Improving the matrix multiplication exponent with modern optimization and AlphaEvolve

Hugging Face Daily Papers Papers
matrix-multiplication optimization alphaevolve machine-learning algorithm exponent-bound arxiv

Summary

The paper proposes improvements to the optimization problem in combination loss analysis using modern techniques and AlphaEvolve, yielding an improved upper bound on the matrix multiplication exponent.

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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Source: https://huggingface.co/papers/2608.16884

Abstract

Refinements to combination loss analysis via reformulated optimization, machine learning-based algorithms, and AlphaEvolve yield an improved upper bound on the matrix multiplication exponent.

The current best bounds on thematrix multiplication exponentω are obtained through a refinement of thelaser methodcalledcombination 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 withAlphaEvolve. Our combined approach yields an upper bound of ω < 2.371177, improving the previous best bound of 2.371339.

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