AlphaEvolve paper reports tighter matrix multiplication exponent bound

The arXiv paper “Improving the matrix multiplication exponent with modern optimization and AlphaEvolve” reports an upper bound of ω < 2.371177, improving the previous best bound of 2.371339, according to its abstract. Hugging Face Papers lists the work under arXiv:2608.16884.

The paper lists ten authors, including Emilien Dupont, Abbas Mehrabian and Matej Balog alongside Josh Alman, Virginia Vassilevska Williams and Renfei Zhou. Its abstract credits the current best bounds to Duan et al. 2022, Williams et al. 2024 and Alman et al. 2025, so several of the researchers behind the earlier records appear on the paper that improves them.

The paper’s abstract says current best bounds on the matrix multiplication exponent are obtained through a refinement of the laser method called combination loss analysis. It says the work addresses the optimization problem at the center of that approach by reformulating it in a larger setting, using machine learning to design a new optimization algorithm, and refining that algorithm with AlphaEvolve.

The paper presents 2.371177 as an upper bound, not as a claim that the exact value of ω is 2.371177. Its abstract compares the result with the previous best upper bound of 2.371339 and describes the difference as the outcome of the combined approach.

The reported result is therefore a tighter numerical bound for the matrix multiplication exponent. The abstract attributes the improvement to the combination of the reformulated optimization problem, a machine-learning-based optimization algorithm, and AlphaEvolve; it does not provide a separate exact value for ω.