AlphaEvolve helps push matrix multiplication ω to 2.371177

The upper bound on the matrix multiplication exponent ω has moved from 2.371339 to 2.371177.

The improvement comes in a short arxiv note submitted on 17 August 2026, "Improving the matrix multiplication exponent with modern optimization and AlphaEvolve." The author list runs to ten names and includes Josh Alman and Virginia Vassilevska Williams, whose 2024 and 2025 papers set the previous bounds, alongside Matej Balog, Francisco J. R. Ruiz, Abigail See and other researchers working with AlphaEvolve.

The paper attacks the optimization problem at the core of "combination loss analysis," a refinement of the laser method used by Duan et al. (2022), Williams et al. (2024) and Alman et al. (2025).

"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," the authors write. The combined pipeline, they report, "yields an upper bound of ω < 2.371177, improving the previous best bound of 2.371339."

The note's abstract stops short of describing the new optimization algorithm, listing compute costs, or claiming the bound is tight. The gain over the prior record lands at the fifth decimal place.