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The Cartographer
Faster Rectangular Matrix Multiplication by Combination Loss Analysis
July 13, 2023 Β· Declared Dead Β· π ACM-SIAM Symposium on Discrete Algorithms
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Authors
François Le Gall
arXiv ID
2307.06535
Category
cs.DS: Data Structures & Algorithms
Cross-listed
cs.CC,
cs.SC
Citations
24
Venue
ACM-SIAM Symposium on Discrete Algorithms
Last Checked
3 months ago
Abstract
Duan, Wu and Zhou (FOCS 2023) recently obtained the improved upper bound on the exponent of square matrix multiplication $Ο<2.3719$ by introducing a new approach to quantify and compensate the ``combination loss" in prior analyses of powers of the Coppersmith-Winograd tensor. In this paper we show how to use this new approach to improve the exponent of rectangular matrix multiplication as well. Our main technical contribution is showing how to combine this analysis of the combination loss and the analysis of the fourth power of the Coppersmith-Winograd tensor in the context of rectangular matrix multiplication developed by Le Gall and Urrutia (SODA 2018).
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