Reviews for this paper are mitigated, in particular some reviewers were concerned about some missing proofs. On the other hand, the paper studies an important problem and carries a nice analysis that integrates numerical experiments, heuristic derivations and rigorous proofs in a meaningful way; and the reader learns a lot about such models (quadratic 2-layer networks with sparse teacher). I thus suggest accept. However, some non-trivial results (Eq. 14, 20, 23,...) were stated and claimed to be true but without proof which is not acceptable. It is thus necessary that the authors spend a lot of effort writing the missing proofs thoroughly because it will not be possible to review those proofs again (and of course all the other changes proposed in the rebuttal should be implemented). Overall, for such a paper that contains true statements, conjectures and heuristics, it is very important to emphasize on the "truth status" of each statement, and "true statements" should have a proof.