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Autori principali: Bison, Anna, Sperduti, Alessandro
Natura: Preprint
Pubblicazione: 2025
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Accesso online:https://arxiv.org/abs/2512.09890
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author Bison, Anna
Sperduti, Alessandro
author_facet Bison, Anna
Sperduti, Alessandro
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2512_09890
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Analysis of Dirichlet Energies as Over-smoothing Measures
Bison, Anna
Sperduti, Alessandro
Machine Learning
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.
title Analysis of Dirichlet Energies as Over-smoothing Measures
topic Machine Learning
url https://arxiv.org/abs/2512.09890