Study Links Label Informativeness to Geometry-Aware Graph Neural Network Performance

Global: Study Links Label Informativeness to Geometry-Aware Graph Neural Network Performance

Background and Core Findings

Researchers have presented a new theoretical framework that clarifies when graph structure can improve the performance of graph neural networks (GNNs). The work demonstrates that gains from geometry‑aware GNNs are possible if and only if the graph carries label‑relevant information beyond what is encoded in node features, a condition they formalize as label informativeness (LI).

Beyond Homophily: The Role of Label Informativeness

While homophily has traditionally been used to explain GNN behavior on low‑homophily graphs, the authors argue that homophily alone is insufficient. They define LI as the mutual information between labels of adjacent nodes and show that it provides a more accurate predictor of when structural cues are useful for classification.

Theoretical Contributions

The paper connects curvature‑guided graph rewiring and positional geometry through the lens of LI. It relates adjusted homophily and LI to the spectral properties of label signals under Laplacian smoothing, and proves that degree‑based Forman curvature does not extend expressivity beyond the one‑dimensional Weisfeiler–Lehman test but instead reshapes information flow. Additionally, the authors establish convergence and Lipschitz‑stability guarantees for a curvature‑guided rewiring process.

Practical Architecture: ASEHybrid

Building on the theory, the authors introduce ASEHybrid, a geometry‑aware architecture that incorporates Forman curvature for edge reweighting and Laplacian positional encodings for node representation. This design operationalizes the theoretical insights without requiring additional learnable parameters.

Empirical Evaluation

Controlled ablation studies were conducted on benchmark datasets including Chameleon, Squirrel, Texas, Tolokers, and Minesweeper. ASEHybrid achieved measurable improvements precisely on heterophilous graphs where LI indicated that structural information was label‑relevant, while showing no significant benefit on high‑baseline or label‑uninformative tasks.

Implications and Future Directions

The findings suggest that geometry‑aware GNNs should be deployed selectively, targeting scenarios where label informativeness is high. The authors propose further investigation into alternative curvature measures and adaptive rewiring strategies to broaden applicability across diverse graph domains.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.