K-VIC: Koopman Dynamics and Variance-Covariance Regularization for Time Series Representation

Self-supervised representation learning for time series has largely bifurcated into contrastive and generative paradigms. However, both approaches can face challenges in capturing underlying physical dynamics: contrastive methods risk altering temporal semantics through heuristic spatial augmentations, while generative masked modeling tends to overfit high-frequency sensor noise rather than abstracting stable evolution laws. In this work, we posit that the semantic identity of a time series is defined not only by static patterns, but also by its invariant laws of transition. To operationalize this, we introduce K-VIC, a novel framework that embeds the Koopman Operator into a Variance-Covariance regularization scheme. By linearizing non-linear temporal dynamics in a high-dimensional latent space, K-VIC acts as a physics-inspired spectral filter that effectively preserves persistent dynamic modes while discarding non-systematic fluctuations. Furthermore, instead of relying on augmented negative pairs or static spatial invariance, we propose predictive and cyclic consistency paired with informational constraints to mitigate representation collapse and encourage orthogonal feature disentanglement. Empirical evaluations across five benchmarks demonstrate that K-VIC achieves state-of-the-art (SotA) accuracy without dataset-specific hyperparameter tuning. Notably, it exhibits strong robustness in noise-heavy industrial scenarios (yielding an over 20 https://github.com/Conrrile/K-VIC .