Strassen's Matrix Multiplication Algorithm Is Still Faster

TL;DR

This paper introduces Matrix Flow, a Python tool for designing and executing fast matrix multiplication algorithms, demonstrating that Strassen's algorithm remains superior on modern CPUs and GPUs despite recent algorithmic advances.

Contribution

The paper presents Matrix Flow, a framework for automatic formulation and implementation of matrix multiplication algorithms, and provides empirical evidence that Strassen's algorithm outperforms newer algorithms on current hardware.

Findings

Strassen's algorithm remains the fastest for modern CPUs and GPUs.

Matrix Flow enables easy design and testing of matrix algorithms.

Integer computations in these algorithms are always correct.

Abstract

Recently, reinforcement algorithms discovered new algorithms that really jump-started a wave of excitements and a flourishing of publications. However, there is little on implementations, applications, and, especially, no absolute performance and, we show here they are not here to replace Strassen's original fast matrix multiplication yet. We present Matrix Flow, this is a simple Python project for the automatic formulation, design, implementation, code generation, and execution of fast matrix multiplication algorithms for CPUs, using BLAS interface GPUs, and in the future other accelerators. We shall not play with module-2 (Z2) algorithms and, for simplicity, we present only square double-precision matrices. By means of factorizing the operand matrices we can express many algorithms and prove them correct. These algorithms are represented by Data Flows and matrix data partitions: a Directed Acyclic Graph. We show that Strassen's original algorithm is still the top choice even for modern GPUs. We also address error analysis in double precision, because integer computations are correct, always