Graph Nonlinear Schrödinger Networks for Anomaly Detection

Supervised graph anomaly detection has to serve two frequency regimes at once because camouflaged fraudsters mimic their neighbors while other anomalies clash with their neighborhoods. Any single spectral response therefore fails in some regime. We introduce G-SNLS, a deterministic graph network whose depth is a bank of Schrödinger-type propagators. Each head learns its own damping, dispersion and time scale so that attenuation and phase velocity separate while several regimes coexist. Intensity-dependent coupling makes the flow nonlinear while paired decoders absorb the class imbalance. We prove an exact energy-decay law per step together with closure of the response family under composition and a full-depth state bound. G-SNLS takes the leading average rank on both ranking metrics across eight public benchmarks. Through ablations, we attribute the gains to the intensity coupling and the channel map. Compared with an unconstrained filter of matched degree, the constraint preserves accuracy while it yields a response that cannot diverge with depth and a loss surface whose most curved direction is flatter per unit change in the response.