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

Sanae Lotfi, Marc Anton Finzi, Sanyam Kapoor, Andres Potapczynski, Micah Goldblum, Andrew Gordon Wilson

Keywords: PAC-Bayes, Generalization, Compression, Generalization Bounds, PAC-Bayes Bounds, Occam's Razor, Transfer Learning, Data-Dependent Priors

TL;DR: We propose state-of-the-art PAC-Bayes compression bounds and use them to understand generalization in deep learning.

Abstract: While there has been progress in developing non-vacuous generalization bounds for deep neural networks, these bounds tend to be uninformative about why deep learning works. In this paper, we develop a compression approach based on quantizing neural network parameters in a linear subspace, profoundly improving on previous results to provide state-of-the-art generalization bounds on a variety of tasks, including transfer learning. We use these tight bounds to better understand the role of model size, equivariance, and the implicit biases of optimization, for generalization in deep learning. Notably, we find large models can be compressed to a much greater extent than previously known, encapsulating Occam’s razor.

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:2211.13609/code)