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Zero-shot Generalizable Graph Anomaly Detection with Mixture of Riemannian Experts

Xinyu Zhao, Qingyun Sun, Jiayi Luo, Xingcheng Fu, Jianxin Li

TL;DR

This work tackles zero-shot generalization for graph anomaly detection by exposing geometric heterogeneity across graph domains. It introduces GAD-MoRE, a framework that combines anomaly-aware multi-curvature feature alignment with a mixture of Riemannian experts and a memory-based dynamic router to adaptively select the most suitable curvature space for each node. Empirical results show state-of-the-art zero-shot performance across 7 unseen graphs, often surpassing few-shot fine-tuned competitors, highlighting the value of geometry-aware generalization. The approach offers a scalable, unsupervised pathway to robust cross-domain GAD, with implications for deploying anomaly detectors in diverse, label-scarce environments.

Abstract

Graph Anomaly Detection (GAD) aims to identify irregular patterns in graph data, and recent works have explored zero-shot generalist GAD to enable generalization to unseen graph datasets. However, existing zero-shot GAD methods largely ignore intrinsic geometric differences across diverse anomaly patterns, substantially limiting their cross-domain generalization. In this work, we reveal that anomaly detectability is highly dependent on the underlying geometric properties and that embedding graphs from different domains into a single static curvature space can distort the structural signatures of anomalies. To address the challenge that a single curvature space cannot capture geometry-dependent graph anomaly patterns, we propose GAD-MoRE, a novel framework for zero-shot Generalizable Graph Anomaly Detection with a Mixture of Riemannian Experts architecture. Specifically, to ensure that each anomaly pattern is modeled in the Riemannian space where it is most detectable, GAD-MoRE employs a set of specialized Riemannian expert networks, each operating in a distinct curvature space. To align raw node features with curvature-specific anomaly characteristics, we introduce an anomaly-aware multi-curvature feature alignment module that projects inputs into parallel Riemannian spaces, enabling the capture of diverse geometric characteristics. Finally, to facilitate better generalization beyond seen patterns, we design a memory-based dynamic router that adaptively assigns each input to the most compatible expert based on historical reconstruction performance on similar anomalies. Extensive experiments in the zero-shot setting demonstrate that GAD-MoRE significantly outperforms state-of-the-art generalist GAD baselines, and even surpasses strong competitors that are few-shot fine-tuned with labeled data from the target domain.

Zero-shot Generalizable Graph Anomaly Detection with Mixture of Riemannian Experts

TL;DR

This work tackles zero-shot generalization for graph anomaly detection by exposing geometric heterogeneity across graph domains. It introduces GAD-MoRE, a framework that combines anomaly-aware multi-curvature feature alignment with a mixture of Riemannian experts and a memory-based dynamic router to adaptively select the most suitable curvature space for each node. Empirical results show state-of-the-art zero-shot performance across 7 unseen graphs, often surpassing few-shot fine-tuned competitors, highlighting the value of geometry-aware generalization. The approach offers a scalable, unsupervised pathway to robust cross-domain GAD, with implications for deploying anomaly detectors in diverse, label-scarce environments.

Abstract

Graph Anomaly Detection (GAD) aims to identify irregular patterns in graph data, and recent works have explored zero-shot generalist GAD to enable generalization to unseen graph datasets. However, existing zero-shot GAD methods largely ignore intrinsic geometric differences across diverse anomaly patterns, substantially limiting their cross-domain generalization. In this work, we reveal that anomaly detectability is highly dependent on the underlying geometric properties and that embedding graphs from different domains into a single static curvature space can distort the structural signatures of anomalies. To address the challenge that a single curvature space cannot capture geometry-dependent graph anomaly patterns, we propose GAD-MoRE, a novel framework for zero-shot Generalizable Graph Anomaly Detection with a Mixture of Riemannian Experts architecture. Specifically, to ensure that each anomaly pattern is modeled in the Riemannian space where it is most detectable, GAD-MoRE employs a set of specialized Riemannian expert networks, each operating in a distinct curvature space. To align raw node features with curvature-specific anomaly characteristics, we introduce an anomaly-aware multi-curvature feature alignment module that projects inputs into parallel Riemannian spaces, enabling the capture of diverse geometric characteristics. Finally, to facilitate better generalization beyond seen patterns, we design a memory-based dynamic router that adaptively assigns each input to the most compatible expert based on historical reconstruction performance on similar anomalies. Extensive experiments in the zero-shot setting demonstrate that GAD-MoRE significantly outperforms state-of-the-art generalist GAD baselines, and even surpasses strong competitors that are few-shot fine-tuned with labeled data from the target domain.
Paper Structure (25 sections, 11 equations, 5 figures, 6 tables, 2 algorithms)

This paper contains 25 sections, 11 equations, 5 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Graph Anomaly Detection
  4. Mixture of Experts for Graph Learning
  5. Riemannian Graph Learning
  6. Preliminaries
  7. Notations and Problem Formulation
  8. Constant Curvature Manifolds
  9. The Proposed GAD-MoRE Framework
  10. Anomaly-aware Multi-curvature Feature Alignment
  11. Mixture of Riemannian Experts Scorer
  12. Memory-based Dynamic Router
  13. Model Training and Optimization
  14. Anomaly Inference
  15. Experiments
  16. ...and 10 more sections

Figures (5)

  • Figure 1: The left part illustrates the projection of graph structures into Hyperbolic ($\kappa < 0$), Euclidean ($\kappa = 0$), and Spherical ($\kappa > 0$) spaces. It highlights that anomalous nodes (red), which are intrinsically hidden within the original graph topology, become significantly more separable and detectable from normal nodes (blue) once mapped into these Riemannian manifolds. The right part quantifies this effect by showing the average AUROC performance of representative GAD methods (including K-Means hartigan1979algorithm, k-NN cover1968estimation, and Isolation Forest liu2008isolation) across varying curvature values $\kappa \in [-1.0, 1.0]$ on four datasets: Amazon rayana2015collective, Weibo kumar2019predicting, Cora sen2008collective, and CiteSeer sen2008collective.
  • Figure 2: The overall architecture of the GAD-MoRE framework. (1) The Anomaly-aware Multi-curvature Feature Alignment module projects raw features into a unified, geometry-aware representation. (2) The Mixture of Riemannian Experts Scorer utilizes a GNN backbone to encode structural context and employs specialized Riemannian expert networks. (3) The Memory-based Dynamic Router adaptively assigns nodes to these experts based on historical reconstruction quality to compute the final anomaly score.
  • Figure 3: AUROC performance of GAD-MoRE and its ablation variants on target GAD datasets. All models are trained exclusively on four source graphs (PubMed, Flickr, Reddit, YelpChi) and evaluated in a zero-shot cross-domain setting.
  • Figure 4: Hyperparameter sensitivity analysis of GAD-MoRE. The left two subplots show the impact of the unified embedding dimension $D$ on AUROC and AUPRC, while the right two subplots illustrate the sensitivity to the number of experts $K$.
  • Figure 5: The anomaly score distributions for Citeseer and Cora show a clear distinction between normal and anomalous nodes. This visual evidence confirms that our approach can effectively detect anomalies in these graph datasets.