We present a new improvement on the laser method for designing fast matrix multiplication algorithms. The new method further develops the recent advances by [Duan, Wu, Zhou FOCS 2023] and [Vassilevska Williams, Xu, Xu, Zhou SODA 2024]. Surprisingly the new improvement is achieved by incorporating more asymmetry in the analysis, circumventing a fundamental tool of prior work that requires two of the three dimensions to be treated identically. The method yields a new bound on the square matrix multiplication exponent $$\omega<2.371339,$$ improved from the previous bound of $\omega<2.371552$. We also improve the bounds of the exponents for multiplying rectangular matrices of various shapes.

翻译：我们提出了一种快速矩阵乘法算法设计的新改进，该改进基于激光方法。新方法进一步发展了[Duan, Wu, Zhou FOCS 2023]和[Vassilevska Williams, Xu, Xu, Zhou SODA 2024]的最新进展。令人惊讶的是，新改进是通过在分析中引入更多不对称性来实现的，规避了先前工作中要求三个维度中有两个维度被同等对待的基本工具。该方法为方阵乘法指数$$\omega<2.371339$$提供了新的界，优于之前的$$\omega<2.371552$$。我们还改进了各种形状矩形矩阵乘法指数的界。