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A Survey on Oversmoothing in Graph Neural Networks

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arxiv 2303.10993 v1 pith:BFGC3K4J submitted 2023-03-20 cs.LG

T. Konstantin Rusch , Michael M. Bronstein , Siddhartha Mishra This is my paper
classification cs.LG
keywords over-smoothinggraphgnnsmeasuresapproachesdefinitiondemonstrateempirically
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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.

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