mlsanityData to 7 Oct 2026

Rethinking Over-Smoothing in Graph Neural Networks: A Perspective from Anderson Localization

arXiv 2507.05263 ↗First posted 20 Jun 2025cs.LG cs.AI q-bio.NCcited by 1

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Abstract (arXiv)

Graph Neural Networks (GNNs) have shown great potential in graph data analysis due to their powerful representation capabilities. However, as the network depth increases, the issue of over-smoothing becomes more severe, causing node representations to lose their distinctiveness. This paper analyzes the mechanism of over-smoothing through the analogy to Anderson localization and introduces participation degree as a metric to quantify this phenomenon. Specifically, as the depth of the GNN increases, node features homogenize after multiple layers of message passing, leading to a loss of distinctiveness, similar to the behavior of vibration modes in disordered systems. In this context, over-smoothing in GNNs can be understood as the expansion of low-frequency modes (increased participation degree) and the localization of high-frequency modes (decreased participation degree). Based on this, we systematically reviewed the potential connection between the Anderson localization behavior in disordered systems and the over-smoothing behavior in Graph Neural Networks. A theoretical analysis was conducted, and we proposed the potential of alleviating over-smoothing by reducing the disorder in information propagation.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 16 of its 32 references that are in the map. First posted on arXiv 20 Jun 2025.

Builds on

16 of 32 references.

References · 16

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2020Scaling Laws for Neural Language Modelscited by 6,411
  3. 2019Graph Neural Networks for Social Recommendationcited by 711
  4. 2019DropEdge: Towards Deep Graph Convolutional Networks on Node Classificationcited by 679
  5. 2019Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological Viewcited by 544
  6. 2019DeepGCNs: Can GCNs Go as Deep as CNNs?cited by 527
  7. 2020Learning from Protein Structure with Geometric Vector Perceptronscited by 308
  8. 2022Graph neural networks for materials science and chemistrycited by 181
  9. 2021PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equationscited by 106
  10. 2023Grokking as a First Order Phase Transition in Two Layer Networkscited by 48
  11. 2018Comparing Dynamics: Deep Neural Networks versus Glassy Systemscited by 42
  12. 2024A phase transition between positional and semantic learning in a solvable model of dot-product attentioncited by 30
4 more
  1. 2023Sampling with flows, diffusion and autoregressive neural networks: A spin-glass perspectivecited by 26
  2. 2021Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networkscited by 18
  3. 2022Statistical Physics of Deep Neural Networks: Initialization toward Optimal Channelscited by 2
  4. 2025Statistical physics analysis of graph neural networks: Approaching optimality in the contextual stochastic block modelcited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Avoiding Over-smoothing in Social Media Rumor Detection with Pre-trained Propagation Tree Transformercited by 0