Ordered Subgraph Aggregation NetworksDownload PDF

Published: 31 Oct 2022, Last Modified: 22 Oct 2023NeurIPS 2022 AcceptReaders: Everyone
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.
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