LogVAMS: Physics-Inspired Anomaly Detection Through Information Geometry and Critical Phenomena

Presents LogVAMS (Log-based Variance and Anomaly Monitoring System), a comprehensive suite of physics-inspired anomaly detection methods for software systems. Implements four complementary detection methods: PhaseMonitor detecting critical slowing down via AR(1) coefficient and variance dynamics; Fisher Information Geometry measuring novelty through geodesic distances on statistical manifolds; Holographic Projection exploiting boundary-bulk duality for dimensional reduction; and Free Energy Alerting using predictive coding principles. On synthetic log data with 162 injected failure events, PhaseMonitor achieves mean lead time of 35.9±12.3 observations with recall 1.00 and AUROC 0.847, significantly outperforming baseline methods (Isolation Forest, One-Class SVM) which achieve lead time ≈0. Demonstrates that physics-inspired mathematics produces actionable predictions for capacity-constrained systems regardless of substrate.