Stronger generalization bounds for deep nets via a compression approach

Sanjeev Arora, Rong Ge, Behnam Neyshabur, Yi Zhang

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

17 Scopus citations

Abstract

Deep nets generalize well despite having more parameters than the number of training samples. Recent works try to give an explanation using PAC-Bayes and Margin-based analyses, but do not as yet result in sample complexity bounds better than naive parameter counting. The current paper shows generalization bounds that are orders of magnitude better in practice. These rely upon new succinct reparametrizations of the trained net - a compression that is explicit and efficient. These yield generalization bounds via a simple compression-based framework introduced here. Our results also provide some theoretical justification for widespread empirical success in compressing deep nets. Analysis of correctness of our compression relies upon some newly identified "noise stability"properties of trained deep nets, which are also experimentally verified. The study of these properties and resulting generalization bounds are also extended to convolutional nets, which had eluded earlier attempts on proving generalization.

Original languageEnglish (US)
Title of host publication35th International Conference on Machine Learning, ICML 2018
EditorsAndreas Krause, Jennifer Dy
PublisherInternational Machine Learning Society (IMLS)
Pages390-418
Number of pages29
ISBN (Electronic)9781510867963
StatePublished - Jan 1 2018
Event35th International Conference on Machine Learning, ICML 2018 - Stockholm, Sweden
Duration: Jul 10 2018Jul 15 2018

Publication series

Name35th International Conference on Machine Learning, ICML 2018
Volume1

Other

Other35th International Conference on Machine Learning, ICML 2018
CountrySweden
CityStockholm
Period7/10/187/15/18

All Science Journal Classification (ASJC) codes

  • Computational Theory and Mathematics
  • Human-Computer Interaction
  • Software

Cite this

Arora, S., Ge, R., Neyshabur, B., & Zhang, Y. (2018). Stronger generalization bounds for deep nets via a compression approach. In A. Krause, & J. Dy (Eds.), 35th International Conference on Machine Learning, ICML 2018 (pp. 390-418). (35th International Conference on Machine Learning, ICML 2018; Vol. 1). International Machine Learning Society (IMLS).