Keep a gradient second moment when AdaBelief beta1 is 0

[shaneraphel]

Summary

With beta1 = 0 the first moment is set to the current gradient, so the belief residual g - m is 0 and the second moment stays at eps. The step is lr * g / sqrt(eps). This port's default eps is 0.001, which hides it, but the paper's eps is 1e-16 (and that is what AdaBelief(..., eps=1e-16) accepts). A scalar quadratic x^2 with learning rate 1e-2 and that eps reached -inf on step 10. The same overflow is juntang-zhuang/Adabelief-Optimizer#67; the fix there is the same idea, kept in that repository's latest package.

Only the degenerate case changes. When beta1 == 0 the residual is g, so the second moment tracks g^2 the way Adam does at beta1 = 0. For any positive beta1 the residual is still g - m after the first-moment update. One step at beta1 = 0.9 still stores (1 - beta2) (g - m)^2 plus the eps this implementation adds into the second-moment state.

Test plan

• pytest tests/test_adabelief_beta1.py
• Positive beta1 matches the residual variance, including the added eps.
• Thirty steps of x^2 at beta1 = 0, eps = 1e-16, learning rate 1e-2 stay finite and the parameter moves from 0.5 toward 0.

This change was produced with assistance from an AI coding tool. I reproduced the overflow at the paper's eps, left the positive-beta1 residual alone, and ran the tests locally.