CHESS: Chebyshev Spectral Synthesis for Trajectory Condensation

Learning from continuous-time trajectories requires modeling multivariate sensor measurements generated by underlying physical or dynamical processes. Under extreme data compression and heterogeneous sampling, directly optimizing synthetic signals as discrete sample values becomes fundamentally misaligned with the underlining \emph{continuous-time physical processes}, often producing high-frequency, non-physical artifacts that overfit specific models and break reuse across architectures and sampling rates. We propose CHESS, a \emph{function-first} synthesis framework shifts optimization from discrete samples to underlying continuous-time signal trajectories. CHESS injects physics-induced structure by jointly enforcing low-rank spatial coherence and piecewise Chebyshev polynomial temporal parameterization, constraining synthesis to a physically meaningful function manifold. We provide theoretical analysis establishing explicit smoothness and stability guaranties. Experiments on diverse sensor testbeds under the dataset distillation protocol demonstrate CHESS consistently outperform state-of-the-art methods with a compression ratios up to $133\times$ for each synthetic sample. Furthermore, CHESS exhibits strong cross-architecture generalization and enables zero-shot adaptation across different sampling resolutions.