Ares: Approximate Representations via Efficient Sparsification -- A Stateless Approach through Polynomial Homomorphism

TL;DR

This paper presents Ares, a stateless compression method using polynomial homomorphism that efficiently compresses high-dimensional data, enabling scalable, interpretable, and algebraically operable data representations without auxiliary metadata.

Contribution

Ares introduces a novel, auxiliary-free polynomial-based compression framework that supports direct algebraic operations and maintains accuracy in streaming and large-scale data scenarios.

Findings

Achieves high compression ratios with minimal error growth

Supports direct algebraic operations in compressed domain

Demonstrates scalability and effectiveness on real-world datasets

Abstract

The increasing prevalence of high-dimensional data demands efficient and scalable compression methods to support modern applications. However, existing techniques like PCA and Autoencoders often rely on auxiliary metadata or intricate architectures, limiting their practicality for streaming or infinite datasets. In this paper, we introduce a stateless compression framework that leverages polynomial representations to achieve compact, interpretable, and scalable data reduction. By eliminating the need for auxiliary data, our method supports direct algebraic operations in the compressed domain while minimizing error growth during computations. Through extensive experiments on synthetic and real-world datasets, we show that our approach achieves high compression ratios without compromising reconstruction accuracy, all while maintaining simplicity and scalability.