AI 中文总结
提出HSO-GAT，利用双曲Sombor指数作为结构先验，实现拓扑自适应的双曲图注意力网络，在节点分类和链接预测上达到最先进性能。
AI 中文摘要
双曲几何已成为表示层次化图的一种有原则的空间。然而，现有的双曲图神经网络通常依赖于共享的曲率配置和特征驱动的注意力机制，未能显式利用局部层次拓扑模式。为弥合这一差距，我们引入双曲Sombor指数（HSO）作为一种轻量级结构先验，用于捕获指示层次的度分层。在此基础上，我们提出HSO-GAT，一种拓扑自适应的双曲图注意力网络，统一了几何适应和消息传播。具体而言，它包含两个互补模块：HSO引导的局部曲率适应，通过聚合节点级HSO信号执行自适应的节点级几何缩放；以及HSO门控的双曲图注意力，通过特征条件门控实现结构感知的消息传递。理论上，我们建立了边级HSO对度不平衡的单调敏感性，并分析了节点自适应双曲映射的有效性和径向缩放性质。在八个基准数据集上的大量实验表明，HSO-GAT在节点分类和链接预测任务中均持续达到最先进的性能。
英文摘要
Hyperbolic geometry has emerged as a principled space for representing hierarchical graphs. However, existing hyperbolic graph neural networks typically rely on shared curvature configurations and feature-driven attention, failing to explicitly exploit local hierarchical topological patterns. To bridge this gap, we introduce the Hyperbolic Sombor Index (HSO) as a lightweight structural prior for capturing hierarchy-indicative degree stratification. Building on this, we propose \textbf{HSO-GAT}, a topology-adaptive hyperbolic graph attention network that unifies geometric adaptation and message propagation. Specifically, it comprises two complementary modules: HSO-Guided Local Curvature Adaptation, which performs adaptive node-wise geometric scaling from aggregated node-level HSO signals, and HSO-Gated Hyperbolic Graph Attention, which enables structure-aware message passing through feature-conditioned gating. Theoretically, we establish the monotonic sensitivity of edge-level HSO to degree imbalance and analyze the validity and radial scaling properties of node-adaptive hyperbolic mappings. Extensive experiments on eight benchmark datasets demonstrate that HSO-GAT consistently achieves state-of-the-art performance in both node classification and link prediction tasks.
