This is an interesting and thorough paper on computing the Lipschitz constant of deep networks. On the positive side, the paper is very thorough, both in terms of theory and practice; personally, I was surprised to find it even included a hardness result, and feel that this paper has many things for many researchers. I look forward to seeing this paper appear, and support the authors in further investigations. --- Minor comment. Some feedback which may be interesting for future directions. Some of the negative points in discussion were the hopelessness of exact computation, and the appearance of MIP in prior work in this field; perhaps there are some interesting relaxed approaches, based on the insights in this paper? Overall, reviews enjoyed the paper, I'm just trying to be helpful for future work.