Hyperbolic GNNs achieve low-distortion embeddings only on tree-like graphs under geometry-aligned tasks

Naddeo, Linkerhägner, Toschi, Skenderi & Lachi (2026) train real HGCN (Poincare-ball) and HyboNet (Lorentz-model) graph neural networks, versus Euclidean GCN/GAT/MLP baselines, on Cora, Citeseer, Pubmed, Disease, Airport, and synthetic tree/grid graphs, measuring embedding distortion delta(h)=d_c(h)/d_e(h), a normalized Stress Loss, and each dataset's exact Gromov delta-hyperbolicity (Disease 0.0, Airport 1.0, Pubmed 3.5, Citeseer 4.5, Cora 11.0) [naddeo-etal-2026-hyperbolic-gnns-under-the-microscope-geometry-task-alignment] On synthetic trees, HyboNet/HGCN show markedly lower stress than Euclidean models at low dimension, but the advantage vanishes by d=128 and reverses entirely on grid graphs; on real-world node classification, none of the models learn metric-preserving embeddings regardless of architecture [naddeo-etal-2026-hyperbolic-gnns-under-the-microscope-geometry-task-alignment] Only link prediction (a geometry-aligned task) shows HGNNs achieving both lower distortion and higher ROC-AUC/AP, especially on low-hyperbolicity datasets (Disease, Airport), confirmed as functionally load-bearing via a feature-corruption experiment where HGNNs retain higher performance and lower distortion than Euclidean models under progressive noise [naddeo-etal-2026-hyperbolic-gnns-under-the-microscope-geometry-task-alignment]