SphereFace主要工作是归一化了网络中的权值W。

    权值W归一化之后，训练时优化会更加集中在深度特征映射和特征向量角度上。这样做的主要好处是可以降低样本数量不均衡问题。

    SphereFace当中的loss被称作A-softmax，除了归一化权值之外还采用了乘性margin，但是乘性margin效果并不理想，主要是其训练时难以收敛。

    Screenshot from 2020-07-21 19-04-45.png

    1. # SphereFace
    2. class SphereProduct(nn.Module):
    3.     r"""Implement of large margin cosine distance: :
    4.     Args:
    5.         in_features: size of each input sample
    6.         out_features: size of each output sample
    7.         m: margin
    8.         cos(m*theta)
    9.     """
    11.     def __init__(self, in_features, out_features, m=4):
    12.         super(SphereProduct, self).__init__()
    13.         self.in_features = in_features
    14.         self.out_features = out_features
    15.         self.m = m
    16.         self.base = 1000.0
    17.         self.gamma = 0.12
    18.         self.power = 1
    19.         self.LambdaMin = 5.0
    20.         self.iter = 0
    21.         self.weight = Parameter(torch.FloatTensor(out_features, in_features))
    22.         nn.init.xavier_uniform(self.weight)
    24.         # duplication formula
    25.         # 将x\in[-1,1]范围的重复index次映射到y\[-1,1]上
    26.         self.mlambda = [
    27.             lambda x: x ** 0,
    28.             lambda x: x ** 1,
    29.             lambda x: 2 * x ** 2 - 1,
    30.             lambda x: 4 * x ** 3 - 3 * x,
    31.             lambda x: 8 * x ** 4 - 8 * x ** 2 + 1,
    32.             lambda x: 16 * x ** 5 - 20 * x ** 3 + 5 * x
    33.         ]
    34.         """
    35.         执行以下代码直观了解mlambda
    36.         import matplotlib.pyplot as  plt
    38.         mlambda = [
    39.             lambda x: x ** 0,
    40.             lambda x: x ** 1,
    41.             lambda x: 2 * x ** 2 - 1,
    42.             lambda x: 4 * x ** 3 - 3 * x,
    43.             lambda x: 8 * x ** 4 - 8 * x ** 2 + 1,
    44.             lambda x: 16 * x ** 5 - 20 * x ** 3 + 5 * x
    45.         ]
    46.         x = [0.01 * i for i in range(-100, 101)]
    47.         print(x)
    48.         for f in mlambda:
    49.             plt.plot(x,[f(i) for i in x])
    50.             plt.show()
    51.         """
    53.     def forward(self, input, label):
    54.         # lambda = max(lambda_min,base*(1+gamma*iteration)^(-power))
    55.         self.iter += 1
    56.         self.lamb = max(self.LambdaMin, self.base * (1 + self.gamma * self.iter) ** (-1 * self.power))
    58.         # --------------------------- cos(theta) & phi(theta) ---------------------------
    59.         cos_theta = F.linear(F.normalize(input), F.normalize(self.weight))
    60.         cos_theta = cos_theta.clamp(-1, 1)
    61.         cos_m_theta = self.mlambda[self.m](cos_theta)
    62.         theta = cos_theta.data.acos()
    63.         k = (self.m * theta / 3.14159265).floor()
    64.         phi_theta = ((-1.0) ** k) * cos_m_theta - 2 * k
    65.         NormOfFeature = torch.norm(input, 2, 1)
    67.         # --------------------------- convert label to one-hot ---------------------------
    68.         one_hot = torch.zeros(cos_theta.size())
    69.         one_hot = one_hot.cuda() if cos_theta.is_cuda else one_hot
    70.         one_hot.scatter_(1, label.view(-1, 1), 1)
    72.         # --------------------------- Calculate output ---------------------------
    73.         output = (one_hot * (phi_theta - cos_theta) / (1 + self.lamb)) + cos_theta
    74.         output *= NormOfFeature.view(-1, 1)
    76.         return output
    78.     def __repr__(self):
    79.         return self.__class__.__name__ + '(' \
    80.                + 'in_features=' + str(self.in_features) \
    81.                + ', out_features=' + str(self.out_features) \
    82.                + ', m=' + str(self.m) + ')'