Lorentzian Graph Isomorphic Network

2025-03-31

AI Summary

Existing Euclidean graph neural networks (GNNs) struggle to effectively capture the intrinsic hierarchical structure and multi-relational semantics inherent in graph-structured data. To address this, we propose the Lorentzian Graph Isomorphic Network (LGIN), the first hyperbolic GNN grounded in the Lorentz model—extending highly expressive GNNs to Riemannian manifolds. Methodologically, LGIN introduces a curvature-aware message aggregation mechanism and a metric-preserving embedding update rule, achieving Weisfeiler–Lehman (WL) test-level expressivity in hyperbolic space. We theoretically prove that LGIN’s graph isomorphism discrimination power is at least as strong as the WL test. Empirically, LGIN is evaluated on nine molecular and protein benchmark datasets, consistently achieving state-of-the-art or competitive performance in graph classification and structural pattern recognition, with significant improvements in accuracy over prior methods.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

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.

Problem

• Enhance graph representation learning in hyperbolic spaces
• Capture hierarchical and multi-relational graph structures
• Distinguish non-isomorphic graphs with high expressiveness

Innovation

• Hyperbolic space GNN with Lorentzian model
• Curvature-aware aggregation preserving Lorentzian metric
• New update rule capturing local and global structures