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Local Search for Fast Matrix Multiplication

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arxiv 1903.11391 v2 pith:TVNGUDVB submitted 2019-03-27 cs.LO cs.SC

Marijn J.H. Heule , Manuel Kauers , Martina Seidl This is my paper · ORCID
classification cs.LOcs.SC
keywords schemescomputinglocalmanymethodsmultiplicationssearchsolvers
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Laderman discovered a scheme for computing the product of two 3x3 matrices using only 23 multiplications in 1976. Since then, some more such schemes were proposed, but it remains open how many there are and whether there exist schemes with fewer than 23 multiplications. In this paper we present two independent SAT-based methods for finding new schemes. Both methods allow computing a few hundred new schemes individually, and many thousands when combined. Local search SAT solvers outperform CDCL solvers consistently in this application.

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  1. Depth-first search for tensor rank and border rank over finite fields

    cs.CC 2024-11 conditional novelty 6.0 of 10

    An exact algorithm with O*(|F|^{(R-max_d n_d)(sum_d n_d)+max_d n_d}) time decides tensor rank over finite fields, with a border-rank variant over F[x]/(x^H).

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