Comment on "A Note on Over-Smoothing for Graph Neural Networks"
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.
Cite
@article{arxiv.2509.04178,
title = {Comment on "A Note on Over-Smoothing for Graph Neural Networks"},
author = {Razi Hasson and Reuven Guetta},
journal= {arXiv preprint arXiv:2509.04178},
year = {2025}
}
Comments
Comment on arXiv:2006.13318 (Cai & Wang, 2020). Revisits their Dirichlet-energy analysis of over-smoothing and extends it to Leaky-ReLU and spectral polynomial filters; includes Proposition 7.1 and a new proof of Lemma 3.3 for Leaky-ReLU. 7 pages