Generalized cyclic symmetric decompositions for the matrix multiplication tensor

TL;DR

This paper introduces a generalized cyclic symmetric structure for matrix multiplication tensor decompositions, reducing variables and improving convergence in numerical optimization, leading to more practical decompositions.

Contribution

It proposes a novel cyclic symmetric structure for tensor decompositions that enhances optimization efficiency for non-square matrix multiplication.

Findings

The new structure reduces the number of variables in the optimization problem.

Numerical experiments show improved convergence and more practical decompositions.

The approach is effective for non-square matrix multiplication tensors.

Abstract

A new generalized cyclic symmetric structure in the factor matrices of polyadic decompositions of matrix multiplication tensors for non-square matrix multiplication is proposed to reduce the number of variables in the optimization problem and in this way improve the convergence. The structure is implemented in an existing numerical optimization algorithm. Extensive numerical experiments are given that the proposed structure indeed finds more (practical) decompositions.