# A Survey on Oversmoothing in Graph Neural Networks

**Authors:** T. Konstantin Rusch, Michael M. Bronstein, Siddhartha Mishra  
**arXiv:** [2303.10993](https://arxiv.org/abs/2303.10993)  
**Date:** 2023-03-20  
**Summary page:** https://www.summarizepaper.com/en/paper/2303.10993v1/

## Key points

- Over-smoothing in graph neural networks (GNNs) occurs as the depth of GNNs increases, causing node features to become more similar and leading to a loss of discriminative power.
- The phenomenon of over-smoothing is characterized by the exponential convergence of similarity measures on node features.
- Authors provide an axiomatically defined framework for over-smoothing, introducing new quantitative measures to assess this phenomenon.
- Empirical analysis on various graphs demonstrates the prevalence of over-smoothing and its impact on GNN performance across different scales.
- Strategies for mitigating over-smoothing are reviewed and evaluated using real-world graph datasets, but it remains a challenge for building expressive deep GNNs.
- Understanding and addressing over-smoothing is essential for enhancing the expressiveness and performance of deep graph neural networks, including traditional and continuous-time GNNs.

## Summary

In their paper titled "A Survey on Oversmoothing in Graph Neural Networks," authors T. Konstantin Rusch, Michael M. Bronstein, and Siddhartha Mishra delve into the phenomenon of over-smoothing in graph neural networks (GNNs). They observe that as the depth of GNNs increases, the node features tend to become more similar, leading to a loss of discriminative power. This effect, known as over-smoothing, is characterized by the exponential convergence of similarity measures on the node features. The authors provide an axiomatically defined framework for over-smoothing which unifies previous approaches and introduces new quantitative measures to assess this phenomenon. Through empirical analysis on various graphs of different scales (small-, medium-, and large-scale), they demonstrate the prevalence of over-smoothing and its impact on GNN performance. Furthermore, the paper reviews several strategies for mitigating over-smoothing and evaluates their effectiveness using real-world graph datasets. Despite efforts to address over-smoothing, the authors emphasize that it is a necessary but not sufficient condition for building deep GNNs that are expressive across a wide range of graph learning tasks. In addition to traditional GNNs, the authors extend their analysis to continuous-time GNNs, highlighting the relevance of understanding and addressing over-smoothing in this rapidly evolving field. Overall,this comprehensive survey sheds light on the challenges posed by over-smoothing in GNNs and provides valuable insights for future research directions in enhancing the expressiveness and performance of deep graph neural networks.