Union Subgraph Neural Networks

TL;DR

This paper introduces Union Subgraph Neural Networks (UnionSNN), a novel GNN model that captures high-order connectivities in local neighborhoods, surpassing the expressiveness of traditional 1-WL-based GNNs and improving performance on various benchmarks.

Contribution

The paper proposes a new substructure called union subgraph and a shortest-path-based descriptor, enhancing GNN expressiveness and enabling integration into existing models.

Findings

UnionSNN is strictly more powerful than 1-WL in distinguishing non-isomorphic graphs.

Incorporating union subgraph encoding improves existing models' performance by up to 11.09%.

Extensive experiments on 18 benchmarks demonstrate state-of-the-art results.

Abstract

Graph Neural Networks (GNNs) are widely used for graph representation learning in many application domains. The expressiveness of vanilla GNNs is upper-bounded by 1-dimensional Weisfeiler-Leman (1-WL) test as they operate on rooted subtrees through iterative message passing. In this paper, we empower GNNs by injecting neighbor-connectivity information extracted from a new type of substructure. We first investigate different kinds of connectivities existing in a local neighborhood and identify a substructure called union subgraph, which is able to capture the complete picture of the 1-hop neighborhood of an edge. We then design a shortest-path-based substructure descriptor that possesses three nice properties and can effectively encode the high-order connectivities in union subgraphs. By infusing the encoded neighbor connectivities, we propose a novel model, namely Union Subgraph Neural Network (UnionSNN), which is proven to be strictly more powerful than 1-WL in distinguishing non-isomorphic graphs. Additionally, the local encoding from union subgraphs can also be injected into arbitrary message-passing neural networks (MPNNs) and Transformer-based models as a plugin. Extensive experiments on 18 benchmarks of both graph-level and node-level tasks demonstrate that UnionSNN outperforms state-of-the-art baseline models, with competitive computational efficiency. The injection of our local encoding to existing models is able to boost the performance by up to 11.09%. Our code is available at https://github.com/AngusMonroe/UnionSNN.