这篇论文用AlphaEvolve把矩阵乘法指数上界刷到2.371177，比原来的2.371339又进一步，算法优化思路值得看看。
论文将矩阵乘法指数ω的优化问题重新表述，从而能在更大范围内求解。作者结合机器学习技术设计新优化算法，并用AlphaEvolve进一步精炼。最终将ω的上界从2.371339降至2.371177，刷新了此前的最好结果。
Improving the matrix multiplication exponent with modern optimization and AlphaEvolve
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.