Duan, Wu and Zhou (FOCS 2023) recently obtained the improved upper bound on the exponent of square matrix multiplication $\omega<2.3719$ by introducing a new approach to quantify and compensate the ``combination loss" in prior analyses of powers of the Coppersmith-Winograd tensor. In this paper we show how to use this new approach to improve the exponent of rectangular matrix multiplication as well. Our main technical contribution is showing how to combine this analysis of the combination loss and the analysis of the fourth power of the Coppersmith-Winograd tensor in the context of rectangular matrix multiplication developed by Le Gall and Urrutia (SODA 2018).

翻译：段、吴和周（FOCS 2023）近期通过引入量化并补偿先前Coppersmith-Winograd张量幂次分析中“组合损失”的新方法，将方阵乘法指数上界改进至$\omega<2.3719$。本文展示如何利用这一新方法改进矩形矩阵乘法的指数。我们的主要技术贡献在于：在Le Gall与Urrutia（SODA 2018）开发的矩形矩阵乘法背景下，将组合损失分析与Coppersmith-Winograd张量四次幂分析相结合。