Koopman Invariants as Drivers of Emergent Time-Series Clustering in Joint-Embedding Predictive Architectures

Joint-Embedding Predictive Architectures (JEPAs), a powerful class of self-supervised models, exhibit an unexplained ability to cluster time-series data by their underlying dynamical regimes. We propose a novel theoretical explanation for this phenomenon, hypothesizing that JEPA's predictive objective implicitly drives it to learn the invariant subspace of the system's Koopman operator. We prove that an idealized JEPA loss is minimized when the encoder represents the system's regime indicator functions, which are Koopman eigenfunctions. This theory was validated on synthetic data with known dynamics, demonstrating that constraining the JEPA's linear predictor to be a near-identity operator is the key inductive bias that forces the encoder to learn these invariants. We further discuss that this constraint is critical for selecting this interpretable solution from a class of mathematically equivalent but entangled optima, revealing the predictor's role in representation disentanglement. This work demystifies a key behavior of JEPAs, provides a principled connection between modern self-supervised learning and dynamical systems theory, and informs the design of more robust and interpretable time-series models.

dtaianomaly: A Python library for time series anomaly detection

dtaianomaly is an open-source Python library for time series anomaly detection, designed to bridge the gap between academic research and real-world applications. Our goal is to (1) accelerate the development of novel state-of-the-art anomaly detection techniques through simple extensibility; (2) offer functionality for large-scale experimental validation; and thereby (3) bring cutting-edge research to business and industry through a standardized API, similar to scikit-learn to lower the entry barrier for both new and experienced users. Besides these key features, dtaianomaly offers (1) a broad range of built-in anomaly detectors, (2) support for time series preprocessing, (3) tools for visual analysis, (4) confidence prediction of anomaly scores, (5) runtime and memory profiling, (6) comprehensive documentation, and (7) cross-platform unit testing. The source code of dtaianomaly, documentation, code examples and installation guides are publicly available at https://github.com/ML-KULeuven/dtaianomaly.