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前言

 为了加深对Focal Loss理解，本文提供了一个简单的手写Demo。

1、FocalLoss

 介绍FocalLoss的文章已经很多了，这里简单提一下：

1.1.公式定义

 Focal Loss 的公式如下：

$$\text{FL}(p_t)=-{\alpha }_t(1-p_t{)}^{\gamma }\log (p_t)$$

 ;根据真实标签 $y$ 的不同，Focal Loss 可以分为两种情况：

 1) 当真实标签 $y=1$ 时，公式变为：

$$\text{FL}(p)=-\alpha (1-p{)}^{\gamma }\log (p)$$

 2) 当真实标签 $y=0$ 时，公式变为：

$$\text{FL}(p)=-(1-\alpha )p^{\gamma }\log (1-p)$$

 Focal Loss 的完整公式可以写为：

$$\text{FL}(y,p)=-\left[y\cdot \alpha (1-p{)}^{\gamma }\log (p)+(1-y)\cdot (1-\alpha )p^{\gamma }\log (1-p)\right]$$

 其中$p$表示经过sigmoid的预测值。本文实现的是完整版的公式，而且没有引入额外的封装函数。

2、代码

python">import torch
import torch.nn as nn
import torch.nn.functional as F

# focal_loss = pos_loss + neg_loss 
# if y == 1: pos_loss = -|1-p|^gamma * log(p)  
# if y == 0: neg_loss = -|0-p|^gamma * log(1-p)
class FocalLoss(nn.Module):
    def __init__(self,alpha=0.25,gamma=2.0,reduce='sum'):
        super(FocalLoss,self).__init__()
        self.alpha = alpha
        self.gamma = gamma
        self.reduce = reduce

    def forward(self,classifications,targets):
        alpha = self.alpha
        gamma = self.gamma
        classifications = classifications.view(-1)
        p = torch.sigmoid(classifications)
        targets = targets.view(-1)
        # 获取pos 和 neg 的索引
        pos_idx = torch.nonzero(targets==1).view(-1)
        neg_idx = torch.nonzero(targets==0).view(-1)
        # step1: cpt pos loss       
        pos_loss = -(1-p[pos_idx]).abs() ** gamma * torch.log(p[pos_idx])
        # step2: cpt neg loss 
        neg_loss = -(0-p[neg_idx]).abs() ** gamma * torch.log(1-p[neg_idx])
        loss = torch.cat((pos_loss, neg_loss), dim=0)
        # targets 也需要重新排序 来跟loss值对应 
        concat_idx = torch.cat((pos_idx, neg_idx), dim=0)
        targets = targets[concat_idx]
        if alpha >= 0:
            alpha_t = alpha * targets + (1 - alpha) * (1 - targets)
            loss = alpha_t * loss
        if self.reduce=='sum':
            loss = loss.sum()
        elif self.reduce=='mean':
            loss = loss.mean()
        else:
            raise ValueError('reduce type is wrong!')
        return loss


# ---test unit --- #
def main():
    # single cls focal loss 
    focal_loss = FocalLoss()
    pred = torch.FloatTensor([0.1,0.9,0.2,0.8,0.7]) # nb_anchors :5
    tgt  = torch.FloatTensor([0,1,0,1,1])           # neg:0 pos:1 ; no ignore
    loss = focal_loss(pred, tgt)
    print('loss:', loss) 

总结

 本文只是简单实现了一个二分类的FocalLoss，旨在加深读者对其理解。欢迎批评指正。