Geometry-Aware Riemannian Residual Displacement for Cross-Broad-Domain Graph Anomaly Detection

Abstract

Cross-Domain Graph Anomaly Detection supports the transfer of knowledge to unknown targets. Nevertheless, current approaches frequently struggle in the Cross-Broad-Domain paradigm which is characterized by two significant discrepancies: feature heterogeneity and structural disparity. Such diverse geometric topologies result in substantial manifold mismatch, as the traditional dependence on linear residuals in flat Euclidean space induces considerable geometric distortion when accommodating various topological patterns. We propose a novel framework termed Geometry-aware Riemannian Anomaly DEtector (GRADE) to tackle these difficulties. To address the semantic gap, we develop a domain-based contrastive learning technique combined with target-adaptive prompt tuning, which dynamically adjusts source representations to align with the target distribution while maintaining local contexts. To tackle the manifold mismatch, we present the Riemannian Residual Displacement (RRD), a curvature-adaptive metric that maps node representations onto multi-curvature Riemannian manifolds. By quantifying geodesic deviations in curved spaces, RRD corrects geometric distortions and identifies anomaly patterns that remain invariant to topological alterations. Additionally, a geometry-aware prototype alignment approach secures these residuals to data-independent priors for resilient inference. Comprehensive experiments on 11 benchmark datasets across 4 distinct domains demonstrate that GRADE significantly outperforms state-of-the-art baselines in both zero-shot and few-shot settings.