Exploring Generalization in Deep Learning
With a goal of understanding what drives generalization in deep networks, we consider several recently suggested explanations, including norm-based control, sharpness and robustness. We study how these measures can ensure generalization, highlighting the importance of scale normalization, and making a connection between sharpness and PAC-Bayes theory. We then investigate how well the measures explain different observed phenomena.
Update after rebuttal: quote the rebuttal "Even this very simple variability in architecture, proves challenging to study using the complexity measures suggested. We certainly intend to study also other architectural differences."
I hope the authors include the discussions (and hopefully some experiment results) about applying the proposed techniques to the comparison of models with different architectures in the final version if it get accepted. The current results are already useful steps towards understanding deep neural networks by their own, but having this results is really a great add on to this paper. 
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This paper investigated primarily two (related) questions: what is the complexity measure that is implicitly enforced to allow good generalization performance of large deep neural networks? Given different global minimizers of the empirical risk, can we tell which one generalize better based on the complexity measure.
Although no definite answer is given in this paper, a few options are explored and some of them seem to be positive choice. More specifically, norm based complexity measure and (average) sharpness based complexity measures are empirically investigated. The sharpness based measure are further justified via PAC-Bayes bound on generalization. 
There is no discussion on how or why those complexity measures are enforced during training of neural networks, but the explorations are interesting by themselves.
Although a theorem is given to control the sharpness of a network under a number of assumptions (C1-C3), this is primarily an empirical paper. Therefore, the reviewer thinks it would be more useful to include more extensive experiments. More specifically, could the proposed measures be useful when comparing across different architectures? Could it be useful when compare to different global minimizers from different algorithms (variants of SGD, or SGD with small / large batches)? etc.