1、 Focal loss theory and code implementation

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Preface

In this paper, the reference ： When can I see Qingmeng blogger's article
Reference to the original ：https://www.jianshu.com/p/30043bcc90b6

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One 、 The basic theory

1. use soft - gamma： Increase periodically in the process of training gamma There may be better performance improvement .
2.alpha It is related to the frequency of each category in the training data .
3.F.nll_loss(torch.log(F.softmax(inputs, dim=1),target) The function function of is similar to F.cross_entropy identical .

F.nll_loss For target Of one-hot encoding, Encode it as input shape same tensor, Then compare with the previous one （ namely F.nll_loss First item entered ） Conduct element-wise production.

be based on alpha=1 Use different gamma Value the result of the experiment

4.focal loss What problems have been solved ？
（1） Different categories are uneven
（2） Difficult and easy sample imbalance

5. stay retinanet in , Besides using focal loss Outside , Special processing is also done for initialization , How to do it ？

stay retinanet in , Yes classification subnet The last floor of conv Set its offset b by :

Two 、 Realization

1. The formula

The standard Cross Entropy and Focal Loss by ：
See Zhihu for the forward and backward derivation of ：https://zhuanlan.zhihu.com/p/32631517

2. Code implementation

1. Based on binary classification cross entropy .

# 1. Based on binary classification cross entropy 
class FocalLoss(nn.Module):
    def __init__(self, alpha=1, gamma=2, logits=False, reduce=True):
        super(FocalLoss, self).__init__()
        self.alpha = alpha
        self.gamma = gamma
        self.logits = logits
        self.reduce = reduce

    def forward(self, inputs, targets):
        if self.logits:
            BCE_loss = F.binary_cross_entropy_with_logits(inputs, targets, reduce=False)
        else:
            BCE_loss = F.binary_cross_entropy(inputs, targets, reduce=False)
        pt = torch.exp(-BCE_loss)
        F_loss = self.alpha * (1-pt)**self.gamma * BCE_loss

        if self.reduce:
            return torch.mean(F_loss)
        else:
            return F_loss

2. The realization of Zhihu boss

import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.autograd import Variable

class FocalLoss(nn.Module):
    r"""
        This criterion is a implemenation of Focal Loss, which is proposed in 
        Focal Loss for Dense Object Detection.

            Loss(x, class) = - \alpha (1-softmax(x)[class])^gamma \log(softmax(x)[class])

        The losses are averaged across observations for each minibatch.

        Args:
            alpha(1D Tensor, Variable) : the scalar factor for this criterion
            gamma(float, double) : gamma > 0; reduces the relative loss for well-classified examples (p > .5), 
                                   putting more focus on hard, misclassified examples
            size_average(bool): By default, the losses are averaged over observations for each minibatch.
                                However, if the field size_average is set to False, the losses are
                                instead summed for each minibatch.

    """
    def __init__(self, class_num, alpha=None, gamma=2, size_average=True):
        super(FocalLoss, self).__init__()
        if alpha is None:
            self.alpha = Variable(torch.ones(class_num, 1))
        else:
            if isinstance(alpha, Variable):
                self.alpha = alpha
            else:
                self.alpha = Variable(alpha)
        self.gamma = gamma
        self.class_num = class_num
        self.size_average = size_average
    def forward(self, inputs, targets):
        N = inputs.size(0)
        C = inputs.size(1)
        P = F.softmax(inputs)

        class_mask = inputs.data.new(N, C).fill_(0)
        class_mask = Variable(class_mask)
        ids = targets.view(-1, 1)
        class_mask.scatter_(1, ids.data, 1.)
        #print(class_mask)
        if inputs.is_cuda and not self.alpha.is_cuda:
            self.alpha = self.alpha.cuda()
        alpha = self.alpha[ids.data.view(-1)]
        probs = (P*class_mask).sum(1).view(-1,1)
        log_p = probs.log()
        #print('probs size= {}'.format(probs.size()))
        #print(probs)
        batch_loss = -alpha*(torch.pow((1-probs), self.gamma))*log_p 
        #print('-----bacth_loss------')
        #print(batch_loss)
        if self.size_average:
            loss = batch_loss.mean()
        else:
            loss = batch_loss.sum()
        return loss
``