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| 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 | |