Spectral Filtering for Temporal Compression in Sequences from Linear & Nonlinear Dynamical Systems

Abstract

We study the problem of compressing streams of observations from nonlinear closed-loop dynamical systems, which present technical challenges for storage and analysis. We propose a compression scheme based on spectral filtering that produces representations whose size is independent of the sequence length T, under the assumption that inputs are observed online. Adopting an improper learning perspective, we obtain provable guaranties on the reconstruction error without requiring knowledge of the true underlying dynamics. Our main insight is a two-step approximation: first approximating a nonlinear system by a high-dimensional linear system via global linearization and then applying spectral filtering to extract a compact representation with exponentially decaying reconstruction error in the number of filters k. We empirically validate our findings across five dynamical systems of varying complexity, consistently outperforming baseline compression filters.