Synthesis of fast multiplication algorithms for arbitrary tensors

TL;DR

This paper introduces a method to synthesize fast multiplication algorithms for any tensor by factorizing the tensor and constructing efficient computational structures for rapid tensor-vector multiplication.

Contribution

It presents a novel tensor factorization-based approach to automatically generate fast multiplication algorithms applicable to arbitrary tensors.

Findings

Effective tensor factorization for algorithm synthesis

Reduced computational complexity in tensor-vector multiplication

Applicable to both software and hardware implementations

Abstract

A method of fast linear transform algorithm synthesis for an arbitrary tensor, matrix, or vector is proposed. The method is based on factorization of a tensor and using the factors for building computational structures performing fast tensor - vector multiplication on a computer or dedicated hardware platform.