Review for NeurIPS paper: Towards Understanding Hierarchical Learning: Benefits of Neural Representations

Weaknesses: Again, I am not an expert, so my questions are conceptual, and my score should be interpreted as "undecided", but if I'm convinced by your answers or the other reviewers that my concerns are invalid, which is very probable, I'll recommend accepting. Since your paper explicitly wants to investigate the effect of having the neural representation, the additional whitening seems like it adds a second effect into the mix. If you need to do this because of the proofs, then at least it seems like you should also whiten the "raw" representations in section 3. Would the bounds for these change if you did? How much of the proofs rely on this whitening? How much is it really still a neural representation and not a simple random up-project of the data?