# CurvGAD: Leveraging Curvature for Enhanced Graph Anomaly Detection

arXiv: https://arxiv.org/abs/2502.08605 · HTML: https://mlsanity.com/paper/2502.08605/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 56 references that are in the map.
- First posted on arXiv 12 Feb 2025.

## Builds on (most cited first, 27 of 27)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks](https://mlsanity.com/paper/1908.01207/) (2019)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Enhancing Graph Neural Network-based Fraud Detectors against Camouflaged Fraudsters](https://mlsanity.com/paper/2008.08692/) (2020)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [Anti-Money Laundering in Bitcoin: Experimenting with Graph Convolutional Networks for Financial Forensics](https://mlsanity.com/paper/1908.02591/) (2019)
- [From Amateurs to Connoisseurs: Modeling the Evolution of User Expertise through Online Reviews](https://mlsanity.com/paper/1303.4402/) (2013)
- [Constant Curvature Graph Convolutional Networks](https://mlsanity.com/paper/1911.05076/) (2019)
- [AnomalyDAE: Dual autoencoder for anomaly detection on attributed networks](https://mlsanity.com/paper/2002.03665/) (2020)
- [BOND: Benchmarking Unsupervised Outlier Node Detection on Static Attributed Graphs](https://mlsanity.com/paper/2206.10071/) (2022)
- [DGraph: A Large-Scale Financial Dataset for Graph Anomaly Detection](https://mlsanity.com/paper/2207.03579/) (2022)
- [GAD-NR: Graph Anomaly Detection via Neighborhood Reconstruction](https://mlsanity.com/paper/2306.01951/) (2023)
- [Pseudo-Riemannian Graph Convolutional Networks](https://mlsanity.com/paper/2106.03134/) (2021)
- [ADA-GAD: Anomaly-Denoised Autoencoders for Graph Anomaly Detection](https://mlsanity.com/paper/2312.14535/) (2023)
- [Network Alignment by Discrete Ollivier-Ricci Flow](https://mlsanity.com/paper/1809.00320/) (2018)
- [Curvature-based Clustering on Graphs](https://mlsanity.com/paper/2307.10155/) (2023)
- [On properties of the Generalized Wasserstein distance](https://mlsanity.com/paper/1304.7014/) (2013)
- [Graph Convolutional Networks for traffic anomaly](https://mlsanity.com/paper/2012.13637/) (2020)

## Built on by (most cited first, 4 of 4)

- [Multi-Domain Riemannian Graph Gluing for Building Graph Foundation Models](https://mlsanity.com/paper/2603.00618/) (2026)
- [Auditing Cascading Risks in Multi-Agent Systems via Semantic-Geometric Co-evolution](https://mlsanity.com/paper/2603.13325/) (2026)
- [Zero-shot Generalizable Graph Anomaly Detection with Mixture of Riemannian Experts](https://mlsanity.com/paper/2602.06859/) (2026)
- [Efficient Mean Curvature Computation on High-Dimensional Data Manifolds](https://mlsanity.com/paper/2606.06329/) (2026)

## Abstract (arXiv)

Does the intrinsic curvature of complex networks hold the key to unveiling graph anomalies that conventional approaches overlook? Reconstruction-based graph anomaly detection (GAD) methods overlook such geometric outliers, focusing only on structural and attribute-level anomalies. To this end, we propose CurvGAD - a mixed-curvature graph autoencoder that introduces the notion of curvature-based geometric anomalies. CurvGAD introduces two parallel pipelines for enhanced anomaly interpretability: (1) Curvature-equivariant geometry reconstruction, which focuses exclusively on reconstructing the edge curvatures using a mixed-curvature, Riemannian encoder and Gaussian kernel-based decoder; and (2) Curvature-invariant structure and attribute reconstruction, which decouples structural and attribute anomalies from geometric irregularities by regularizing graph curvature under discrete Ollivier-Ricci flow, thereby isolating the non-geometric anomalies. By leveraging curvature, CurvGAD refines the existing anomaly classifications and identifies new curvature-driven anomalies. Extensive experimentation over 10 real-world datasets (both homophilic and heterophilic) demonstrates an improvement of up to 6.5% over state-of-the-art GAD methods. The code is available at: https://github.com/karish-grover/curvgad.