TipAD: Multivariate Anomaly Detection via Critical-Transition Theory

Anomaly detection is essential for applications from industrial monitoring to financial risk management. Progress in anomaly detection has largely come from architectural innovation, while the nature of anomalies has received comparatively little attention. We revisit anomaly detection from a dynamical-systems perspective. A system generating normal data operates near a stable attractor, and detecting an anomaly is essentially detecting a crossing, the process by which the system departs from this stable state. This is precisely what critical-transition theory studies. Motivated by this, we propose TipAD, a multivariate anomaly detection method. TipAD combines a dual-path predictor that models fast and slow dynamics separately with a Kalman-filter-based criticality estimator that converts the prediction residual into a stress statistic. On the TSB-AD-M benchmark, which covers 17 datasets and 30 baseline methods, TipAD achieves the second-best average rank under the threshold-independent VUS-PR metric, demonstrating strong competitiveness and consistency across datasets. Beyond the method itself, we further find that critical-transition theory derives a variance equation whose form matches the covariance-prediction equation in Kalman estimation theory, grounding our design in theory. To our knowledge, this correspondence has not been recognized or used for anomaly detection.