ASEHybrid: When Geometry Matters Beyond Homophily in Graph Neural Networks
This work addresses the challenge of improving GNN performance on heterophilous graphs for researchers and practitioners in graph machine learning, though it is incremental as it builds on existing concepts like label informativeness and curvature.
The paper tackled the problem of graph neural networks (GNNs) struggling on graphs with low homophily by developing a theoretical framework linking curvature-guided rewiring and positional geometry to label informativeness, resulting in the ASEHybrid architecture that achieved gains on label-informative heterophilous benchmarks like Chameleon, Squirrel, Texas, Tolokers, and Minesweeper.
Standard message-passing graph neural networks (GNNs) often struggle on graphs with low homophily, yet homophily alone does not explain this behavior, as graphs with similar homophily levels can exhibit markedly different performance and some heterophilous graphs remain easy for vanilla GCNs. Recent work suggests that label informativeness (LI), the mutual information between labels of adjacent nodes, provides a more faithful characterization of when graph structure is useful. In this work, we develop a unified theoretical framework that connects curvature-guided rewiring and positional geometry through the lens of label informativeness, and instantiate it in a practical geometry-aware architecture, ASEHybrid. Our analysis provides a necessary-and-sufficient characterization of when geometry-aware GNNs can improve over feature-only baselines: such gains are possible if and only if graph structure carries label-relevant information beyond node features. Theoretically, we relate adjusted homophily and label informativeness to the spectral behavior of label signals under Laplacian smoothing, show that degree-based Forman curvature does not increase expressivity beyond the one-dimensional Weisfeiler--Lehman test but instead reshapes information flow, and establish convergence and Lipschitz stability guarantees for a curvature-guided rewiring process. Empirically, we instantiate ASEHybrid using Forman curvature and Laplacian positional encodings and conduct controlled ablations on Chameleon, Squirrel, Texas, Tolokers, and Minesweeper, observing gains precisely on label-informative heterophilous benchmarks where graph structure provides label-relevant information beyond node features, and no meaningful improvement in high-baseline regimes.