Title: JacobiGAD: Jacobi Polynomial–Powered Heterogeneous Graph-Level Anomaly Detection
Primary area: learning on graphs and other geometries & topologies
Keywords: Heterogeneous Graph, Anomaly Detection, Jacobi Polynomials

Abstract: Heterogeneous graph-level anomaly detection is vital for applications such as fraud detection and drug discovery, yet remains challenging due to mixed features, complex structures, and severe class imbalance. This paper introduces JacobiGAD, a unified framework that addresses these challenges through three key innovations. First, learnable multiscale filters based on Jacobi Polynomials adapt to different node and edge types, fusing multiple graph views to enhance anomaly signals. Second, these polynomials enable efficient approximation of targeted functions and naturally encode diverse geometries. Third, a Ricci Flow-inspired loss amplifies gradients for rare anomalies, mitigating class imbalance without distorting graph embeddings, ensuring stable convergence. Extensive experiments on real-world benchmarks show JacobiGAD outperforms the best baseline by up to 2.79\% (AUROC), 7.78\% (AUPRC), 7.11\% (Recall@k), and 5.96\% (F1-score) on average.