Ordered Subgraph Aggregation Networks

Chendi Qian, Gaurav Rattan, Floris Geerts, Mathias Niepert, Christopher Morris

Keywords: GNNs, expressivity, subgraphs, differentiating through discrete structures

TL;DR: We propose a unified theoretical framework to study the expressivity of recently proposed subgraph-enhanced GNNs and explore how to sample subgraphs in a driven-driven fashion.

Abstract: Numerous subgraph-enhanced graph neural networks (GNNs) have emerged recently, provably boosting the expressive power of standard (message-passing) GNNs. However, there is a limited understanding of how these approaches relate to each other and to the Weisfeiler-Leman hierarchy. Moreover, current approaches either use all subgraphs of a given size, sample them uniformly at random, or use hand-crafted heuristics instead of learning to select subgraphs in a data-driven manner. Here, we offer a unified way to study such architectures by introducing a theoretical framework and extending the known expressivity results of subgraph-enhanced GNNs. Concretely, we show that increasing subgraph size always increases the expressive power and develop a better understanding of their limitations by relating them to the established $k\mathsf{\text{-}WL}$ hierarchy. In addition, we explore different approaches for learning to sample subgraphs using recent methods for backpropagating through complex discrete probability distributions. Empirically, we study the predictive performance of different subgraph-enhanced GNNs, showing that our data-driven architectures increase prediction accuracy on standard benchmark datasets compared to non-data-driven subgraph-enhanced graph neural networks while reducing computation time.

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:2206.11168/code)