Abstract:We present a new improvement on the laser method for designing fast matrix multiplication algorithms. The new method further develops the recent advances by [Duan, Wu, Zhou FOCS 2023] and [Vassilevska Williams, Xu, Xu, Zhou SODA 2024]. Surprisingly the new improvement is achieved by incorporating more asymmetry in the analysis, circumventing a fundamental tool of prior work that requires two of the three dimensions to be treated identically. Together with recent advances in numerical optimization [Dupont et al. arXiv:2608.16884], the method yields a new bound on the square matrix multiplication exponent $\omega<2.371177$, improved from the previous bound of $\omega<2.371552$. We also improve the bounds of the exponents for multiplying rectangular matrices of various shapes.
From: Renfei Zhou [view email]
[v1]
Thu, 25 Apr 2024 05:59:44 UTC (46 KB)
[v2]
Sun, 20 Oct 2024 04:13:13 UTC (46 KB)
[v3]
Wed, 19 Aug 2026 03:11:55 UTC (47 KB)
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