Question about the fundamental

[jizongFox]

Hi,
Thanks for sharing this great work.
I just draw the gradient for the Entropy and the proposed loss in your work and found hard to tell.
You said
After plotting the gradient function image on Fig. 1, we can see that the gradient of the high probability point is much larger than the mediate point. As a result, the key principle behind the entropy minimization method is that the training of target samples is guided by the high probability area, which is assumed to be more accurate.
In fact, the gradient is dominant when the probability is near 82% and the gradient vanishes when prediction becomes confident. It is very hard to imagine that when more confident you are, the larger gradient you have. Usually, Entropy minimization leads to a more stable model.
Entroy_loss and gradient

Your proposed loss indeed exhibits a lower gradient for high confident regions, that is true.
The proposed loss and gradient

The loss is plotted as -p ** 2 - (1 - p) ** 2 + 1. I added a constant to make the loss to be all positive.
Thanks in advance for your attention and comments.