Defying Dimensions Mod 6

TL;DR

This paper demonstrates that specific matrix-product representations can be computed efficiently with sub-polynomial multiplications and can be significantly compressed, advancing matrix computation techniques.

Contribution

It introduces a novel method for efficiently computing and compressing matrix-product representations using sub-polynomial multiplications.

Findings

Matrix-product representations can be computed with $n^{o(1)}$ multiplications.

Such representations can be compressed substantially.

The methods improve efficiency in matrix computations.

Abstract

We show that a certain representation of the matrix-product can be computed with $n^{o(1)}$ multiplications. We also show, that siumilar representations of matrices can be compressed enormously.