Discovering the Representation Bottleneck of Graph Neural Networks from Multi-order Interactions

Most graph neural networks (GNNs) rely on the message passing paradigm to propagate node features and build interactions. Recent works point out that different graph learning tasks require different ranges of interactions between nodes. To investigate its underlying mechanism, we explore the capacity of GNNs to capture pairwise interactions between nodes under contexts with different complexities, especially for their graph-level and node-level applications in scientific domains like biochemistry and physics. When formulating pairwise interactions, we study two common graph construction methods in scientific domains, i.e., \emph{K-nearest neighbor} (KNN) graphs and \emph{fully-connected} (FC) graphs. Furthermore, we demonstrate that the inductive bias introduced by KNN-graphs and FC-graphs hinders GNNs to learn the most informative order of interactions. {Such a phenomenon is broadly shared by several GNNs for different graph learning tasks and forbids GNNs to achieve the global minimum loss, so we name it a \emph{representation bottleneck}.} To overcome that, we propose a novel graph rewiring approach based on the pairwise interaction strengths to dynamically adjust the reception fields of each node. Extensive experiments in molecular property prediction and dynamic system forecast prove the superiority of our method over state-of-the-art GNN baselines. More importantly, this paper provides a reasonable explanation of why subgraphs play an important role in the determination of graph properties.