Graph Neural Networks Do Not Always Oversmooth

Graph neural networks (GNNs) have emerged as powerful tools for processing relational data in applications. However, GNNs suffer from the problem of oversmoothing, the property that features of all nodes exponentially converge to the same vector over layers, prohibiting the design of deep GNNs. In this work we study oversmoothing in graph convolutional networks (GCNs) by using their Gaussian process (GP) equivalence in the limit of infinitely many hidden features. By generalizing methods from conventional deep neural networks (DNNs), we can describe the distribution of features at the output layer of deep GCNs in terms of a GP: as expected, we find that typical parameter choices from the literature lead to oversmoothing. The theory, however, allows us to identify a new, non-oversmoothing phase: if the initial weights of the network have sufficiently large variance, GCNs do not oversmooth, and node features remain informative even at large depth.