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In this work, we prove limitations on the known methods for designing matrix multiplication algorithms.
Gaussian elimination is not optimal
Volker Strassen · 1969
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Border rank of ap × \times q × \times 2 tensor and the optimal approximation of a pair of bilinear forms
Dario Bini · 1980
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Partial and total matrix multiplication
A. Schönhage · 1981
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On the asymptotic complexity of matrix multiplication
Don Coppersmith and Shmuel Winograd · 1982
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The asymptotic spectrum of tensors and the exponent of matrix multiplication
Volker Strassen · 1986
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Relative bilinear complexity and matrix multiplication
V. Strassen · 1987
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Matrix multiplication via arithmetic progressions
Don Coppersmith and Shmuel Winograd · 1990
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Degeneration and complexity of bilinear maps: some asymptotic spectra
Volker Strassen · 1991
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A group-theoretic approach to fast matrix multiplication
Henry Cohn and Christopher Umans · 2003
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Faster algorithms for rectangular matrix multiplication
François Le Gall · 2012
Cited alongside, same era.
Multiplying matrices faster than Coppersmith-Winograd
Virginia Vassilevska Williams · 2012
Cited alongside, same era.
Fast matrix multiplication using coherent configurations
Henry Cohn and Christopher Umans · 2013
Cited alongside, same era.
Improved bound for complexity of matrix multiplication
A.M. Davie and A. J. Stothers · 2013
Cited alongside, same era.
Powers of tensors and fast matrix multiplication
François Le Gall · 2014
Cited alongside, same era.
Fast matrix multiplication: limitations of the Coppersmith-Winograd method
Andris Ambainis, Yuval Filmus, and François Le Gall · 2015
Cited alongside, same era.
Further limitations of the known approaches for matrix multiplication
Josh Alman and Virginia Vassilevska Williams · 2018
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Limits on all known (and some unknown) approaches to matrix multiplication
Josh Alman and Virginia Vassilevska Williams · 2018
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Solving linear programs in the current matrix multiplication time
Michael B Cohen, Yin Tat Lee, and Zhao Song · 2018
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Barriers for fast matrix multiplication from irreversibility
Matthias Christandl, Péter Vrana, and Jeroen Zuiddam · 2018
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Universal points in the asymptotic spectrum of tensors
Matthias Christandl, Péter Vrana, and Jeroen Zuiddam · 2018
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A symmetric formulation of the croot-lev-pach-ellenberg-gijswijt capset bound
Terence Tao · 2016
Cited alongside, same era.
Notes on the “slice rank” of tensors
Terence Tao and Will Sawin · 2016
Cited alongside, same era.
On cap sets and the group-theoretic approach to matrix multiplication
Jonah Blasiak, Thomas Church, Henry Cohn, Joshua A Grochow, Eric Naslund, William F Sawin, and Chris Umans · 2017
Cited alongside, same era.
Improved rectangular matrix multiplication using powers of the coppersmith-winograd tensor
Francois Le Gall and Florent Urrutia · 2018
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The growth rate of tri-colored sum-free sets
Robert Kleinberg, Will Sawin, and David Speyer · 2018
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Probabilistic tensors and opportunistic boolean matrix multiplication
Matti Karppa and Petteri Kaski · 2019
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