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

arXiv: https://arxiv.org/abs/2412.10623 · HTML: https://mlsanity.com/paper/2412.10623/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 31 references that are in the map.
- First posted on arXiv 14 Dec 2024.

## Builds on (most cited first, 3 of 3)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Lossy Image Compression with Compressive Autoencoders](https://mlsanity.com/paper/1703.00395/) (2017)

## Abstract (arXiv)

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.