I believe the authors' results merit publication in a specialized journal rather than in ICLR. The main reasons are the following
1. The authors do not give any compelling numerical evidence that their bound is tight or even "log-tight".
2. The authors' derivation falls into classical learning theory-based bounds, which, to the best of my knowledge, does not yield realistic bounds, unless Bayesian considerations are taken into account (e.g. Bayesian-PAC based bounds).
3. Even if one maintains that VC-dimension-style learning theory is an important part of the theory of deep learning, my hunch would be that the current work does not contain sufficient mathematical interest to be published in ICLR.
My more minor comments are that
1. The introduction is very wordy and contains many repetitions of similar statements.
2. I found what I believe are various math typos, for instance around Lemma 3.5. I think n and m are used interchangeably. Furthermore calligraphic R with an n sub-script and regular R. Similarly, capital and non-capital l are mixed in assumption 4.8. Runaway subscripts also appear many times in Appendix A2.
2. The authors' derivation falls into classical learning theory-based bounds, which, to the best of my knowledge, does not yield realistic bounds, unless Bayesian considerations are taken into account (e.g. Bayesian-PAC based bounds).