English
File size: 6,095 Bytes
5019d3f
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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
156
157
158
159
160
161
162
163
164
165
166
167
168
import torch
import math
import torch.nn.functional as F


def log_sum_exp(x, axis=None):
    """
    Log sum exp function
    Args:
        x: Input.
        axis: Axis over which to perform sum.
    Returns:
        torch.Tensor: log sum exp
    """
    x_max = torch.max(x, axis)[0]
    y = torch.log((torch.exp(x - x_max)).sum(axis)) + x_max
    return y


def get_positive_expectation(p_samples, measure='JSD', average=True):
    """
    Computes the positive part of a divergence / difference.
    Args:
        p_samples: Positive samples.
        measure: Measure to compute for.
        average: Average the result over samples.
    Returns:
        torch.Tensor
    """
    log_2 = math.log(2.)
    if measure == 'GAN':
        Ep = - F.softplus(-p_samples)
    elif measure == 'JSD':
        Ep = log_2 - F.softplus(-p_samples)
    elif measure == 'X2':
        Ep = p_samples ** 2
    elif measure == 'KL':
        Ep = p_samples + 1.
    elif measure == 'RKL':
        Ep = -torch.exp(-p_samples)
    elif measure == 'DV':
        Ep = p_samples
    elif measure == 'H2':
        Ep = torch.ones_like(p_samples) - torch.exp(-p_samples)
    elif measure == 'W1':
        Ep = p_samples
    else:
        raise ValueError('Unknown measurement {}'.format(measure))
    if average:
        return Ep.mean()
    else:
        return Ep


def get_negative_expectation(q_samples, measure='JSD', average=True):
    """
    Computes the negative part of a divergence / difference.
    Args:
        q_samples: Negative samples.
        measure: Measure to compute for.
        average: Average the result over samples.
    Returns:
        torch.Tensor
    """
    log_2 = math.log(2.)
    if measure == 'GAN':
        Eq = F.softplus(-q_samples) + q_samples
    elif measure == 'JSD':
        Eq = F.softplus(-q_samples) + q_samples - log_2
    elif measure == 'X2':
        Eq = -0.5 * ((torch.sqrt(q_samples ** 2) + 1.) ** 2)
    elif measure == 'KL':
        Eq = torch.exp(q_samples)
    elif measure == 'RKL':
        Eq = q_samples - 1.
    elif measure == 'DV':
        Eq = log_sum_exp(q_samples, 0) - math.log(q_samples.size(0))
    elif measure == 'H2':
        Eq = torch.exp(q_samples) - 1.
    elif measure == 'W1':
        Eq = q_samples
    else:
        raise ValueError('Unknown measurement {}'.format(measure))
    if average:
        return Eq.mean()
    else:
        return Eq


def batch_video_query_loss(video, query, match_labels, mask, measure='JSD'):
    """
        QV-CL module
        Computing the Contrastive Loss between the video and query.
        :param video: video rep (bsz, Lv, dim)
        :param query: query rep (bsz, dim)
        :param match_labels: match labels (bsz, Lv)
        :param mask: mask (bsz, Lv)
        :param measure: estimator of the mutual information
        :return: L_{qv}
    """
    # generate mask
    pos_mask = match_labels.type(torch.float32)  # (bsz, Lv)
    neg_mask = (torch.ones_like(pos_mask) - pos_mask) * mask  # (bsz, Lv)

    # compute scores
    query = query.unsqueeze(2)  # (bsz, dim, 1)
    res = torch.matmul(video, query).squeeze(2)  # (bsz, Lv)

    # computing expectation for the MI between the target moment (positive samples) and query.
    E_pos = get_positive_expectation(res * pos_mask, measure, average=False)
    E_pos = torch.sum(E_pos * pos_mask, dim=1) / (torch.sum(pos_mask, dim=1) + 1e-12)  # (bsz, )

    # computing expectation for the MI between clips except target moment (negative samples) and query.
    E_neg = get_negative_expectation(res * neg_mask, measure, average=False)
    E_neg = torch.sum(E_neg * neg_mask, dim=1) / (torch.sum(neg_mask, dim=1) + 1e-12)  # (bsz, )

    E = E_neg - E_pos  # (bsz, )
    # return torch.mean(E)
    return E


def batch_video_video_loss(video, st_ed_indices, match_labels, mask, measure='JSD'):
    """
        VV-CL module
        Computing the Contrastive loss between the start/end clips and the video
        :param video: video rep (bsz, Lv, dim)
        :param st_ed_indices: (bsz, 2)
        :param match_labels: match labels (bsz, Lv)
        :param mask: mask (bsz, Lv)
        :param measure: estimator of the mutual information
        :return: L_{vv}
    """
    # generate mask
    pos_mask = match_labels.type(torch.float32)  # (bsz, Lv)
    neg_mask = (torch.ones_like(pos_mask) - pos_mask) * mask  # (bsz, Lv)

    # select start and end indices features
    st_indices, ed_indices = st_ed_indices[:, 0], st_ed_indices[:, 1]  # (bsz, )
    batch_indices = torch.arange(0, video.shape[0]).long()  # (bsz, )
    video_s = video[batch_indices, st_indices, :]  # (bsz, dim)
    video_e = video[batch_indices, ed_indices, :]  # (bsz, dim)

    # compute scores
    video_s = video_s.unsqueeze(2)  # (bsz, dim, 1)
    res_s = torch.matmul(video, video_s).squeeze(2)  # (bsz, Lv), fusion between the start clips and the video
    video_e = video_e.unsqueeze(2)  # (bsz, dim, 1)
    res_e = torch.matmul(video, video_e).squeeze(2)  # (bsz, Lv), fusion between the end clips and the video

    # start clips: MI expectation for all positive samples
    E_s_pos = get_positive_expectation(res_s * pos_mask, measure, average=False)
    E_s_pos = torch.sum(E_s_pos * pos_mask, dim=1) / (torch.sum(pos_mask, dim=1) + 1e-12)  # (bsz, )
    # end clips: MI expectation for all positive samples
    E_e_pos = get_positive_expectation(res_e * pos_mask, measure, average=False)
    E_e_pos = torch.sum(E_e_pos * pos_mask, dim=1) / (torch.sum(pos_mask, dim=1) + 1e-12)
    E_pos = E_s_pos + E_e_pos

    # start clips: MI expectation for all negative samples
    E_s_neg = get_negative_expectation(res_s * neg_mask, measure, average=False)
    E_s_neg = torch.sum(E_s_neg * neg_mask, dim=1) / (torch.sum(neg_mask, dim=1) + 1e-12)

    # end clips: MI expectation for all negative samples
    E_e_neg = get_negative_expectation(res_e * neg_mask, measure, average=False)
    E_e_neg = torch.sum(E_e_neg * neg_mask, dim=1) / (torch.sum(neg_mask, dim=1) + 1e-12)
    E_neg = E_s_neg + E_e_neg

    E = E_neg - E_pos  # (bsz, )
    return torch.mean(E)