Lorentzian Graph Isomorphic Network (LGIN) is a novel HGNN proposed to address the limited discriminative power of hyperbolic GNNs, which are promising for hierarchical data. To improve the low representational power caused by non-partial aggregation of conventional hyperbolic GNNs, we introduce a novel update rule that effectively captures rich structural information while preserving the Lorentzian metric. Through extensive evaluations on nine benchmark datasets, we demonstrate its ability to capture complex graph structures, outperforming or on par with state-of-the-art hyperbolic and Euclidean baseline models. LGIN is the first model to apply the principles of powerful and highly discriminative GNN architectures to the Riemannian manifold.
