What Operations can be Performed Directly on Compressed Arrays, and with What Error?

TL;DR

This paper introduces PyBlaz, a novel lossy compressor enabling fundamental operations directly on compressed data, reducing data movement costs while maintaining acceptable errors and scalability.

Contribution

The work presents the first lossy compressor supporting direct compressed-domain operations with good performance and controlled errors, implemented on GPU using PyTorch.

Findings

Supports a dozen fundamental operations directly on compressed data

Achieves good scalability with problem size

Maintains errors within acceptable limits

Abstract

In response to the rapidly escalating costs of computing with large matrices and tensors caused by data movement, several lossy compression methods have been developed to significantly reduce data volumes. Unfortunately, all these methods require the data to be decompressed before further computations are done. In this work, we develop a lossy compressor that allows a dozen fairly fundamental operations directly on compressed data while offering good compression ratios and modest errors. We implement a new compressor PyBlaz based on the familiar GPU-powered PyTorch framework, and evaluate it on three non-trivial applications, choosing different number systems for internal representation. Our results demonstrate that the compressed-domain operations achieve good scalability with problem sizes while incurring errors well within acceptable limits. To our best knowledge, this is the first such lossy compressor that supports compressed-domain operations while achieving acceptable performance as well as error.