发表机构
Karlsruhe Institute of Technology; University of Michigan（卡尔斯鲁厄理工学院; 密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对GNN中节点自同构导致链接预测性能下降的问题，提出边自同构比定量框架及EO-GNN架构，通过自同构感知丢弃和子图轨道偏置聚合，在合成与真实图上分别提升高达42.36%和28.44%。
AI 中文摘要
图神经网络（GNN）通过置换等变聚合学习节点和链接嵌入是有效的。然而，标准GNN会将自同构节点（即具有相同结构角色或轨道的节点）折叠成不可区分的表示，导致节点自同构问题。这种折叠限制了其表达能力并降低了链接预测性能。现有的表征GNN表达能力的方法主要依赖于Weisfeiler-Lehman（WL）分析，但这些方法通常是定性的，且往往与实证结果不一致。为解决这一差距，我们首先引入一种新颖的定量框架来评估GNN在链接预测中的表达能力。我们首先通过边轨道形式化边级自同构，边轨道捕获共享链接的节点的结构角色对集合。然后，我们引入边自同构比（EAR），一个标量度量，量化GNN在给定图中区分链接的能力。我们实证表明EAR与性能强相关，验证了其实际益处。基于这一见解，我们设计了边轨道等变图神经网络（EO-GNN），一种解决自同构折叠同时保持等变性并产生最小计算开销的GNN架构。EO-GNN通过两个核心设计结合基于WL的节点哈希实现这一点：（i）自同构感知的丢弃和（ii）子图轨道偏置聚合。在合成图和真实图上的实证评估显示，在高自同构场景下，链接预测分别提高了高达42.36%和28.44%。
英文摘要
Graph Neural Networks (GNNs) are effective for learning node and link embeddings through permutation-equivariant aggregation. However, standard GNNs collapse automorphic nodes, i.e., those with identical structural roles (or orbits) into indistinguishable representations, leading to the node automorphism problem. This collapse limits their expressive power and degrades link prediction performance. Existing approaches to characterize GNN expressiveness rely primarily on Weisfeiler-Lehman (WL) analyses, but these methods are typically qualitative and often misaligned with empirical results. To address this gap, we begin by introducing a novel quantitative framework to assess GNN expressiveness for link prediction. We first formalize edge-level automorphism through edge orbits, which capture the set of structural role pairs for nodes that share a link. Then, we introduce the edge automorphism ratio (EAR), a scalar metric that quantifies a GNN's ability to distinguish links in a given graph. We empirically demonstrate that EAR correlates strongly with performance, validating its practical benefit. Building on this insight, we design EDGE-ORBIT EQUIVARIANT GRAPH NEURAL NETWORK (EO-GNN), a GNN architecture that addresses automorphism collapse while preserving equivariance and incurring minimal computational overhead. EO-GNN accomplishes this through two core designs combined with WL-based node hashes: (i) automorphism-aware dropouts and (ii) subgraph orbit-biased aggregation. Empirical evaluations on synthetic and real graphs show improvements of up to 42.36% and 28.44%, respectively, in predicting links in scenarios with high automorphism.
Comments10 pages, figure 7
