Torque-based Graph Surgery:Enhancing Graph Neural Networks with Hierarchical Rewiring

Abstract: Graph Neural Networks (GNNs) have emerged as powerful tools for learning from graph-structured data, leveraging message passing to diffuse information and update node representations. However, most efforts have suggested that native interactions encoded in the graph may not be friendly for this process, motivating the development of graph rewiring methods. In this work, we propose a torque-driven hierarchical rewiring strategy, inspired by the notion of torque in classical mechanics, dynamically modulating message passing to improve representation learning in heterophilous graphs and enhance robustness against noisy graphs. Specifically, we define an interference-aware torque metric that integrates structural distance and energy scores to quantify the perturbation induced by edges, thereby encouraging each node to aggregate information from its nearest low-energy neighbors. We use the metric to hierarchically reconfigure the receptive field of each layer by judiciously pruning high-torque edges and adding low-torque links, suppressing propagation noise and boosting pertinent signals. Extensive evaluations on benchmark datasets show that our approach surpasses state-of-the-art methods on both heterophilous and homophilous graphs, and maintains high accuracy on noisy graph.