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| import math | |
| import torch | |
| from torch import nn | |
| from torch.nn import functional as F | |
| import commons | |
| import modules | |
| import attentions | |
| import monotonic_align | |
| from torch.nn import Conv1d, ConvTranspose1d, Conv2d | |
| from torch.nn.utils import weight_norm, remove_weight_norm, spectral_norm | |
| from commons import init_weights, get_padding | |
| class StochasticDurationPredictor(nn.Module): | |
| def __init__(self, in_channels, filter_channels, kernel_size, p_dropout, n_flows=4, gin_channels=0): | |
| super().__init__() | |
| filter_channels = in_channels # it needs to be removed from future version. | |
| self.in_channels = in_channels | |
| self.filter_channels = filter_channels | |
| self.kernel_size = kernel_size | |
| self.p_dropout = p_dropout | |
| self.n_flows = n_flows | |
| self.gin_channels = gin_channels | |
| self.log_flow = modules.Log() | |
| self.flows = nn.ModuleList() | |
| self.flows.append(modules.ElementwiseAffine(2)) | |
| for i in range(n_flows): | |
| self.flows.append(modules.ConvFlow(2, filter_channels, kernel_size, n_layers=3)) | |
| self.flows.append(modules.Flip()) | |
| self.post_pre = nn.Conv1d(1, filter_channels, 1) | |
| self.post_proj = nn.Conv1d(filter_channels, filter_channels, 1) | |
| self.post_convs = modules.DDSConv(filter_channels, kernel_size, n_layers=3, p_dropout=p_dropout) | |
| self.post_flows = nn.ModuleList() | |
| self.post_flows.append(modules.ElementwiseAffine(2)) | |
| for i in range(4): | |
| self.post_flows.append(modules.ConvFlow(2, filter_channels, kernel_size, n_layers=3)) | |
| self.post_flows.append(modules.Flip()) | |
| self.pre = nn.Conv1d(in_channels, filter_channels, 1) | |
| self.proj = nn.Conv1d(filter_channels, filter_channels, 1) | |
| self.convs = modules.DDSConv(filter_channels, kernel_size, n_layers=3, p_dropout=p_dropout) | |
| if gin_channels != 0: | |
| self.cond = nn.Conv1d(gin_channels, filter_channels, 1) | |
| def forward(self, x, x_mask, w=None, g=None, reverse=False, noise_scale=1.0): | |
| x = torch.detach(x) | |
| x = self.pre(x) | |
| if g is not None: | |
| g = torch.detach(g) | |
| x = x + self.cond(g) | |
| x = self.convs(x, x_mask) | |
| x = self.proj(x) * x_mask | |
| if not reverse: | |
| flows = self.flows | |
| assert w is not None | |
| logdet_tot_q = 0 | |
| h_w = self.post_pre(w) | |
| h_w = self.post_convs(h_w, x_mask) | |
| h_w = self.post_proj(h_w) * x_mask | |
| e_q = torch.randn(w.size(0), 2, w.size(2)).to(device=x.device, dtype=x.dtype) * x_mask | |
| z_q = e_q | |
| for flow in self.post_flows: | |
| z_q, logdet_q = flow(z_q, x_mask, g=(x + h_w)) | |
| logdet_tot_q += logdet_q | |
| z_u, z1 = torch.split(z_q, [1, 1], 1) | |
| u = torch.sigmoid(z_u) * x_mask | |
| z0 = (w - u) * x_mask | |
| logdet_tot_q += torch.sum((F.logsigmoid(z_u) + F.logsigmoid(-z_u)) * x_mask, [1,2]) | |
| logq = torch.sum(-0.5 * (math.log(2*math.pi) + (e_q**2)) * x_mask, [1,2]) - logdet_tot_q | |
| logdet_tot = 0 | |
| z0, logdet = self.log_flow(z0, x_mask) | |
| logdet_tot += logdet | |
| z = torch.cat([z0, z1], 1) | |
| for flow in flows: | |
| z, logdet = flow(z, x_mask, g=x, reverse=reverse) | |
| logdet_tot = logdet_tot + logdet | |
