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.

Can integrating spectral and curvature signals unlock new potential in graph representation learning? Non-Euclidean geometries, particularly Riemannian manifolds such as hyperbolic (negative curvature) and spherical (positive curvature), offer powerful inductive biases for embedding complex graph structures like scale-free, hierarchical, and cyclic patterns. Meanwhile, spectral filtering excels at processing signal variations across graphs, making it effective in homophilic and heterophilic settings. Leveraging both can significantly enhance the learned representations. To this end, we propose Spectro-Riemannian Graph Neural Networks (CUSP) - the first graph representation learning paradigm that unifies both CUrvature (geometric) and SPectral insights. CUSP is a mixed-curvature spectral GNN that learns spectral filters to optimize node embeddings in products of constant-curvature manifolds (hyperbolic, spherical, and Euclidean). Specifically, CUSP introduces three novel components: (a) Cusp Laplacian, an extension of the traditional graph Laplacian based on Ollivier-Ricci curvature, designed to capture the curvature signals better; (b) Cusp Filtering, which employs multiple Riemannian graph filters to obtain cues from various bands in the eigenspectrum; and (c) Cusp Pooling, a hierarchical attention mechanism combined with a curvature-based positional encoding to assess the relative importance of differently curved substructures in our graph. Empirical evaluation across eight homophilic and heterophilic datasets demonstrates the superiority of CUSP in node classification and link prediction tasks, with a gain of up to 5.3% over state-of-the-art models.

Despite significant reliability efforts, large-scale cloud services inevitably experience production incidents that can significantly impact service availability and customer's satisfaction. Worse, in many cases one incident can lead to multiple downstream failures due to cascading effects that creates several related incidents across different dependent services. Often time On-call Engineers (OCEs) examine these incidents in silos that lead to significant amount of manual toil and increase the overall time-to-mitigate incidents. Therefore, developing efficient incident linking models is of paramount importance for grouping related incidents into clusters so as to quickly resolve major outages and reduce on-call fatigue. Existing incident linking methods mostly leverages textual and contextual information of incidents (e.g., title, description, severity, impacted components), thus failing to leverage the inter-dependencies between services. In this paper, we propose the dependency-aware incident linking (DiLink) framework which leverages both textual and service dependency graph information to improve the accuracy and coverage of incident links not only coming from same service, but also from different services and workloads. Furthermore, we propose a novel method to align the embeddings of multi-modal (i.e., textual and graphical) data using Orthogonal Procrustes. Extensive experimental results on real-world incidents from 5 workloads of Microsoft demonstrate that our alignment method has an F1-score of 0.96 (14% gain over current state-of-the-art methods). We are also in the process of deploying this solution across 610 services from these 5 workloads for continuously supporting OCEs improving incident management and reducing manual toil.