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

arXiv: https://arxiv.org/abs/2507.05263 · HTML: https://mlsanity.com/paper/2507.05263/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 20 Jun 2025.

## Builds on (most cited first, 16 of 16)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/2108.01938/) (2021)
- [Grokking as a First Order Phase Transition in Two Layer Networks](https://mlsanity.com/paper/2310.03789/) (2023)
- [Comparing Dynamics: Deep Neural Networks versus Glassy Systems](https://mlsanity.com/paper/1803.06969/) (2018)
- [A phase transition between positional and semantic learning in a solvable model of dot-product attention](https://mlsanity.com/paper/2402.03902/) (2024)
- [Sampling with flows, diffusion and autoregressive neural networks: A spin-glass perspective](https://mlsanity.com/paper/2308.14085/) (2023)
- [Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks](https://mlsanity.com/paper/2107.10234/) (2021)
- [Statistical Physics of Deep Neural Networks: Initialization toward Optimal Channels](https://mlsanity.com/paper/2212.01744/) (2022)
- [Statistical physics analysis of graph neural networks: Approaching optimality in the contextual stochastic block model](https://mlsanity.com/paper/2503.01361/) (2025)

## Built on by (most cited first, 1 of 1)

- [Avoiding Over-smoothing in Social Media Rumor Detection with Pre-trained Propagation Tree Transformer](https://mlsanity.com/paper/2603.22854/) (2026)

## 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.