通过现代优化与AlphaEvolve改进矩阵乘法指数
Improving the matrix multiplication exponent with modern optimization and AlphaEvolve
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中文总结 AI 辅助
本研究通过重新构建优化问题、结合机器学习新进展及AlphaEvolve改进算法，将矩阵乘法指数ω的最优上界从2.371339提升至2.371177。
中文摘要 AI 辅助
当前矩阵乘法指数ω的最优上界是通过激光方法的改进版本——组合损失分析（Duan等人，2022；Williams等人，2024；Alman等人，2025）得到的。在本研究中，我们解决该方法核心的优化问题并提出多项改进：首先，我们重新构建优化问题，使其可在比以往更大的规模下求解；其次，我们利用近期机器学习领域的进展，为该问题设计新的优化算法；最后，我们用AlphaEvolve对所得优化算法进行改进。我们的组合方法得到ω < 2.371177的上界，优于此前最优的2.371339。
英文摘要
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.
发表机构
- Carnegie Mellon University（卡内基梅隆大学）
- Columbia University（哥伦比亚大学）
- MIT（麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。
