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Improving matrix multiplication exponent with optimization and AlphaEvolve (arxiv.org)
8 points by sonabinu 46 days ago | hide | past | pdf | discuss on HN

In plain words: They reshaped the optimization problem behind the standard fast-matrix-multiplication analysis so it can be solved more widely, then used machine learning and an evolutionary program to build and polish a solver. This cuts the upper bound on the matrix multiplication exponent from 2.371339 to 2.371177.

Abstract · Improving the matrix multiplication exponent with modern optimization and AlphaEvolve

The current best bounds on the matrix multiplication exponent $ω$ are obtained through a refinement of the laser method called combination loss analysis (Duan et al., 2022; Williams et al., 2024; Alman et al., 2025). In this note, we address the optimization problem at the core of this approach and propose several improvements. First, we reformulate the optimization problem allowing us to solve it in a larger setting than was previously possible. Second, we leverage recent advances in machine learning to design a new optimization algorithm for this problem. Finally, we refine the resulting optimization algorithm with AlphaEvolve. Our combined approach yields an upper bound of $ω$ < 2.371177, improving the previous best bound of 2.371339.

Emilien Dupont, Marvin Eisenberger, Borislav Kozlovskii, Abbas Mehrabian, Francisco J. R. Ruiz, Abigail See, Renfei Zhou, Josh Alman, Virginia Vassilevska Williams, Matej Balog
arXiv:2608.16884 · cs.DS, cs.AI, cs.CC, cs.LG · submitted Aug 17, 2026
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