Hierarchical Lowrank Arithmetic with Binary Compression

TL;DR

This paper explores hierarchical low-rank matrix approximations combined with adaptive binary compression techniques to reduce storage and improve efficiency, especially for data lacking global low-rank properties.

Contribution

It introduces a novel approach that integrates adaptive binary compression with hierarchical low-rank arithmetic, surpassing traditional floating-point formats in storage efficiency.

Findings

Adaptive compression reduces storage significantly.

Hierarchical low-rank arithmetic maintains accuracy with compressed data.

The approach outperforms standard IEEE754 formats in storage efficiency.

Abstract

With lowrank approximation the storage requirements for dense data are reduced down to linear complexity and with the addition of hierarchy this also works for data without global lowrank properties. However, the lowrank factors itself are often still stored using double precision numbers. Newer approaches exploit the different IEEE754 floating point formats available nowadays in a mixed precision approach. However, these formats show a significant gap in storage (and accuracy), e.g. between half, single and double precision. We therefore look beyond these standard formats and use adaptive compression for storing the lowrank and dense data and investigate how that affects the arithmetic of such matrices.