target logit and its curves

[xuezhongcailian]

hi,I read your paper and your target logit curves code ,I feel puzzled,your paper say that Wf is also called as the target logit ,but I feel that your target logit curves is not correspond with the definied Wf,it seems not to think about the f.

[Feng Wang]

The definition of logit is from this paper: https://arxiv.org/pdf/1701.06548.pdf (z_i in Section 3). It originally means the values that are fed into Softmax loss, and we define the target logit as the logit which is corresponding to the ground truth label.

In the original Softmax, the target logit is W_y^T f. In AM-Softmax, we normalize the W and f and modify the target logit to be s*(W_y^T f - m). Here y is the ground-truth label of the optimizing sample.

[xuezhongcailian]

hi，I read your target logit curves matlab code on your github draw_psi_curve.m ,I always feel the Angular softmax and AM softmax curves plot the ψ(θ).but conventional softmax plot cos(θ), the target logit is W_y^T f.Angular softmax target logit ||f|| ψ(θ),I feel not corresponding.

[Feng Wang]

You are right. I will change the y-label to ψ(θ) in the final version of my paper.

[xuezhongcailian]

I do not know whether arcface target logit curves have also the problem.

[Feng Wang]

Yeah... ArcFace shows a similar figure, and suffers from the same problem.