Review for NeurIPS paper: Bayesian filtering unifies adaptive and non-adaptive neural network optimization methods

Summary and Contributions: Post-rebuttal: Dear authors, thank you for your detailed response and offering to fix many points we raised. I would like to sum up my thoughts after having read the other reviews and your rebuttal: On a high level, the following aspects were most significant how I approached towards my final score: 1) The perspective is novel, and has interesting potential. Re 1: I think we all agree that this is a pro for the paper and should be considered its main strength. Re 2: Questioning the approximations is a valid point. However, as you argue, you provided sufficient empirical evidence for the mini-batch Gaussianity, and I think that Gaussianity is often assumed without further justification in other Bayesian inference applications as well, simply to keep the computations tractable. Even if the assumptions are not fully realistic, they seem to be "less concerning than those in past work" (rebuttal, line 19).