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

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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. We also argue for data-independent bounds in explaining generalization.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
EditorsS. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh
PublisherNeural information processing systems foundation
ISBN (Electronic)9781713871088
StatePublished - 2022
Event36th Conference on Neural Information Processing Systems, NeurIPS 2022 - New Orleans, United States
Duration: Nov 28 2022Dec 9 2022

Publication series

NameAdvances in Neural Information Processing Systems
Volume35
ISSN (Print)1049-5258

Conference

Conference36th Conference on Neural Information Processing Systems, NeurIPS 2022
Country/TerritoryUnited States
CityNew Orleans
Period11/28/2212/9/22

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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