无需额外数据，用多项式压缩高维数据并支持直接计算
Ares: Approximate Representations via Efficient Sparsification -- A Stateless Approach through Polynomial Homomorphism
- 用多项式同态实现无状态稀疏化压缩
- 压缩比高且重建误差小，计算过程误差增长可控
- 适合流式数据或无限数据集的实时处理
高维数据日益普遍，亟需高效可扩展的压缩方法以支撑现代应用。然而，现有方法如PCA和自编码器常依赖辅助元数据或复杂架构，限制了其在流式或无限数据集中的实用性。本文提出一种无状态压缩框架，利用多项式表示实现紧凑、可解释且可扩展的数据降维。通过消除对辅助数据的需求，该方法可在压缩域中直接进行代数运算，同时最小化计算过程中的误差增长。在合成与真实世界数据集上的大量实验表明，本方法在不牺牲重建精度的前提下实现了高压缩比，且保持了简单性与可扩展性。
原文摘要 · Abstract (English)
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.
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