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

arXiv: https://arxiv.org/abs/2406.11209 · HTML: https://mlsanity.com/paper/2406.11209/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 37 references that are in the map.
- First posted on arXiv 17 Jun 2024.

## Builds on (most cited first, 5 of 5)

- [Deep Residual Learning in the JPEG Transform Domain](https://mlsanity.com/paper/1812.11690/) (2018)
- [cuSZ: An Efficient GPU-Based Error-Bounded Lossy Compression Framework for Scientific Data](https://mlsanity.com/paper/2007.09625/) (2020)
- [Going Beyond Classification Accuracy Metrics in Model Compression](https://mlsanity.com/paper/2012.01604/) (2020)
- [Topological Feature Search in Time-Varying Multifield Data](https://mlsanity.com/paper/1911.00687/) (2019)
- [Compressed Matrix Computations](https://mlsanity.com/paper/2202.13007/) (2022)

## Abstract (arXiv)

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.