-1)
# (B, T) -> (B, T, nr_mix)
one_hot = to_one_hot(argmax, nr_mix)
# select logistic parameters
means = torch.sum(y[:, :, nr_mix : 2 * nr_mix] * one_hot, dim=-1)
log_scales = torch.clamp(torch.sum(y[:, :, 2 * nr_mix : 3 * nr_mix] * one_hot, dim=-1), min=log_scale_min)
# sample from logistic & clip to interval
# we don't actually round to the nearest 8bit value when sampling
u = means.data.new(means.size()).uniform_(1e-5, 1.0 - 1e-5)
x = means + torch.exp(log_scales) * (torch.log(u) - torch.log(1.0 - u))
x = torch.clamp(torch.clamp(x, min=-1.0), max=1.0)
return x
def to_one_hot(tensor, n, fill_with=1.0):
# we perform one hot encore with respect to the last axis
one_hot = torch.FloatTensor(tensor.size() + (n,)).zero_().type_as(tensor)
one_hot.scatter_(len(tensor.size()), tensor.unsqueeze(-1), fill_with)
return one_hot
|