通过机器学习优化矩阵乘法，新上限突破2.371177
Improving the matrix multiplication exponent with modern optimization and AlphaEvolve
- 重构优化问题，扩大求解空间
- 结合机器学习与AlphaEvolve，提升算法性能
- 适用于理论计算与算法优化研究者
目前矩阵乘法指数 $ω$ 的最佳上界是通过改进激光法的组合损失分析得到的（Duan et al., 2022；Williams et al., 2024；Alman et al., 2025）。本文针对该方法的核心优化问题提出多项改进：首先重构优化问题，使求解范围比以往更大；其次利用机器学习最新进展设计新优化算法；最后通过AlphaEvolve进一步精炼算法。所提综合方法将 $ω$ 的上界改进至小于 2.371177，优于此前最优的 2.371339。
原文摘要 · Abstract (English)
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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