reviewers ' questions below and will incorporate feedback into the final revision

We thank the reviewers for the detailed and insightful reviews. As the reviewers noted, our work 1) contributes to "a Thank you for the valuable feedback on this section -- we will incorporate this in our next revision. The intuition for the proof of Theorem 3.3 is that the optimization problem is convex over the space of probability By weak regularization, we refer to the fact that λ 0 for our Theorem 4.1 to hold. The difficulty with ReLU networks is that if the gradient flow pushes neurons towards 0, issues of differentiability arise. One potential approach to circumvent this issue is arguing that with correct initialization, the iterates will never reach 0. This is an interesting direction for future work and we thank the reviewer for this suggestion.