Title: Free Point-wise Anomaly Detection via Fold-bifurcation
Primary area: learning on time series and dynamical systems
Keywords: time-series, anomly detection

Abstract: Anomaly detection in time series is essential for applications from industrial monitoring to financial risk management. Recent methods --- including forecasting error models, representation learning, augmentation, and weak-label learning --- have achieved strong results for specific anomaly types such as sudden point or gradual collective anomalies. However, most approaches are evaluated under coarse window-level settings, which can mask their limitations in the stricter point-wise anomaly detection scenario. We introduce \textbf{FREE} (Free point-wise Anomaly Detection via fold-bifurcation), a framework that reframes detection as tracking a system’s proximity to a critical transition. FREE extracts stress signals from a forecasting model and integrates them with a fold-bifurcation inspired ODE to produce the risk state, flagging anomalies once it crosses a threshold calibrated on normal data. This requires no anomaly labels and detector training, enabling free and efficient detection. By modeling anomalies as stress accumulation toward a tipping point, FREE naturally aligns with point-wise detection, providing a unifying and interpretable perspective that complements type-specific methods. Experiments on 9 benchmarks against 10 state-of-the-art baselines show that FREE achieves competitive or superior performance, with particular strength under strict point-wise evaluation.

TL;DR: point-wise anomaly detection via fold-bifurcation