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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.04178 |
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| _version_ | 1866914022376341504 |
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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 |