A Simple Spectral Failure Mode for Graph Convolutional Networks
This work highlights a theoretical limitation of GCNs for graph learning, which is incremental in understanding their performance relative to spectral methods.
The paper identifies a failure mode of unsupervised graph convolutional networks (GCNs) in certain approximately regular graphs, where they miss inference signals in non-leading eigenvectors, while adjacency spectral embedding succeeds, as shown through simulations.
Neural networks have achieved remarkable successes in machine learning tasks. This has recently been extended to graph learning using neural networks. However, there is limited theoretical work in understanding how and when they perform well, especially relative to established statistical learning techniques such as spectral embedding. In this short paper, we present a simple generative model where unsupervised graph convolutional network fails, while the adjacency spectral embedding succeeds. Specifically, unsupervised graph convolutional network is unable to look beyond the first eigenvector in certain approximately regular graphs, thus missing inference signals in non-leading eigenvectors. The phenomenon is demonstrated by visual illustrations and comprehensive simulations.