Beyond Simple Aggregation: Decoupling Frequency-Aware Representation Learning and Gradient Boosting for Graph Anomaly Detection

Abstract

In knowledge-intensive systems such as cybersecurity and financial risk control, graph data encode business rules, interaction constraints, and risk propagation paths through entities and relations. As a result, supervised graph anomaly detection (GAD) goes beyond conventional attribute outlier identification and becomes a problem of discovering anomalous structural behavior patterns. Under such conditions, the area under the precision–recall curve (AUPRC) better reflects practical risk-control objectives. From a mechanistic perspective, fixed neighborhood aggregation in end-to-end graph neural networks (GNNs) exhibits a low-pass bias in graph signal processing terms. At the same time, joint training tightly couples structural representation learning with a shallow classifier head of limited capacity, making high-curvature nonlinear decision boundaries difficult to learn under extreme imbalance and creating a capacity mismatch. However, upstream feature construction remains constrained by fixed low-pass operators, which creates spectral conflict because a strong classifier receives weak features. More importantly, structural camouflage is often common, whereas feature spectra may shift either left or right, leading to structural-spectral decoupling and spectral divergence. To address spectral conflict and capacity mismatch, we propose TAFH (Task-Aware Frequency Hybrid) for graph anomaly detection. TAFH explicitly decomposes multi-hop neighborhood propagation into low-frequency smooth components and high-frequency residual components, and then constructs an adaptive band-pass response through learnable hop weighting and node-level gated routing. To reduce objective drift under class imbalance, TAFH introduces a lightweight proxy head with a proxy objective, including a focal-loss variant, to inject hard-sample and minority-class preferences into representation learning. On the discrimination side, gradient boosted decision trees (XGBoost) provide high-capacity nonlinear interaction modeling through a decoupled boosting interface. Across five benchmark datasets (Reddit, YelpChi, Amazon, Tolokers, and Questions), TAFH consistently improves AUPRC over the strong baseline built from XGBoost and fixed neighborhood aggregation, with absolute gains from +1.12% to +6.35% and relative gains from 1.88% to 19.75%. These results show that supervised GAD can be cast as a coordinated process of structural knowledge encoding, adaptive frequency enhancement, and discriminative knowledge learning.