[2608.16884] Improving the matrix multiplication exponent with modern optimization and AlphaEvolve

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arXiv:2608.16884 (cs)

[Submitted on 17 Aug 2026]

Title:Improving the matrix multiplication exponent with modern optimization and AlphaEvolve

Authors:Emilien Dupont, Marvin Eisenberger, Borislav Kozlovskii, Abbas Mehrabian, Francisco J. R. Ruiz, Abigail See, Renfei Zhou, Josh Alman, Virginia Vassilevska Williams, Matej Balog<br>View a PDF of the paper titled Improving the matrix multiplication exponent with modern optimization and AlphaEvolve, by Emilien Dupont and 9 other authors

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Abstract:The current best bounds on the matrix multiplication exponent $\omega$ 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 $\omega$

Subjects:

Data Structures and Algorithms (cs.DS); Artificial Intelligence (cs.AI); Computational Complexity (cs.CC); Machine Learning (cs.LG)

Cite as:<br>arXiv:2608.16884 [cs.DS]

(or<br>arXiv:2608.16884v1 [cs.DS] for this version)

https://doi.org/10.48550/arXiv.2608.16884

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arXiv-issued DOI via DataCite (pending registration)

Submission history<br>From: Emilien Dupont [view email]<br>[v1]<br>Mon, 17 Aug 2026 17:59:05 UTC (223 KB)

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