We present a new algorithm for fast matrix multiplication using tensor decompositions which have special features. Thanks to these features we obtain exponents lower than what the rank of the tensor decomposition suggests. In particular for $6\times 6$ matrix multiplication we reduce the exponent of the recent algorithm by Moosbauer and Poole from $2.8075$ to $2.8016$, while retaining a reasonable leading coefficient.

翻译：本文提出一种基于特殊结构张量分解的快速矩阵乘法新算法。借助这些结构特性，我们获得的指数低于张量分解秩所对应的理论值。特别针对 $6\times 6$ 矩阵乘法，我们在保持合理首项系数的前提下，将 Moosbauer 与 Poole 近期算法中的指数从 $2.8075$ 降至 $2.8016$。