How Powerful are Graph Neural Networks?

Keyulu Xu*, Weihua Hu*, Jure Leskovec, Stefanie Jegelka

Sep 27, 2018 ICLR 2019 Conference Blind Submission readers: everyone Show Bibtex
  • Abstract: Graph Neural Networks (GNNs) for representation learning of graphs broadly follow a neighborhood aggregation framework, where the representation vector of a node is computed by recursively aggregating and transforming feature vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs in capturing different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance.
  • Keywords: graph neural networks, theory, deep learning, representational power, graph isomorphism, deep multisets
  • TL;DR: We develop theoretical foundations for expressive power of GNNs and design a provably most powerful GNN.
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