Analysis of Dirichlet Energies as Over-smoothing Measures

Anna Bison, Alessandro Sperduti
12/10/2025
cs.LG

No official code found. Best implementation: annabison/dirichlet-oversmoothing-measures (0 stars, MIT, last commit 2025-12-16).

Abstract

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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annabison/dirichlet-oversmoothing-measuresCommunity66%
MIT

Official implementation of the paper "Analysis of Dirichlet Energies as Over-smoothing Measures".

00PythonNov 25, 202510 months agoMIT

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Cite this paper

@article{bison2025analysis,
  title  = {Analysis of Dirichlet Energies as Over-smoothing Measures},
  author = {Anna Bison and Alessandro Sperduti},
  year   = {2025},
  eprint = {2512.09890},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2512.09890v1}
}

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