Improving the expressiveness of k-hop message-passing gnns by injecting contextualized substructure information

Yingxu Wang

Abstract: Graph neural networks (GNNs) have become the de facto standard for representational learning in graphs, and have achieved state-of-the-art performance in many graph-related tasks; however, it has been shown that the expressive power of standard GNNs are equivalent maximally to 1-dimensional Weisfeiler-Lehman (1-WL) Test. Recently, there is a line of works aiming to enhance the expressive power of graph neural networks. One line of such works aim at developing 𝐾-hop message-passing GNNs where node representation is updated by aggregating information from not only direct neighbors but all neighbors within 𝐾-hop of the node. Another line of works leverages subgraph information to enhance the expressive power which is proven to be strictly more powerful than 1-WL test. In this work, we discuss the limitation of 𝐾-hop message-passing GNNs and propose substructure encoding function to uplift the expressive power of any 𝐾-hop message-passing GNN. We further inject contextualized substructure information to enhance the expressiveness of 𝐾-hop message-passing GNNs. Our method is provably more powerful than previous works on 𝐾-hop graph neural networks and 1-WL subgraph GNNs, which is a specific type of subgraph based GNN models, and not less powerful than 3-WL. Empirically, our proposed method set new state-of-the-art performance or achieves comparable performance for a variety of datasets.