提出LGIN模型，提升双曲图神经网络的区分能力
Can we ease the Injectivity Bottleneck on Lorentzian Manifolds for Graph Neural Networks?
- 设计保留洛伦兹度量的新更新规则，增强结构捕捉能力
- 在9个数据集上超越或持平现有最优模型
- 首个将强区分性架构适配黎曼流形的图神经网络
尽管双曲图神经网络在层次化数据上表现良好，但其区分能力常弱于欧氏模型或WL测试，主要受限于非单射聚合。为解决这一表达力差距，本文提出洛伦兹图同构网络（LGIN），一种面向洛伦兹模型的新型超曲面图神经网络。LGIN引入新更新规则，在保持洛伦兹度量的同时有效捕获更丰富的结构信息。在九个基准数据集上的广泛实验表明，LGIN性能显著优于或匹配当前最优的双曲与欧氏基线模型，展现出对复杂图结构的建模能力。LGIN是首个将强大且高区分性的图神经网络架构适配黎曼流形的工作。代码见：https://github.com/Deceptrax123/LGIN
原文摘要 · Abstract (English)
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
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