LEED：用于GNN中过平滑估计与虚拟节点选择的局部嵌入演化距离
LEED: Local Embedding Evolution Distance for over-smoothing estimation and virtual node selection in GNN
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中文总结 AI 辅助
针对GNN的过平滑与过压缩问题，提出局部指标LEED，可细粒度分析过平滑并作为准则指导虚拟节点选择，提升了GNN在多数据集上的性能。
中文摘要 AI 辅助
图神经网络（GNN）存在两个基本局限：过平滑（即节点表示随网络深度增加变得无法区分）与过压缩（即长程信息通过有限消息传递通道被压缩）。现有指标如Dirichlet能量可对过平滑进行全局表征，但缺乏分析节点级行为及指导架构改进的分辨率。本文提出LEED（Local Embedding Evolution Distance，局部嵌入演化距离），这是一种新型局部指标，通过追踪各层单个节点嵌入的演化来量化过平滑。由于在节点层面操作，LEED可对训练过程中的表示动态进行细粒度分析，揭示基于全局能量的指标无法察觉的异质过平滑模式。这种局部性产生了可解释的信息节点重要性得分，即嵌入驱动的中心性度量。我们利用LEED设计更高效的虚拟节点选择策略：与依赖多种启发式中心性度量的现有方法不同，我们的方法以LEED为唯一准则指导局部虚拟节点的构建，以缓解过压缩。实验表明，LEED在保留全局评估能力的同时，提供了比Dirichlet能量更具信息量的诊断结果，且能实现更有效的虚拟节点集成，提升GNN在各数据集上的性能。
英文摘要
Graph Neural Networks (GNNs) suffer from two fundamental limitations: over-smoothing, where node representations become indistinguishable with depth, and over-squashing, where long-range information is compressed through limited message-passing channels. Existing metrics such as Dirichlet energy provide global characterizations of over-smoothing but lack the resolution to analyze node-level behavior and guide architectural improvements. In this paper, we propose LEED (Local Embedding Evolution Distance), a novel local metric that quantifies over-smoothing by tracking the evolution of individual node embeddings across layers. By operating at the node level, LEED enables fine-grained analysis of representation dynamics during training, revealing heterogeneous over-smoothing patterns that are invisible to global energy-based measures. This locality induces informative node importance scores, interpreted as embedding-driven centrality measures. We leverage LEED to design a more efficient strategy for virtual node selection. Unlike existing approaches that depend on multiple heuristic centrality measures, our method uses LEED as a unique criterion to guide the construction of Local Virtual Nodes to mitigate over-squashing. Experiments show that LEED provides more informative diagnostics than Dirichlet energy while preserving global evaluation, and enables more effective virtual node integration, improving GNN performance across datasets.
发表机构
- Conservatoire National des Arts et Métiers (Cnam)（法国国立工艺学院）
- CEDRIC Lab（塞德里克实验室）
机构由 AI 辅助整理，请以论文原文为准。
