Dynamic Triangulation-Based Graph Rewiring for Graph Neural Networks

2025-08-26

AI Summary

Graph Neural Networks (GNNs) suffer from over-squashing and over-smoothing, primarily due to inefficient information propagation induced by the original graph topology. To address this, we propose a dynamic triangulation-based graph rewiring framework that jointly optimizes triangle selection and downstream task objectives across multiple views via a learnable, non-planar triangulation mechanism. The method is end-to-end differentiable and grounded in spectral graph theory, yielding significant improvements in key structural properties—including reduced graph diameter, enlarged spectral gap, and lowered effective resistance. Extensive experiments on diverse homogeneous and heterogeneous graph benchmarks demonstrate superior node classification performance over state-of-the-art methods. Our core contribution is the first integration of *learnable non-planar triangulation* into GNN architecture optimization, enabling synergistic enhancement of topological restructuring and representation learning.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Learning to Search
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Graph Neural Networks (GNNs) have emerged as the leading paradigm for learning over graph-structured data. However, their performance is limited by issues inherent to graph topology, most notably oversquashing and oversmoothing. Recent advances in graph rewiring aim to mitigate these limitations by modifying the graph topology to promote more effective information propagation. In this work, we introduce TRIGON, a novel framework that constructs enriched, non-planar triangulations by learning to select relevant triangles from multiple graph views. By jointly optimizing triangle selection and downstream classification performance, our method produces a rewired graph with markedly improved structural properties such as reduced diameter, increased spectral gap, and lower effective resistance compared to existing rewiring methods. Empirical results demonstrate that TRIGON outperforms state-of-the-art approaches on node classification tasks across a range of homophilic and heterophilic benchmarks.

Problem

• Addresses oversquashing and oversmoothing in GNNs
• Improves graph topology for better information propagation
• Enhances structural properties through dynamic triangulation rewiring

Innovation

• Dynamic triangulation-based graph rewiring framework
• Learns relevant triangles from multiple graph views
• Jointly optimizes topology and classification performance