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While there has been progress in developing non-vacuous generalization boundsfor deep neural networks, these bounds tend to be uninformative about why deeplearning works. In this paper, we develop a compression approach based onquantizing neural network parameters in a linear subspace, profoundly improvingon previous results to provide state-of-the-art generalization bounds on avariety of tasks, including transfer learning. We use these tight bounds tobetter understand the role of model size, equivariance, and the implicit biasesof optimization, for generalization in deep learning. Notably, we find largemodels can be compressed to a much greater extent than previously known,encapsulating Occam's razor. We also argue for data-independent bounds inexplaining generalization.

PAC-Bayes Compression Bounds So Tight That They Can Explain Generalization