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arXiv · 2404.16349

More Asymmetry Yields Faster Matrix Multiplication

Josh Alman·Ran Duan·Virginia Vassilevska Williams·Yinzhan Xu·Zixuan Xu·Renfei Zhou
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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.

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Josh Alman, Ran Duan, Virginia Vassilevska Williams, Yinzhan Xu, Zixuan Xu, Renfei Zhou. 2024-04-25. More Asymmetry Yields Faster Matrix Multiplication. https://arxiv.org/abs/2404.16349

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