Can we ease the Injectivity Bottleneck on Lorentzian Manifolds for Graph Neural Networks?

While hyperbolic GNNs show promise for hierarchical data, they often have limited discriminative power compared to Euclidean counterparts or the WL test, due to non-injective aggregation. To address this expressivity gap, we propose the Lorentzian Graph Isomorphic Network (LGIN), a novel HGNN designed for enhanced discrimination within the Lorentzian model. LGIN introduces a new update rule that preserves the Lorentzian metric while effectively capturing richer structural information. This marks a significant step towards more expressive GNNs on Riemannian manifolds. Extensive evaluations across nine benchmark datasets demonstrate LGIN's superior performance, consistently outperforming or matching state-of-the-art hyperbolic and Euclidean baselines, showcasing its ability to capture complex graph structures. LGIN is the first to adapt principles of powerful, highly discriminative GNN architectures to a Riemannian manifold. The code for our paper can be found at https://github.com/Deceptrax123/LGIN