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

2025-07-28

AI Summary

To address the limited representation learning performance of Graph Neural Networks (GNNs) on heterophilic and noisy graphs, this paper proposes Torque-Driven Hierarchical Graph Rewiring (TDR). Unlike static graph structures, TDR introduces a novel perturbation-aware torque metric—integrating structural distance and edge energy scores—to dynamically quantify each edge’s influence on message propagation. Based on this metric, TDR hierarchically rewires the graph by preserving high-torque edges and reconstructing low-torque ones, thereby adaptively optimizing neighborhood aggregation topology. Inspired by classical mechanical torque, the method offers both physical interpretability and computational efficiency. Extensive experiments on multiple benchmark datasets—including heterophilic, homophilic, and noisy graphs—demonstrate that TDR consistently outperforms state-of-the-art methods, while significantly enhancing model robustness and generalization capability.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Improving GNNs by dynamically rewiring graphs for better message passing
• Enhancing robustness and accuracy in noisy and heterophilous graphs
• Quantifying edge perturbations to optimize neighbor information aggregation

Innovation

• Torque-driven hierarchical rewiring strategy
• Interference-aware torque metric
• Hierarchical receptive field reconfiguration