| nll = torch.sum(0.5 * (math.log(2*math.pi) + (z**2)) * x_mask, [1,2]) - logdet_tot | |
| return nll + logq # [b] | |
| else: | |
| flows = list(reversed(self.flows)) | |
| flows = flows[:-2] + [flows[-1]] # remove a useless vflow | |
| z = torch.randn(x.size(0), 2, x.size(2)).to(device=x.device, dtype=x.dtype) * noise_scale | |
| for flow in flows: | |
| z = flow(z, x_mask, g=x, reverse=reverse) | |
| z0, z1 = torch.split(z, [1, 1], 1) | |
| logw = z0 | |
| return logw | |
| class DurationPredictor(nn.Module): | |
| def __init__(self, in_channels, filter_channels, kernel_size, p_dropout, gin_channels=0): | |
| super().__init__() | |
| self.in_channels = in_channels | |
| self.filter_channels = filter_channels | |
| self.kernel_size = kernel_size | |
| self.p_dropout = p_dropout | |
| self.gin_channels = gin_channels | |
| self.drop = nn.Dropout(p_dropout) | |
| self.conv_1 = nn.Conv1d(in_channels, filter_channels, kernel_size, padding=kernel_size//2) | |
| self.norm_1 = modules.LayerNorm(filter_channels) | |
| self.conv_2 = nn.Conv1d(filter_channels, filter_channels, kernel_size, padding=kernel_size//2) | |
| self.norm_2 = modules.LayerNorm(filter_channels) | |
| self.proj = nn.Conv1d(filter_channels, 1, 1) | |
| if gin_channels != 0: | |
| self.cond = nn.Conv1d(gin_channels, in_channels, 1) | |
| def forward(self, x, x_mask, g=None): | |
| x = torch.detach(x) | |
| if g is not None: | |
| g = torch.detach(g) | |
| x = x + self.cond(g) | |
| x = self.conv_1(x * x_mask) | |
| x = torch.relu(x) | |
| x = self.norm_1(x) | |
| x = self.drop(x) | |
| x = self.conv_2(x * x_mask) | |
| x = torch.relu(x) | |
| x = self.norm_2(x) | |
| x = self.drop(x) | |
| x = self.proj(x * x_mask) | |
| return x * x_mask | |
| class TextEncoder(nn.Module): | |
| def __init__(self, | |
| n_vocab, | |
| out_channels, | |
| hidden_channels, | |
| filter_channels, | |
| n_heads, | |
| n_layers, | |
| kernel_size, | |
| p_dropout): | |
| super().__init__() | |
| self.n_vocab = n_vocab | |
| self.out_channels = out_channels | |
| self.hidden_channels = hidden_channels | |
| self.filter_channels = filter_channels | |
| self.n_heads = n_heads | |
| self.n_layers = n_layers | |
| self.kernel_size = kernel_size | |
| self.p_dropout = p_dropout | |
| if self.n_vocab!=0: | |
| self.emb = nn.Embedding(n_vocab, hidden_channels) | |
| nn.init.normal_(self.emb.weight, 0.0, hidden_channels**-0.5) | |
| self.encoder = attentions.Encoder( | |
| hidden_channels, | |
| filter_channels, | |
| n_heads, | |
| n_layers, | |
| kernel_size, | |
| p_dropout) | |
| self.proj= nn.Conv1d(hidden_channels, out_channels * 2, 1) | |
| def forward(self, x, x_lengths): | |
| if self.n_vocab!=0: | |
| x = self.emb(x) * math.sqrt(self.hidden_channels) # [b, t, h] | |
| x = torch.transpose(x, 1, -1) # [b, h, t] | |
| x_mask = torch.unsqueeze(commons.sequence_mask(x_lengths, x.size(2)), 1).to(x.dtype) | |
| x = self.encoder(x * x_mask, x_mask) | |
| stats = self.proj(x) * x_mask | |
| m, logs = torch.split(stats, self.out_channels, dim=1) | |
| return x, m, logs, x_mask | |
| class ResidualCouplingBlock(nn.Module): | |
| def __init__(self, | |
| channels, | |
| hidden_channels, | |
| kernel_size, | |
| dilation_rate, | |
| n_layers, | |
