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CurvGAD: Leveraging Curvature for Enhanced Graph Anomaly Detection
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Proposes CurvGAD, a mixed-curvature graph autoencoder that reconstructs Ollivier-Ricci edge curvature on a product manifold alongside Ricci-flow-regularized structure and attribute reconstruction, for node-level graph anomaly detection.
Problem
Reconstruction-based graph anomaly detection overlooks geometric (curvature-based) anomalies and struggles on heterophilic graphs, and existing methods assume Euclidean representations.
Approach
Two parallel pipelines: a mixed-curvature (product manifold) Chebyshev filterbank encoder with a Gaussian-kernel decoder that reconstructs Ollivier-Ricci curvature, and a Euclidean encoder/decoder that reconstructs adjacency and features on a graph first regularized by discrete Ollivier-Ricci flow, so that the latter is curvature-invariant.
Key results
- CurvGAD achieves the best AUROC on all 10 datasets, e.g., 99.62 on Amazon and 99.04 on Weibo, with reported gains of up to 6.5% over the second-best model (DGraph-Fin).
- Ablation: the Euclidean-only variant drops about 5% on average; removing Ricci flow drops 10.77% on Tolokers and 3.94% on Reddit.
- Removing the curvature reconstruction loss (invariant-only variant) drops 8.39% on Reddit and 6.86% on Amazon.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CurvGAD's mixed-curvature dual-pipeline method instead of the strongest listed baseline | node-level graph anomaly detection · 10 datasets: Reddit, Weibo, Amazon, YelpChi, T-Finance, Elliptic, Tolokers, Questions, DGraph, T-Social | AUROC: 5.09%; 1.05%; 2.34%; 4.15%; 2.23%; 4.79%; 4.61%; 1.78%; 6.50%; 4.18% | Helped |
| Add mixed-curvature embeddings rather than using Euclidean-only embeddings (ablation) | CurvGAD · Reddit | AUROC: 63.34 -> 70.42; -7.08% | Helped |
| Add Ricci flow to regularize curvature before structure and attribute reconstruction (ablation) | CurvGAD · Tolokers | AUROC: 74.45 -> 85.22; -10.77% | Helped |
| Add Ricci flow to regularize curvature before structure and attribute reconstruction (ablation) | CurvGAD · Weibo | AUROC: 98.77 -> 99.04; -0.27% | No clear effect |
| Add curvature reconstruction to structure and attribute reconstruction (ablation) | CurvGAD · Reddit | AUROC: 62.03 -> 70.42; -8.39% | Helped |
| Add curvature reconstruction to structure and attribute reconstruction (ablation) | CurvGAD · Amazon | AUROC: 92.76 -> 99.62; -6.86% | Helped |
| Add structure and attribute reconstruction to curvature reconstruction (ablation) | CurvGAD · Reddit | AUROC: +6.72% | Helped |
| Add structure and attribute reconstruction to curvature reconstruction (ablation) | CurvGAD · Amazon | AUROC: +4.89% | Helped |
| Add supervised classification loss (ablation) | CurvGAD · 10 datasets | AUROC: ~1.5% avg. | Helped |
| Vary the product-manifold signature to match dataset geometry (ablation) | CurvGAD · multiple datasets | AUROC | Mixed |
Surprising findings
- Removing the supervised classification loss causes only a minor (~1.5% average) drop, so the method works nearly as well unsupervised.
- Weibo shows only a minimal drop (-0.27%) when Ricci flow is removed, attributed to low curvature variance in its ORC distribution.
Limitations
- Manifold signature is chosen heuristically from the ORC distribution rather than learned.
- Gains are smaller on some datasets (e.g., Weibo +1.05%), and benefit is minimal where curvature variance is low.
- Performance on the T-Finance dataset is less affected by the Euclidean-only ablation because its ORC is predominantly zero.
Experimental setup
Datasets: Weibo Reddit Questions T-Social Tolokers Amazon YelpChi T-Finance Elliptic DGraph-Fin
Benchmarks: Weibo Reddit Questions T-Social Tolokers Amazon YelpChi T-Finance Elliptic DGraph-Fin
Metrics: AUROC
Baselines: GCN GAT GraphSAGE BernNet ChebyNet HGCN HGAT kappaGCN QGCN DCI PCGNN BWGNN
Builds on: DOMINANT AnomalyDAE kappa-stereographic model BernNet ChebyNet
Closest papers by meaning
- Rethinking Reconstruction-based Graph-Level Anomaly Detection: Limitations and a Simple Remedy (NeurIPS 2024 · similarity 0.88)
- UniGAD: Unifying Multi-level Graph Anomaly Detection (NeurIPS 2024 · similarity 0.87)
- DiffGAD: A Diffusion-based Unsupervised Graph Anomaly Detector (ICLR 2025 · similarity 0.87)
- ADA-GAD: Anomaly-Denoised Autoencoders for Graph Anomaly Detection (AAAI 2024 · similarity 0.87)
- Graph Anomaly Detection as Dynamical Transport: Training-Free Scoring via Empirical Bayes (NeurIPS 2026 · similarity 0.87)
- ARC: A Generalist Graph Anomaly Detector with In-Context Learning (NeurIPS 2024 · similarity 0.87)
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