Review for NeurIPS paper: On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

The paper has claimed three contributions, answering three questions. In general, I think removing boundedness assumption is useful. But Reviewer 3 pointed out that this work adds the "bounded level set" assumption and bounded gradient assumption, which do not seem much stronger than "bounded iterates". In particular, the gap between "bounded level-set" and "bounded iterates" is quite technical (not necessarily small, but not necessarily large), thus requires more explanation. R1 clarified that he was not claiming "[17, 18] or Pemantle alone already covered this paper's result", but asking whether a simple combination of [17, 18] and Pemantle [27] would give their result (that's why R1 used "morally" in the review).