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A Survey on Oversmoothing in Graph Neural Networks

by T. K. Rusch and M. M. Bronstein and S. Mishra

(Report number 2023-17)

Abstract
Node features of graph neural networks (GNNs) tend to become more similar with the increase of the network depth. This effect is known as over-smoothing, which we axiomatically define as the exponential convergence of suitable similarity measures on the node features. Our definition unifies previous approaches and gives rise to new quantitative measures of over-smoothing. Moreover, we empirically demonstrate this behavior for several over-smoothing measures on different graphs (small-, medium-, and large-scale). We also review several approaches for mitigating over-smoothing and empirically test their effectiveness on real-world graph datasets. Through illustrative examples, we demonstrate that mitigating over-smoothing is a necessary but not sufficient condition for building deep GNNs that are expressive on a wide range of graph learning tasks. Finally, we extend our definition of over-smoothing to the rapidly emerging field of continuous-time GNNs.

Keywords: Graph Neural Network (GNN), oversmoothing, Deep Learning

@Techreport{RBM23_1054,
  author = {T. K. Rusch and M. M. Bronstein and S. Mishra},
  title = {A Survey on Oversmoothing in Graph Neural Networks},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2023-17},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2023/2023-17.pdf },
  year = {2023}
}

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