Performance Enhancement of the Ozaki Scheme on Integer Matrix Multiplication Unit

TL;DR

This paper enhances the Ozaki scheme for integer matrix multiplication by proposing methods to reduce computational steps, aiming to improve accuracy and performance on architectures like GPUs designed for low-precision calculations.

Contribution

It introduces alternative approaches that decrease the number of lower-precision multiplications and higher-precision additions in the Ozaki scheme, boosting efficiency.

Findings

Numerical experiments confirm the accuracy of the proposed methods.

Performance benchmarks show improved efficiency over previous implementations.

Approaches are suitable for next-generation architectures with low-precision units.

Abstract

This study was aimed at simultaneously achieving sufficient accuracy and high performance for general matrix multiplications. Recent architectures, such as NVIDIA GPUs, feature high-performance units designed for low-precision matrix multiplications in machine learning models, and next-generation architectures are expected to follow the same design principle. The key to achieving superior performance is to fully leverage such architectures. The Ozaki scheme, a highly accurate matrix multiplication algorithm using error-free transformations, enables higher-precision matrix multiplication to be performed through multiple lower-precision matrix multiplications and higher-precision matrix additions. Ootomo et al. implemented the Ozaki scheme on high-performance matrix multiplication units with the aim of achieving both sufficient accuracy and high performance. This paper proposes alternative approaches to improving performance by reducing the numbers of lower-precision matrix multiplications and higher-precision matrix additions. Numerical experiments demonstrate the accuracy of the results and conduct performance benchmarks of the proposed approaches. These approaches are expected to yield more efficient results in next-generation architectures.