Rethinking Time Series Anomaly Detection from a Dynamic Perspective: Temporal-Frequency-Curvature Fusion

Time series anomaly detection (TSAD) plays a pivotal role in domains ranging from industrial automation to IT operations and healthcare monitoring. Despite significant advances in point-wise outlier detection, real anomalies are often not obvious spikes. Instead, they frequently manifest as mechanism shifts, subtle changes in how a signal bends, drifts, or evolves, whose point-wise residuals can remain small and be further suppressed by the smoothing bias of modern deep detectors. Motivated by a dynamical perspective that treats a time series as a trajectory generated by an evolving system, we introduce TFC, a unified TSAD framework that, to our knowledge, is the first to integrate a curvature perspective alongside established temporal and frequency analyses. TFC introduces a curvature perspective based on second-order differences to amplify geometry level deviations, and uses a Multi-Span Attention reader to capture dynamical signatures across short, mid, and long range supports. To avoid false alarms caused by benign oscillations, TFC adopts a two-stage fusion strategy: (i) frequency and curvature cross-attention calibrates curvature sensitivity with periodic robustness, and (ii) an expert router adaptively balances fused pattern evidence with temporal cues at each timestamp. Across six benchmarks and baselines, TFC achieves state of the art average Best-F1 and Event-F1, yielding a 10.8% average improvement over a strong baseline while maintaining stable performance across window lengths and favorable accuracy and latency trade offs.