提出高阶特征差分能量度量，更全面评估图神经网络过平滑问题。
Measuring Over-smoothing beyond Dirichlet energy
- 基于高阶特征导数能量构建节点相似性度量新家族。
- 揭示了过平滑衰减速率与图拉普拉斯谱隙的内在关联。
- 实验证明注意力机制GNN在新度量下仍存在过平滑现象。
尽管狄利克雷能量是衡量过平滑的常用指标，但其仅能捕捉一阶特征导数。为克服此局限，本文提出基于高阶特征导数能量的广义节点相似性度量族。通过严谨的理论分析，我们建立了这些度量之间的关系，并推导出连续热扩散与离散聚合算子下狄利克雷能量的衰减速率。进一步分析表明，过平滑衰减速率与图拉普拉斯的谱隙存在内在联系。最后，实验结果表明，在所提出的度量下，基于注意力的图神经网络（GNNs）仍表现出显著的过平滑现象。
原文摘要 · Abstract (English)
While Dirichlet energy serves as a prevalent metric for quantifying over-smoothing, it is inherently restricted to capturing first-order feature derivatives. To address this limitation, we propose a generalized family of node similarity measures based on the energy of higher-order feature derivatives. Through a rigorous theoretical analysis of the relationships among these measures, we establish the decay rates of Dirichlet energy under both continuous heat diffusion and discrete aggregation operators. Furthermore, our analysis reveals an intrinsic connection between the over-smoothing decay rate and the spectral gap of the graph Laplacian. Finally, empirical results demonstrate that attention-based Graph Neural Networks (GNNs) suffer from over-smoothing when evaluated under these proposed metrics.
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