An Efficient Subgraph GNN with Provable Substructure Counting Power

Zuoyu Yan, Junru Zhou, Liangcai Gao, Zhi Tang, Muhan Zhang

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Keywords: Subgraph GNN, Count substructures, Subgraph Isomorphism counting, Graph Isomorphism test, Graph Neural Network

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Abstract: Enhancing the representation power of graph neural networks (GNNs) through their ability to count substructures is a recent trend in graph learning. Among these works, a popular way is to use subgraph GNNs, which decompose the input graph into a collection of subgraphs and enhance the representation of the graph by applying GNN to individual subgraphs. Although subgraph GNNs are able to count complicated substructures, they suffer from high computational and memory costs. In this paper, we address a non-trivial question: can we count substructures efficiently and provably with GNNs? To answer the question, we first theoretically show that the distance to the rooted nodes within subgraphs is key to boosting the counting power of subgraph GNNs. We then precompute structural embeddings that encode such information to avoid extracting information over all subgraphs via GNNs repeatedly. Experiments show that the proposed model can preserve the counting power of subgraph GNNs while running orders of magnitude faster.

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Submission Number: 3297