Question about Varifocal loss

[HAOCHENYE]

In the paper, the negtive weight of BCE loss is alpha*p^gamma. However, in varifocal_loss.py， the loss is implemented by:

focal_weight = target * (target > 0.0).float() +
alpha * (pred_sigmoid - target).abs().pow(gamma) *
(target <= 0.0).float()

The negtive weight is alpha(p-q)^gamma*, why?

[hyz-xmaster]

This is the initial version of implementation of VFL and I forgot to refine it.
alpha * (pred_sigmoid - target).abs().pow(gamma) * (target <= 0.0).float() actually equals to alpha * pred_sigmoid.pow(gamma) * (target == 0.0).float(), because there is a multiplier (target <= 0.0).float() in that formula and the target is always >= 0.

[HAOCHENYE]

This is the initial version of implementation of VFL and I forgot to refine it.
alpha * (pred_sigmoid - target).abs().pow(gamma) * (target <= 0.0).float() actually equals to alpha * pred_sigmoid.pow(gamma) * (target == 0.0).float(), because there is a multiplier (target <= 0.0).float() in that formula and the target is always >= 0.

You means alpha * pred_sigmoid.abs().pow(gamma) * (target <= 0.0).float() equals alpha * pred_sigmoid.pow(gamma) * (target == 0.0).float() or alpha * (pred_sigmoid - target).abs().pow(gamma) * (target <= 0.0).float() equals to alpha * pred_sigmoid.pow(gamma) * (target == 0.0).float()? I'd understand the situation if it is the former one.

According to paper, the negtive weight should be alpha * pred_sigmoid.abs().pow(gamma) * (target <= 0.0).float().Is the formular of paper current version?

[hyz-xmaster]

Hi, target is the IoU so it is always >= 0, which implies target <= 0 <=> target == 0.
In this way,
alpha * (pred_sigmoid - target).abs().pow(gamma) * (target <= 0.0).float() <=>
alpha * (pred_sigmoid - target).abs().pow(gamma) * (target == 0.0).float() <=>
alpha * pred_sigmoid.abs().pow(gamma) * (target == 0.0).float().

[HAOCHENYE]

Ohhh! Thanks, I understand it now.

[feiyuhuahuo]

Hi @hyz-xmaster ,

1. I did not find the q in the red circle according to the code.
2. I can't understand the item above the green line. Since log(1-p) is used to predict negative samples, why it appears in the q>0 case? And anyway, I did not find the related implementation from the code. I just understand the code by the following way:
   
   Looking forward to your reply, thanks.

[hyz-xmaster]

Hi @feiyuhuahuo,

1. target in the code represents q in that formula.
2. qlog(p)+(1-q)log(1-p) is the binary cross entropy loss, which is calculated by F.binary_cross_entropy_with_logits. When q = 0, qlog(p)+(1-q)log(1-p) reduces to log(1-p). When q > 0, it keeps unchanged.

[yxx-byte]

This is the initial version of implementation of VFL and I forgot to refine it.
alpha * (pred_sigmoid - target).abs().pow(gamma) * (target <= 0.0).float() actually equals to alpha * pred_sigmoid.pow(gamma) * (target == 0.0).float(), because there is a multiplier (target <= 0.0).float() in that formula and the target is always >= 0.

You means alpha * pred_sigmoid.abs().pow(gamma) * (target <= 0.0).float() equals alpha * pred_sigmoid.pow(gamma) * (target == 0.0).float() or alpha * (pred_sigmoid - target).abs().pow(gamma) * (target <= 0.0).float() equals to alpha * pred_sigmoid.pow(gamma) * (target == 0.0).float()? I'd understand the situation if it is the former one.

According to paper, the negtive weight should be alpha * pred_sigmoid.abs().pow(gamma) * (target <= 0.0).float().Is the formular of paper current version?

Hello, did you add your loss to yolov5? Judge which place needs to be adjusted?