| n_flows=4, | |
| gin_channels=0): | |
| super().__init__() | |
| self.channels = channels | |
| self.hidden_channels = hidden_channels | |
| self.kernel_size = kernel_size | |
| self.dilation_rate = dilation_rate | |
| self.n_layers = n_layers | |
| self.n_flows = n_flows | |
| self.gin_channels = gin_channels | |
| self.flows = nn.ModuleList() | |
| for i in range(n_flows): | |
| self.flows.append(modules.ResidualCouplingLayer(channels, hidden_channels, kernel_size, dilation_rate, n_layers, gin_channels=gin_channels, mean_only=True)) | |
| self.flows.append(modules.Flip()) | |
| def forward(self, x, x_mask, g=None, reverse=False): | |
| if not reverse: | |
| for flow in self.flows: | |
| x, _ = flow(x, x_mask, g=g, reverse=reverse) | |
| else: | |
| for flow in reversed(self.flows): | |
| x = flow(x, x_mask, g=g, reverse=reverse) | |
| return x | |
| class PosteriorEncoder(nn.Module): | |
| def __init__(self, | |
| in_channels, | |
| out_channels, | |
| hidden_channels, | |
| kernel_size, | |
| dilation_rate, | |
| n_layers, | |
| gin_channels=0): | |
| super().__init__() | |
| self.in_channels = in_channels | |
| self.out_channels = out_channels | |
| self.hidden_channels = hidden_channels | |
| self.kernel_size = kernel_size | |
| self.dilation_rate = dilation_rate | |
| self.n_layers = n_layers | |
| self.gin_channels = gin_channels | |
| self.pre = nn.Conv1d(in_channels, hidden_channels, 1) | |
| self.enc = modules.WN(hidden_channels, kernel_size, dilation_rate, n_layers, gin_channels=gin_channels) | |
| self.proj = nn.Conv1d(hidden_channels, out_channels * 2, 1) | |
| def forward(self, x, x_lengths, g=None): | |
| x_mask = torch.unsqueeze(commons.sequence_mask(x_lengths, x.size(2)), 1).to(x.dtype) | |
| x = self.pre(x) * x_mask | |
| x = self.enc(x, x_mask, g=g) | |
| stats = self.proj(x) * x_mask | |
| m, logs = torch.split(stats, self.out_channels, dim=1) | |
| z = (m + torch.randn_like(m) * torch.exp(logs)) * x_mask | |
| return z, m, logs, x_mask | |
| class Generator(torch.nn.Module): | |
| def __init__(self, initial_channel, resblock, resblock_kernel_sizes, resblock_dilation_sizes, upsample_rates, upsample_initial_channel, upsample_kernel_sizes, gin_channels=0): | |
| super(Generator, self).__init__() | |
| self.num_kernels = len(resblock_kernel_sizes) | |
| self.num_upsamples = len(upsample_rates) | |
| self.conv_pre = Conv1d(initial_channel, upsample_initial_channel, 7, 1, padding=3) | |
| resblock = modules.ResBlock1 if resblock == '1' else modules.ResBlock2 | |
| self.ups = nn.ModuleList() | |
| for i, (u, k) in enumerate(zip(upsample_rates, upsample_kernel_sizes)): | |
| self.ups.append(weight_norm( | |
| ConvTranspose1d(upsample_initial_channel//(2**i), upsample_initial_channel//(2**(i+1)), | |
| k, u, padding=(k-u)//2))) | |
| self.resblocks = nn.ModuleList() | |
| for i in range(len(self.ups)): | |
| ch = upsample_initial_channel//(2**(i+1)) | |
| for j, (k, d) in enumerate(zip(resblock_kernel_sizes, resblock_dilation_sizes)): | |
| self.resblocks.append(resblock(ch, k, d)) | |
| self.conv_post = Conv1d(ch, 1, 7, 1, padding=3, bias=False) | |
| self.ups.apply(init_weights) | |
| if gin_channels != 0: | |
| self.cond = nn.Conv1d(gin_channels, upsample_initial_channel, 1) | |
