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

Razi Hasson; Reuven Guetta

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arXiv · 2509.04178

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

Razi Hasson·Reuven Guetta

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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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Razi Hasson, Reuven Guetta. 2025-09-04. Comment on "A Note on Over-Smoothing for Graph Neural Networks". https://arxiv.org/abs/2509.04178

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