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

• URL: http://arxiv.org/abs/2507.05263v1
• Date: Fri, 20 Jun 2025 18:54:10 GMT
• Title: Rethinking Over-Smoothing in Graph Neural Networks: A Perspective from Anderson Localization
• Authors: Kaichen Ouyang,
• Abstract summary: Graph Neural Networks (GNNs) have shown great potential in graph data analysis due to their powerful representation capabilities.<n>As the network depth increases, the issue of over-smoothing becomes more severe, causing node representations to lose their distinctiveness.<n>This paper analyzes the mechanism of over-smoothing through the analogy to Anderson localization.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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