ICML 2025

CurvGAD: Leveraging Curvature for Enhanced Graph Anomaly Detection
Karish Grover 1 Geoffrey J. Gordon 1 Christos Faloutsos 1
Abstract
Does the intrinsic curvature of complex net-
works hold the key to unveiling graph anoma-
lies 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 in-
troduces the notion of curvature-based geomet-
ric anomalies. CurvGAD introduces two parallel
pipelines for enhanced anomaly interpretability:
(1) Curvature-equivariant geometry reconstruc-
tion, which focuses exclusively on reconstruct-
ing 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 geomet-
ric irregularities by regularizing graph curvature
under discrete Ollivier-Ricci flow, thereby isolat-
ing 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 het-
erophilic) 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.
1. Introduction
Detecting anomalies in graph-structured data is a pivotal
task across diverse fields, including social networks (Has-
sanzadeh et al., 2012), cybersecurity (Wang & Zhu, 2022),
transportation systems (Hu et al., 2020), and biological net-
works (Singh & Vig, 2017). Traditional methods primarily
1Carnegie Mellon University.
Correspondence to: Karish
Grover <karishg@cs.cmu.edu>.
Proceedings of the 42 nd International Conference on Machine
Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025
by the author(...