Strong data processing inequality in neural networks with noisy neurons and its implications

Chuteng Zhou, Quntao Zhuang, Matthew Mattina, Paul N. Whatmough

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

Abstract

Neural networks have gained importance as the machine learning models that achieve state-of-the-art performance on large-scale image classification, object detection and natural language processing tasks. In this paper, we consider noisy binary neural networks, where each neuron has a non-zero probability of producing an incorrect output. These noisy models may arise from biological, physical and electronic contexts and constitute an important class of models that are relevant to the physical world. Intuitively, the number of neurons in such systems has to grow to compensate for the noise while maintaining the same level of expressive power and computation reliability. Our key finding is a lower bound for the required number of neurons in noisy neural networks, which is first of its kind. To prove this lower bound, we take an information theoretic approach and obtain a strong data processing inequality (SDPI), which not only generalizes the Evans-Schulman results for binary channels to general channels but also improves the tightness drastically when applied to estimate end-to-end information contraction. Applying the SDPI in noisy binary neural networks, we obtain our key lower bound and investigate its implications on network depth-width trade-offs, our results suggest a depth-width trade-off for noisy neural networks that is very different from the established understanding regarding noiseless neural networks. This paper offers new understanding of noisy information processing systems through the lens of information theory.

Original languageEnglish (US)
Title of host publication2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1170-1175
Number of pages6
ISBN (Electronic)9781538682098
DOIs
StatePublished - Jul 12 2021
Externally publishedYes
Event2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia
Duration: Jul 12 2021Jul 20 2021

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2021-July
ISSN (Print)2157-8095

Conference

Conference2021 IEEE International Symposium on Information Theory, ISIT 2021
Country/TerritoryAustralia
CityVirtual, Melbourne
Period7/12/217/20/21

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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