We thank all the reviewers for their time and constructive comments. We also planned on moving the table and more in detailed discussion back for the final paper if accepted. Another application of this problem is learning decision trees with bounded depth [7,8]. All in all, we will make sure to rewrite the motivation part of the intro and mention all these applications more clearly. The sentence "Therefore, the family of Fourier sparse set functions whose Fourier support only contains low order Exact recovery of sparse functions in sublinear time is indeed possible. We show in section 3.1 that if the frequency The result of [8] is not able to exactly recover sparse set functions in the noiseless setting. We thank the reviewer for the acknowledgment of our hashing schemes. Our hash function (Definition 7) is in fact similar to the projection defined in the paper "New Results for Learning Noisy LWE problem, whose hardness has been used as a cryptographic assumption.

This is indeed an omission, but it is not terribly complicated and we will add it to the paper.

We thank all reviewers for their time and constructive comments. We first address concerns that were brought up by multiple reviewers. NMODE is more sample efficient than other methods (Appendix C.2, first paragraph), so for density estimation The quantifier for Prop 5.1 should be "for some"; this will be fixed. Note that for small dimensions (e.g. Riemannian metric, and are thus Riemannian.

This is indeed an omission, but it is not terribly complicated and we will add it to the paper.

We thank all reviewers for their time and constructive comments. We first address concerns that were brought up by multiple reviewers. NMODE is more sample efficient than other methods (Appendix C.2, first paragraph), so for density estimation The quantifier for Prop 5.1 should be "for some"; this will be fixed. Note that for small dimensions (e.g. Riemannian metric, and are thus Riemannian.