| def forward(self, x, g=None): | |
| x = self.conv_pre(x) | |
| if g is not None: | |
| x = x + self.cond(g) | |
| for i in range(self.num_upsamples): | |
| x = F.leaky_relu(x, modules.LRELU_SLOPE) | |
| x = self.ups[i](x) | |
| xs = None | |
| for j in range(self.num_kernels): | |
| if xs is None: | |
| xs = self.resblocks[i*self.num_kernels+j](x) | |
| else: | |
| xs += self.resblocks[i*self.num_kernels+j](x) | |
| x = xs / self.num_kernels | |
| x = F.leaky_relu(x) | |
| x = self.conv_post(x) | |
| x = torch.tanh(x) | |
| return x | |
| def remove_weight_norm(self): | |
| print('Removing weight norm...') | |
| for l in self.ups: | |
| remove_weight_norm(l) | |
| for l in self.resblocks: | |
| l.remove_weight_norm() | |
| class DiscriminatorP(torch.nn.Module): | |
| def __init__(self, period, kernel_size=5, stride=3, use_spectral_norm=False): | |
| super(DiscriminatorP, self).__init__() | |
| self.period = period | |
| self.use_spectral_norm = use_spectral_norm | |
| norm_f = weight_norm if use_spectral_norm == False else spectral_norm | |
| self.convs = nn.ModuleList([ | |
| norm_f(Conv2d(1, 32, (kernel_size, 1), (stride, 1), padding=(get_padding(kernel_size, 1), 0))), | |
| norm_f(Conv2d(32, 128, (kernel_size, 1), (stride, 1), padding=(get_padding(kernel_size, 1), 0))), | |
| norm_f(Conv2d(128, 512, (kernel_size, 1), (stride, 1), padding=(get_padding(kernel_size, 1), 0))), | |
| norm_f(Conv2d(512, 1024, (kernel_size, 1), (stride, 1), padding=(get_padding(kernel_size, 1), 0))), | |
| norm_f(Conv2d(1024, 1024, (kernel_size, 1), 1, padding=(get_padding(kernel_size, 1), 0))), | |
| ]) | |
| self.conv_post = norm_f(Conv2d(1024, 1, (3, 1), 1, padding=(1, 0))) | |
| def forward(self, x): | |
| fmap = [] | |
| # 1d to 2d | |
| b, c, t = x.shape | |
| if t % self.period != 0: # pad first | |
| n_pad = self.period - (t % self.period) | |
| x = F.pad(x, (0, n_pad), "reflect") | |
| t = t + n_pad | |
| x = x.view(b, c, t // self.period, self.period) | |
| for l in self.convs: | |
| x = l(x) | |
| x = F.leaky_relu(x, modules.LRELU_SLOPE) | |
| fmap.append(x) | |
| x = self.conv_post(x) | |
| fmap.append(x) | |
| x = torch.flatten(x, 1, -1) | |
| return x, fmap | |
| class DiscriminatorS(torch.nn.Module): | |
| def __init__(self, use_spectral_norm=False): | |
| super(DiscriminatorS, self).__init__() | |
| norm_f = weight_norm if use_spectral_norm == False else spectral_norm | |
| self.convs = nn.ModuleList([ | |
| norm_f(Conv1d(1, 16, 15, 1, padding=7)), | |
| norm_f(Conv1d(16, 64, 41, 4, groups=4, padding=20)), | |
| norm_f(Conv1d(64, 256, 41, 4, groups=16, padding=20)), | |
| norm_f(Conv1d(256, 1024, 41, 4, groups=64, padding=20)), | |
| norm_f(Conv1d(1024, 1024, 41, 4, groups=256, padding=20)), | |
| norm_f(Conv1d(1024, 1024, 5, 1, padding=2)), | |
| ]) | |
| self.conv_post = norm_f(Conv1d(1024, 1, 3, 1, padding=1)) | |
| def forward(self, x): | |
| fmap = [] | |
| for l in self.convs: | |
| x = l(x) | |
| x = F.leaky_relu(x, modules.LRELU_SLOPE) | |
| fmap.append(x) | |
| x = self.conv_post(x) | |
| fmap.append(x) | |
| x = torch.flatten(x, 1, -1) | |
| return x, fmap | |
| class MultiPeriodDiscriminator(torch.nn.Module): | |
| def __init__(self, use_spectral_norm=False): | |
