对比两种图神经网络过平滑度量，发现归一化拉普拉斯能量不满足节点相似性定义。
Analysis of Dirichlet Energies as Over-smoothing Measures
- 比较未归一化与归一化图拉普拉斯的狄利克雷能量差异
- 证明归一化版本不满足节点相似性公理要求
- 为GNN架构选择合适平滑度量提供理论依据
我们分析了两种常用于衡量过平滑现象的泛函：由未归一化图拉普拉斯和归一化图拉普拉斯诱导的狄利克雷能量。结果表明，后者不满足Rusch等人提出的节点相似性度量的公理化定义。通过形式化这两个定义的基本谱性质，我们揭示了在选择与GNN架构谱兼容的度量时的关键区别，从而解决了监测动态过程中的模糊性问题。
原文摘要 · Abstract (English)
We analyze the distinctions between two functionals often used as over-smoothing measures: the Dirichlet energies induced by the unnormalized graph Laplacian and the normalized graph Laplacian. We demonstrate that the latter fails to satisfy the axiomatic definition of a node-similarity measure proposed by Rusch \textit{et al.} By formalizing fundamental spectral properties of these two definitions, we highlight critical distinctions necessary to select the metric that is spectrally compatible with the GNN architecture, thereby resolving ambiguities in monitoring the dynamics.
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