Response to R1

We thank all reviewers for comments. We are glad to see our work commented as "promising"(R3), "effective"(R6), We address their concerns below. Writing We'll rephrase remarks, e.g."Examples give hints to local behavior of optimizers in deep learning". Q2.a Assumptions We list assumptions (1)-(3) as below: Numerically, we need a small β (e.g 0.3) or large t . We also tried default β with large t, results similar to Fig.3(d).