But it's not a problem, it's actually a good thing that OP's explanation is more general. One of the main points in the OP paper is that you do not in fact need proxies or simplification. You can derive generalization bounds that do explain this behavior, without needing to rely on optimization dynamics. This exactly responds to the tests set forth in Zhang et al. OP does not "rely on Bayesian ensembles, or other proxies/simplifications". That seems to be a misunderstanding of the paper. It's analyzing the solutions that neural networks
actually reach, which differentiates it from a lot of other work. It also additionally shows how other simple model classes can reproduce the same behavior, and these reproductions do not depend on optimization.
"and that already requires studying the specific optimization algorithm in order to understand why it picks certain hypothesis over others in the space." But the OP paper explains how even "guess and check" can generalize similarly to SGD. It's becoming more well understood that the role of the optimizer may have been historically overstated for understanding DL generalization. It seems to be more about loss landscapes.
Don't get me wrong, these references you're linking are super interesting. But they don't take away from the OP paper which is adding something quite valuable to the discussion.
"and that already requires studying the specific optimization algorithm in order to understand why it picks certain hypothesis over others in the space." But the OP paper explains how even "guess and check" can generalize similarly to SGD. It's becoming more well understood that the role of the optimizer may have been historically overstated for understanding DL generalization. It seems to be more about loss landscapes.
Don't get me wrong, these references you're linking are super interesting. But they don't take away from the OP paper which is adding something quite valuable to the discussion.