"Parse" focalloss to solve the problem of data imbalance

• Focal Loss for Dense Object Detection
• Official code ：https://github.com/facebookresearch/Detectron

FocalLoss Appearance , Mainly to solve anchor-based (one-stage) Classification of target detection networks . Later instance segmentation is also often used .

Be careful
Here is Classification of target detection networks , It is not a simple classification problem , The two are different .
The difference lies in , For the distribution problem , A picture must belong to a certain class ; And the classification in the detection task , There are a lot of anchor Aimless （ It can be called negative sample ）.

Classification task

natural K Class classification task The label of , Use one. K Length vector as label , use one-hot（ perhaps +smooth, Don't think about it here ） To code , The final label is a shape like [1,…, 0, …, 0] In this way . So if you want to separate the background , Naturally, you can think of adding one 1 dimension , If the target detection task has K class , Here just use K+1 Dimension represents classification , among 1 Dimension represents no goal . For classified tasks , Finally, it is generally used softmax Laiguiyi , Make the output of all categories add up to 1.

But in the detection task , For aimless anchor, We don't want the final result to add up to 1, Instead, all probability outputs are 0. Then it can be like this , We regard a multi classification task as Multiple binary tasks (sigmoid), For each category , I output a probability , If you are close to 0 It means that it is not in this category , If you are close to 1, It stands for this anchor Is this category .

So the network output does not need to use softmax Laiguiyi , It's right K Each component of the length vector sigmoid Activate , Let its output value represent the probability of two classifications . For aimless anchor,gt All components in are 0, The probability of belonging to each class is 0, That is, marked as background .

thus ,FocalLoss The problem to be solved is not a multi classification problem , It is Multiple binary classification problems .

Formula analysis

First look at the formula ： Only label $y=1$ when , The formula / Cross entropy makes sense ,$p_t$ That is, the label is 1 The predicted value corresponding to / Probability of correct model classification
$p_t=(1-pred\_sigmoid)\ast target+pred\_sigmoid\ast (1-target)$

$$\begin{gathered} CE(p_t)=-{\alpha }_t\log (p_t) \\ FL(p_t)=-{\alpha }_t(1-p_t{)}^{\gamma }\log (p_t) \\ FL(p)=\{\begin{array}{llc}-\alpha (1-p{)}^{\gamma }\log (p)& ,ify=1& \\ -(1-\alpha )p^{\gamma }\log (1-p)& ,ify=0& \end{array} \end{gathered}$$

1. Parameters p[ The formula 3]： When p->0 when （ The probability is very low / It is difficult to distinguish which category ）, Modulation factor (1-p) near 1, The loss is not affected , When p->1 when ,(1-p) near 0, So as to reduce the total number of easy samples loss The contribution of
2. Parameters $\gamma$： When $\gamma =0$ when ,Focal loss Is the traditional cross entropy ,
   When $\gamma$ increases , Adjustment factor $(1-p_t)$ Also increases .
   When $\gamma$ When it is a fixed value , such as $\gamma =2$ ️ about easy example(p>0.5) p=0.9 Of loss Smaller than the standard cross entropy 100 times , When p=0.968 when , smaller 1000+ times ;️ about hard example(p<0.5) loss smaller 4 times
   In this case , hard example The weight of has increased a lot , Thus increasing the importance of what misclassification .
   Experiments show that ,$\gamma =2,\alpha =0.75$ It works best when
3. $\alpha$ Adjust the unbalance coefficient of positive and negative samples ,$\gamma$ Control the imbalance of difficult and easy samples

Code reappearance

In the official code , did not target = F.one_hot(target, num_clas) This line of code , This is because

# Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.

import torch
from torch.nn import functional as F


def sigmoid_focal_loss( inputs: torch.Tensor, targets: torch.Tensor, alpha: float = -1, 
    					gamma: float = 2, reduction: str = "none") -> torch.Tensor:

    inputs  = inputs.float()
    targets = targets.float()
    p 	    = torch.sigmoid(inputs)
    target  = F.one_hot(target, num_clas+1)
    ce_loss = F.binary_cross_entropy_with_logits(inputs, targets, reduction="none")
    p_t 	= p * targets + (1 - p) * (1 - targets)
    loss 	= ce_loss * ((1 - p_t) ** gamma)

    if alpha >= 0:
        alpha_t = alpha * targets + (1 - alpha) * (1 - targets)
        loss = alpha_t * loss

    if reduction == "mean":
        loss = loss.mean()
    elif reduction == "sum":
        loss = loss.sum()

    return loss


sigmoid_focal_loss_jit: "torch.jit.ScriptModule" = torch.jit.script(sigmoid_focal_loss)

Besides ,torchvision China also supports focal loss

Complete code

Official full code ：https://github.com/facebookresearch/

Reference resources

• https://zhuanlan.zhihu.com/p/391186824