Exploiting the Structure in Tensor Decompositions for Matrix Multiplication
This work provides an incremental improvement in the exponent for matrix multiplication, a fundamental problem in computer science.
The paper presents a new algorithm for fast matrix multiplication that exploits special features in tensor decompositions to achieve lower exponents than the tensor rank suggests. For 6×6 matrix multiplication, the exponent is reduced from 2.8075 to 2.8019 with a reasonable leading coefficient.
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 $2.8019$, while retaining a reasonable leading coefficient.