Paper Overview
Field: Machine Learning / Computational Complexity Authors: Emilien Dupont, Marvin Eisenberger, Borislav Kozlovskii et al. (10 authors) Published: 2026-08-17 arXiv: 2608.16884
Summary
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, the authors address the optimization problem at the core of this approach and propose several improvements:
1. Reformulation: The optimization problem is reformulated, allowing it to be solved in a larger setting than was previously possible. 2. Machine learning: Recent advances in machine learning are leveraged to design a new optimization algorithm for this problem. 3. AlphaEvolve refinement: The resulting optimization algorithm is further refined with AlphaEvolve.
Result
The combined approach yields an upper bound of ω < 2.371177, improving the previous best bound of 2.371339.
Original Abstract
> 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.
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