| super(MultiPeriodDiscriminator, self).__init__() | |
| periods = [2,3,5,7,11] | |
| discs = [DiscriminatorS(use_spectral_norm=use_spectral_norm)] | |
| discs = discs + [DiscriminatorP(i, use_spectral_norm=use_spectral_norm) for i in periods] | |
| self.discriminators = nn.ModuleList(discs) | |
| def forward(self, y, y_hat): | |
| y_d_rs = [] | |
| y_d_gs = [] | |
| fmap_rs = [] | |
| fmap_gs = [] | |
| for i, d in enumerate(self.discriminators): | |
| y_d_r, fmap_r = d(y) | |
| y_d_g, fmap_g = d(y_hat) | |
| y_d_rs.append(y_d_r) | |
| y_d_gs.append(y_d_g) | |
| fmap_rs.append(fmap_r) | |
| fmap_gs.append(fmap_g) | |
| return y_d_rs, y_d_gs, fmap_rs, fmap_gs | |
| class SynthesizerTrn(nn.Module): | |
| """ | |
| Synthesizer for Training | |
| """ | |
| def __init__(self, | |
| n_vocab, | |
| spec_channels, | |
| segment_size, | |
| inter_channels, | |
| hidden_channels, | |
| filter_channels, | |
| n_heads, | |
| n_layers, | |
| kernel_size, | |
| p_dropout, | |
| resblock, | |
| resblock_kernel_sizes, | |
| resblock_dilation_sizes, | |
| upsample_rates, | |
| upsample_initial_channel, | |
| upsample_kernel_sizes, | |
| n_speakers=0, | |
| gin_channels=0, | |
| use_sdp=True, | |
| **kwargs): | |
| super().__init__() | |
| self.n_vocab = n_vocab | |
| self.spec_channels = spec_channels | |
| self.inter_channels = inter_channels | |
| self.hidden_channels = hidden_channels | |
| self.filter_channels = filter_channels | |
| self.n_heads = n_heads | |
| self.n_layers = n_layers | |
| self.kernel_size = kernel_size | |
| self.p_dropout = p_dropout | |
| self.resblock = resblock | |
| self.resblock_kernel_sizes = resblock_kernel_sizes | |
| self.resblock_dilation_sizes = resblock_dilation_sizes | |
| self.upsample_rates = upsample_rates | |
| self.upsample_initial_channel = upsample_initial_channel | |
| self.upsample_kernel_sizes = upsample_kernel_sizes | |
| self.segment_size = segment_size | |
| self.n_speakers = n_speakers | |
| self.gin_channels = gin_channels | |
| self.use_sdp = use_sdp | |
| self.enc_p = TextEncoder(n_vocab, | |
| inter_channels, | |
| hidden_channels, | |
| filter_channels, | |
| n_heads, | |
| n_layers, | |
| kernel_size, | |
| p_dropout) | |
| self.dec = Generator(inter_channels, resblock, resblock_kernel_sizes, resblock_dilation_sizes, upsample_rates, upsample_initial_channel, upsample_kernel_sizes, gin_channels=gin_channels) | |
| self.enc_q = PosteriorEncoder(spec_channels, inter_channels, hidden_channels, 5, 1, 16, gin_channels=gin_channels) | |
| self.flow = ResidualCouplingBlock(inter_channels, hidden_channels, 5, 1, 4, gin_channels=gin_channels) | |
| if use_sdp: | |
| self.dp = StochasticDurationPredictor(hidden_channels, 192, 3, 0.5, 4, gin_channels=gin_channels) | |
| else: | |
| self.dp = DurationPredictor(hidden_channels, 256, 3, 0.5, gin_channels=gin_channels) | |
| if n_speakers > 1: | |
| self.emb_g = nn.Embedding(n_speakers, gin_channels) | |
| def forward(self, x, x_lengths, y, y_lengths, sid=None): | |
| x, m_p, logs_p, x_mask = self.enc_p(x, x_lengths) | |
| if self.n_speakers > 0: | |
| g = self.emb_g(sid).unsqueeze(-1) # [b, h, 1] | |
| else: | |
| g = None | |
| z, m_q, logs_q, y_mask = self.enc_q(y, y_lengths, g=g) | |
| z_p = self.flow(z, y_mask, g=g) | |
