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Statistical Mechanics of Deep Learning

Authors
  • Bahri, Yasaman
  • Kadmon, Jonathan
  • Pennington, Jeffrey
  • Schoenholz, Sam S.
  • Sohl-Dickstein, Jascha
  • Ganguli, Surya
Type
Published Article
Journal
Annual Review of Condensed Matter Physics
Publisher
Annual Reviews
Publication Date
Mar 10, 2020
Volume
11
Pages
501–528
Identifiers
DOI: 10.1146/annurev-conmatphys-031119-050745
Source
Annual Reviews
Keywords
License
Yellow

Abstract

The recent striking success of deep neural networks in machine learning raises profound questions about the theoretical principles underlying their success. For example, what can such deep networks compute? How can we train them? How does information propagate through them? Why can they generalize? And how can we teach them to imagine? We review recent work in which methods of physical analysis rooted in statistical mechanics have begun to provide conceptual insights into these questions. These insights yield connections between deep learning and diverse physical and mathematical topics, including random landscapes, spin glasses, jamming, dynamical phase transitions, chaos, Riemannian geometry, random matrix theory, free probability, and nonequilibrium statistical mechanics. Indeed, the fields of statistical mechanics and machine learning have long enjoyed a rich history of strongly coupled interactions, and recent advances at the intersection of statistical mechanics and deep learning suggest these interactions will only deepen going forward.

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