File size: 6,312 Bytes
fc24795
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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
from encoder.params_model import *
from encoder.params_data import *
from scipy.interpolate import interp1d
from sklearn.metrics import roc_curve
from torch.nn.utils import clip_grad_norm_
from scipy.optimize import brentq
from torch import nn
import numpy as np
import torch


class SpeakerEncoder(nn.Module):
    def __init__(self, device, loss_device):
        super().__init__()
        self.loss_device = loss_device
        
        # Network defition
        self.lstm = nn.LSTM(input_size=mel_n_channels,
                            hidden_size=model_hidden_size, 
                            num_layers=model_num_layers, 
                            batch_first=True).to(device)
        self.linear = nn.Linear(in_features=model_hidden_size, 
                                out_features=model_embedding_size).to(device)
        self.relu = torch.nn.ReLU().to(device)
        
        # Cosine similarity scaling (with fixed initial parameter values)
        self.similarity_weight = nn.Parameter(torch.tensor([10.])).to(loss_device)
        self.similarity_bias = nn.Parameter(torch.tensor([-5.])).to(loss_device)

        # Loss
        self.loss_fn = nn.CrossEntropyLoss().to(loss_device)
        
    def do_gradient_ops(self):
        # Gradient scale
        self.similarity_weight.grad *= 0.01
        self.similarity_bias.grad *= 0.01
            
        # Gradient clipping
        clip_grad_norm_(self.parameters(), 3, norm_type=2)
    
    def forward(self, utterances, hidden_init=None):
        """
        Computes the embeddings of a batch of utterance spectrograms.
        
        :param utterances: batch of mel-scale filterbanks of same duration as a tensor of shape 
        (batch_size, n_frames, n_channels) 
        :param hidden_init: initial hidden state of the LSTM as a tensor of shape (num_layers, 
        batch_size, hidden_size). Will default to a tensor of zeros if None.
        :return: the embeddings as a tensor of shape (batch_size, embedding_size)
        """
        # Pass the input through the LSTM layers and retrieve all outputs, the final hidden state
        # and the final cell state.
        out, (hidden, cell) = self.lstm(utterances, hidden_init)
        
        # We take only the hidden state of the last layer
        embeds_raw = self.relu(self.linear(hidden[-1]))
        
        # L2-normalize it
        embeds = embeds_raw / (torch.norm(embeds_raw, dim=1, keepdim=True) + 1e-5)        

        return embeds
    
    def similarity_matrix(self, embeds):
        """
        Computes the similarity matrix according the section 2.1 of GE2E.

        :param embeds: the embeddings as a tensor of shape (speakers_per_batch, 
        utterances_per_speaker, embedding_size)
        :return: the similarity matrix as a tensor of shape (speakers_per_batch,
        utterances_per_speaker, speakers_per_batch)
        """
        speakers_per_batch, utterances_per_speaker = embeds.shape[:2]
        
        # Inclusive centroids (1 per speaker). Cloning is needed for reverse differentiation
        centroids_incl = torch.mean(embeds, dim=1, keepdim=True)
        centroids_incl = centroids_incl.clone() / (torch.norm(centroids_incl, dim=2, keepdim=True) + 1e-5)

        # Exclusive centroids (1 per utterance)
        centroids_excl = (torch.sum(embeds, dim=1, keepdim=True) - embeds)
        centroids_excl /= (utterances_per_speaker - 1)
        centroids_excl = centroids_excl.clone() / (torch.norm(centroids_excl, dim=2, keepdim=True) + 1e-5)

        # Similarity matrix. The cosine similarity of already 2-normed vectors is simply the dot
        # product of these vectors (which is just an element-wise multiplication reduced by a sum).
        # We vectorize the computation for efficiency.
        sim_matrix = torch.zeros(speakers_per_batch, utterances_per_speaker,
                                 speakers_per_batch).to(self.loss_device)
        mask_matrix = 1 - np.eye(speakers_per_batch, dtype=np.int)
        for j in range(speakers_per_batch):
            mask = np.where(mask_matrix[j])[0]
            sim_matrix[mask, :, j] = (embeds[mask] * centroids_incl[j]).sum(dim=2)
            sim_matrix[j, :, j] = (embeds[j] * centroids_excl[j]).sum(dim=1)
        
        ## Even more vectorized version (slower maybe because of transpose)
        # sim_matrix2 = torch.zeros(speakers_per_batch, speakers_per_batch, utterances_per_speaker
        #                           ).to(self.loss_device)
        # eye = np.eye(speakers_per_batch, dtype=np.int)
        # mask = np.where(1 - eye)
        # sim_matrix2[mask] = (embeds[mask[0]] * centroids_incl[mask[1]]).sum(dim=2)
        # mask = np.where(eye)
        # sim_matrix2[mask] = (embeds * centroids_excl).sum(dim=2)
        # sim_matrix2 = sim_matrix2.transpose(1, 2)
        
        sim_matrix = sim_matrix * self.similarity_weight + self.similarity_bias
        return sim_matrix
    
    def loss(self, embeds):
        """
        Computes the softmax loss according the section 2.1 of GE2E.
        
        :param embeds: the embeddings as a tensor of shape (speakers_per_batch, 
        utterances_per_speaker, embedding_size)
        :return: the loss and the EER for this batch of embeddings.
        """
        speakers_per_batch, utterances_per_speaker = embeds.shape[:2]
        
        # Loss
        sim_matrix = self.similarity_matrix(embeds)
        sim_matrix = sim_matrix.reshape((speakers_per_batch * utterances_per_speaker, 
                                         speakers_per_batch))
        ground_truth = np.repeat(np.arange(speakers_per_batch), utterances_per_speaker)
        target = torch.from_numpy(ground_truth).long().to(self.loss_device)
        loss = self.loss_fn(sim_matrix, target)
        
        # EER (not backpropagated)
        with torch.no_grad():
            inv_argmax = lambda i: np.eye(1, speakers_per_batch, i, dtype=np.int)[0]
            labels = np.array([inv_argmax(i) for i in ground_truth])
            preds = sim_matrix.detach().cpu().numpy()

            # Snippet from https://yangcha.github.io/EER-ROC/
            fpr, tpr, thresholds = roc_curve(labels.flatten(), preds.flatten())           
            eer = brentq(lambda x: 1. - x - interp1d(fpr, tpr)(x), 0., 1.)
            
        return loss, eer