| with torch.no_grad(): | |
| # negative cross-entropy | |
| s_p_sq_r = torch.exp(-2 * logs_p) # [b, d, t] | |
| neg_cent1 = torch.sum(-0.5 * math.log(2 * math.pi) - logs_p, [1], keepdim=True) # [b, 1, t_s] | |
| neg_cent2 = torch.matmul(-0.5 * (z_p ** 2).transpose(1, 2), s_p_sq_r) # [b, t_t, d] x [b, d, t_s] = [b, t_t, t_s] | |
| neg_cent3 = torch.matmul(z_p.transpose(1, 2), (m_p * s_p_sq_r)) # [b, t_t, d] x [b, d, t_s] = [b, t_t, t_s] | |
| neg_cent4 = torch.sum(-0.5 * (m_p ** 2) * s_p_sq_r, [1], keepdim=True) # [b, 1, t_s] | |
| neg_cent = neg_cent1 + neg_cent2 + neg_cent3 + neg_cent4 | |
| attn_mask = torch.unsqueeze(x_mask, 2) * torch.unsqueeze(y_mask, -1) | |
| attn = monotonic_align.maximum_path(neg_cent, attn_mask.squeeze(1)).unsqueeze(1).detach() | |
| w = attn.sum(2) | |
| if self.use_sdp: | |
| l_length = self.dp(x, x_mask, w, g=g) | |
| l_length = l_length / torch.sum(x_mask) | |
| else: | |
| logw_ = torch.log(w + 1e-6) * x_mask | |
| logw = self.dp(x, x_mask, g=g) | |
| l_length = torch.sum((logw - logw_)**2, [1,2]) / torch.sum(x_mask) # for averaging | |
| # expand prior | |
| m_p = torch.matmul(attn.squeeze(1), m_p.transpose(1, 2)).transpose(1, 2) | |
| logs_p = torch.matmul(attn.squeeze(1), logs_p.transpose(1, 2)).transpose(1, 2) | |
| z_slice, ids_slice = commons.rand_slice_segments(z, y_lengths, self.segment_size) | |
| o = self.dec(z_slice, g=g) | |
| return o, l_length, attn, ids_slice, x_mask, y_mask, (z, z_p, m_p, logs_p, m_q, logs_q) | |
| def infer(self, x, x_lengths, sid=None, noise_scale=1, length_scale=1, noise_scale_w=1., max_len=None): | |
| x, m_p, logs_p, x_mask = self.enc_p(x, x_lengths) | |
| if self.n_speakers > 0: | |
| g = self.emb_g(sid).unsqueeze(-1) # [b, h, 1] | |
| else: | |
| g = None | |
| if self.use_sdp: | |
| logw = self.dp(x, x_mask, g=g, reverse=True, noise_scale=noise_scale_w) | |
| else: | |
| logw = self.dp(x, x_mask, g=g) | |
| w = torch.exp(logw) * x_mask * length_scale | |
| w_ceil = torch.ceil(w) | |
| y_lengths = torch.clamp_min(torch.sum(w_ceil, [1, 2]), 1).long() | |
| y_mask = torch.unsqueeze(commons.sequence_mask(y_lengths, None), 1).to(x_mask.dtype) | |
| attn_mask = torch.unsqueeze(x_mask, 2) * torch.unsqueeze(y_mask, -1) | |
| attn = commons.generate_path(w_ceil, attn_mask) | |
| m_p = torch.matmul(attn.squeeze(1), m_p.transpose(1, 2)).transpose(1, 2) # [b, t', t], [b, t, d] -> [b, d, t'] | |
| logs_p = torch.matmul(attn.squeeze(1), logs_p.transpose(1, 2)).transpose(1, 2) # [b, t', t], [b, t, d] -> [b, d, t'] | |
| z_p = m_p + torch.randn_like(m_p) * torch.exp(logs_p) * noise_scale | |
| z = self.flow(z_p, y_mask, g=g, reverse=True) | |
| o = self.dec((z * y_mask)[:,:,:max_len], g=g) | |
| return o, attn, y_mask, (z, z_p, m_p, logs_p) | |
| def voice_conversion(self, y, y_lengths, sid_src, sid_tgt): | |
| assert self.n_speakers > 0, "n_speakers have to be larger than 0." | |
| g_src = self.emb_g(sid_src).unsqueeze(-1) | |
| g_tgt = self.emb_g(sid_tgt).unsqueeze(-1) | |
| z, m_q, logs_q, y_mask = self.enc_q(y, y_lengths, g=g_src) | |
| z_p = self.flow(z, y_mask, g=g_src) | |
| z_hat = self.flow(z_p, y_mask, g=g_tgt, reverse=True) | |
| o_hat = self.dec(z_hat * y_mask, g=g_tgt) | |
| return o_hat, y_mask, (z, z_p, z_hat) | |