Comment on "A Note on Over-Smoothing for Graph Neural Networks"

Razi Hasson, Reuven Guetta
9/4/2025
cs.LG

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Abstract

We comment on Cai and Wang (2020, arXiv:2006.13318), who analyze over-smoothing in GNNs via Dirichlet energy. We show that under mild spectral conditions (including with Leaky-ReLU), the Dirichlet energy of node embeddings decreases exponentially with depth; we further extend the result to spectral polynomial filters and provide a short proof for the Leaky-ReLU case. Experiments on edge deletion and weight amplification illustrate when Dirichlet energy increases, hinting at practical ways to relieve over-smoothing.

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Cite this paper

@article{hasson2025comment,
  title  = {Comment on "A Note on Over-Smoothing for Graph Neural Networks"},
  author = {Razi Hasson and Reuven Guetta},
  year   = {2025},
  eprint = {2509.04178},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2509.04178v1}
}

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