[论文] Improving the matrix multiplication exponent with modern optimization ...

论文概要

研究领域: ML
作者: Emilien Dupont, Marvin Eisenberger, Borislav Kozlovskii et al. (10 authors)
发布时间: 2026-08-17
arXiv: 2608.16884

中文摘要

当前矩阵乘法指数ω的最佳界是通过激光方法的改进——组合损失分析获得的（Duan等人，2022；Williams等人，2024；Alman等人，2025）。本文针对这一方法核心的优化问题提出了多项改进。首先，我们重新表述优化问题，使其能在比以往更大的设置中求解。其次，我们利用机器学习的最新进展为这一问题设计了新的优化算法。最后，我们用AlphaEvolve进一步完善所得优化算法。我们的综合方法得到ω < 2.371177的上界，改进了此前最佳的2.371339。

原文摘要

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.

自动采集于 2026-08-19

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