File size: 4,799 Bytes
24829a1
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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
import numpy as np
import torch
import torch.nn.functional as F


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. / (num_classes - 1))
    cdf_plus = torch.sigmoid(plus_in)
    min_in = inv_stdv * (centered_y - 1. / (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. * 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. - 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. - inner_cond) * inner_inner_out
    cond = (y < -0.999).float()
    log_probs = cond * log_cdf_plus + (1. - cond) * inner_out

    log_probs = log_probs + F.log_softmax(logit_probs, -1)

    if reduce:
        return -torch.mean(log_sum_exp(log_probs))
    else:
        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): B x C x 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. - u))

    x = torch.clamp(torch.clamp(x, min=-1.), max=1.)

    return x


def to_one_hot(tensor, n, fill_with=1.):
    # we perform one hot encore with respect to the last axis
    one_hot = torch.FloatTensor(tensor.size() + (n,)).zero_()
    if tensor.is_cuda:
        one_hot = one_hot.cuda()
    one_hot.scatter_(len(tensor.size()), tensor.unsqueeze(-1), fill_with)
    return one_hot