On the Expressive Power of Deep Polynomial Neural Networks

We thank the reviewers for their positive and useful comments. "close" to the variety (nearness could be formalized by considering tubular neighborhoods of the variety). In fact, motivated by the reviewers' " See our detailed answer above. " In addition to our general answer above, we believe that the algebraic framework may be Specifically, one could consider "empirical filling", i.e., whether I suggest the authors emphasize this aspect in the paper . " Our computations are based on finite The focus of this paper was on expressivity, and we only briefly touched upon optimization/learning in Sec.2.3.