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：本文提出一种基于具有特殊结构的张量分解的快速矩阵乘法新算法。得益于这些结构特性，我们获得的指数低于张量分解的秩所对应的理论值。特别地，对于$6\times 6$矩阵乘法，我们将Moosbauer与Poole近期算法中的指数从$2.8075$降低至$2.8016$，同时保持了合理的主导系数。