E-Approximate Coded Matrix Multiplication is Nearly Twice as Efficient as Exact Multiplication

Viveck R. Cadambe, Flavio P. Calmon, Ateet Devulapalli, Haewon Jeong

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

Abstract

We study coded distributed matrix multiplication from an approximate recovery viewpoint. We consider a system of P computation nodes where each node stores 1/m of each multiplicand via linear encoding. Our main result shows that the matrix product can be recovered with relative error from any m of the P nodes for any >0. We obtain this result through a careful specialization of MatDot codes-a class of matrix multiplication code previously developed in the context of exact recovery ( = 0). Since previous results showed that the MatDot code is tight for a class of linear coding schemes for exact recovery, our result shows that allowing for mild approximations leads to a system that is nearly twice as efficient as exact reconstruction. Moreover, we develop an optimization framework based on alternating minimization that enables the discovery of new codes for approximate matrix multiplication.

Original languageEnglish (US)
Title of host publication2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1582-1587
Number of pages6
ISBN (Electronic)9781538682098
DOIs
StatePublished - Jul 12 2021
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

All Science Journal Classification (ASJC) codes

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

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