ArcFace/AAMLoss實現詳解

ArcFace/AAMLoss實現詳解：

Arcface 的 PyTorch 實現

原版 ArcFace 使用 MXNet 實現，這裏介紹 PyTorch 上的第三方實現。 

    # implementation of additive margin softmax loss in https://arxiv.org/abs/1801.05599    
    def __init__(self, embedding_size=512, classnum=51332,  s=64., m=0.5):
        super(Arcface, self).__init__()
        self.classnum = classnum
        self.kernel = Parameter(torch.Tensor(embedding_size,classnum))
        # initial kernel
        self.kernel.data.uniform_(-1, 1).renorm_(2,1,1e-5).mul_(1e5)
        self.m = m # the margin value, default is 0.5
        self.s = s # scalar value default is 64, see normface https://arxiv.org/abs/1704.06369
        self.cos_m = math.cos(m)
        self.sin_m = math.sin(m)
        self.mm = self.sin_m * m  # issue 1
        self.threshold = math.cos(math.pi - m)

• forward

l2_norm 會求導嗎？

        # weights norm
        nB = len(embbedings)
        kernel_norm = l2_norm(self.kernel,axis=0)

• torch.mm 執行矩陣mat1和mat2的矩陣乘法。
  torch.clamp 將輸入中的所有元素夾在[min，max]範圍內並返回結果張量：
  
  如果輸入的類型爲FloatTensor或DoubleTensor，則 args min和max必須是實數，否則它們應該是整數。
  
  
  

        # cos(theta+m)
        cos_theta = torch.mm(embbedings,kernel_norm)
        # output = torch.mm(embbedings,kernel_norm)
        cos_theta = cos_theta.clamp(-1,1) # for numerical stability
        cos_theta_2 = torch.pow(cos_theta, 2)
        sin_theta_2 = 1 - cos_theta_2
        sin_theta = torch.sqrt(sin_theta_2)
        cos_theta_m = (cos_theta * self.cos_m - sin_theta * self.sin_m)

# this condition controls the theta+m should in range [0, pi]
        #      0<=theta+m<=pi
        #     -m<=theta<=pi-m
        cond_v = cos_theta - self.threshold
        cond_mask = cond_v <= 0
        keep_val = (cos_theta - self.mm) # when theta not in [0,pi], use cosface instead
        cos_theta_m[cond_mask] = keep_val[cond_mask]
        output = cos_theta * 1.0 # a little bit hacky way to prevent in_place operation on cos_theta
        idx_ = torch.arange(0, nB, dtype=torch.long)
        output[idx_, label] = cos_theta_m[idx_, label]
        output *= self.s # scale up in order to make softmax work, first introduced in normface
        return output

• l2_norm

def l2_norm(input,axis=1):
    norm = torch.norm(input,2,axis,True)
    output = torch.div(input, norm)
    return output

• 轉載：https://blog.csdn.net/yiran103/article/details/83684613