Title: GraphTorque: Torque-Driven Rewiring Graph Neural Network
Primary area: learning on graphs and other geometries & topologies
Keywords: Graph Neural Network, Graph Rewiring, Heterophily and Homophily, Message Passing

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 enhance representation learning in heterophilous and homophilous graphs. Specifically, we define the torque by treating the feature distance as a lever arm vector and the neighbor feature as a  force vector weighted by the homophily ratio disparity between node pairs. We use the metric to hierarchically reconfigure each layer’s receptive field by automatically pruning high-torque edges and adding low-torque links based on a Bernoulli-guided learnable sampling process, suppressing the impact of irrelevant information and boosting pertinent signals during message passing. Extensive evaluations on benchmark datasets show that the proposed approach surpasses state-of-the-art rewiring methods on both heterophilous and homophilous graphs.

TL;DR: We propose a torque-driven hierarchical rewiring strategy to enhance message passing in heterophilous and homophilous graphs.