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arXiv · 1905.12560

On the equivalence between graph isomorphism testing and function approximation with GNNs

Zhengdao Chen·Soledad Villar·Lei Chen·Joan Bruna
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Abstract

Graph Neural Networks (GNNs) have achieved much success on graph-structured data. In light of this, there have been increasing interests in studying their expressive power. One line of work studies the capability of GNNs to approximate permutation-invariant functions on graphs, and another focuses on the their power as tests for graph isomorphism. Our work connects these two perspectives and proves their equivalence. We further develop a framework of the expressive power of GNNs that incorporates both of these viewpoints using the language of sigma-algebra, through which we compare the expressive power of different types of GNNs together with other graph isomorphism tests. In particular, we prove that the second-order Invariant Graph Network fails to distinguish non-isomorphic regular graphs with the same degree. Then, we extend it to a new architecture, Ring-GNN, which succeeds in distinguishing these graphs and achieves good performances on real-world datasets.

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Zhengdao Chen, Soledad Villar, Lei Chen, Joan Bruna. 2019-05-29. On the equivalence between graph isomorphism testing and function approximation with GNNs. https://arxiv.org/abs/1905.12560

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