Lorentzian Graph Isomorphic Network

We introduce the Lorentzian Graph Isomorphic Network (LGIN), a novel graph neural network (GNN) designed to operate in hyperbolic spaces, leveraging the Lorentzian model to enhance graph representation learning. Existing GNNs primarily operate in Euclidean spaces, which can limit their ability to capture hierarchical and multi-relational structures inherent to complex graphs. LGIN addresses this by incorporating curvature-aware aggregation functions that preserve the Lorentzian metric tensor, ensuring embeddings remain constrained within the hyperbolic space by proposing a new update rule that effectively captures both local neighborhood interactions and global structural properties, enabling LGIN to distinguish non-isomorphic graphs with expressiveness at least as powerful as the Weisfeiler-Lehman test. Through extensive evaluation across nine benchmark datasets, including molecular and protein structures, LGIN consistently outperforms or matches state-of-the-art GNNs, demonstrating its robustness and efficacy in modeling complex graph structures. To the best of our knowledge, this is the first study to extend the concept of a powerful graph neural network to Riemannian manifolds, paving the way for future advancements in hyperbolic graph learning. The code for our paper can be found at https://github.com/Deceptrax123/LGIN.