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Main Authors: Hasson, Razi, Guetta, Reuven
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2509.04178
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author Hasson, Razi
Guetta, Reuven
author_facet Hasson, Razi
Guetta, Reuven
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2509_04178
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Comment on "A Note on Over-Smoothing for Graph Neural Networks"
Hasson, Razi
Guetta, Reuven
Machine Learning
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.
title Comment on "A Note on Over-Smoothing for Graph Neural Networks"
topic Machine Learning
url https://arxiv.org/abs/2509.04178