On the CVP for the root lattices via folding with deep ReLU neural networks

Vincent Corlay, Joseph J. Boutros, Philippe Ciblat, Loic Brunel

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

Abstract

Point lattices and their decoding via neural networks are considered in this paper. Lattice decoding in reals n, known as the closest vector problem (CVP), becomes a classification problem in the fundamental parallelotope with a piecewise linear function defining the boundary. Theoretical results are obtained by studying root lattices. We show how the number of pieces in the boundary function reduces dramatically with folding, from exponential to linear. This translates into a two-layer ReLU neural network requiring a number of neurons growing exponentially in n to solve the CVP, whereas this complexity becomes polynomial in n for a deep ReLU neural network.

Original languageEnglish
Title of host publication2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1622-1626
Number of pages5
ISBN (Electronic)9781538692912
DOIs
Publication statusPublished - Jul 2019
Event2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France
Duration: 7 Jul 201912 Jul 2019

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2019-July
ISSN (Print)2157-8095

Conference

Conference2019 IEEE International Symposium on Information Theory, ISIT 2019
CountryFrance
CityParis
Period7/7/1912/7/19

ASJC Scopus subject areas

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

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    Corlay, V., Boutros, J. J., Ciblat, P., & Brunel, L. (2019). On the CVP for the root lattices via folding with deep ReLU neural networks. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings (pp. 1622-1626). [8849501] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2019.8849501