Dynamic Triangulation-Based Graph Rewiring for Graph Neural Networks

TL;DR

TRIGON is a novel graph rewiring framework that enhances GNN performance by learning to select relevant triangles, improving structural properties and outperforming existing methods on node classification benchmarks.

Contribution

Introduces TRIGON, a framework that constructs enriched triangulations for graph rewiring by learning to select relevant triangles, addressing oversquashing and oversmoothing issues.

Findings

TRIGON improves structural properties like reduced diameter and increased spectral gap.

TRIGON outperforms state-of-the-art methods on various node classification benchmarks.

The method effectively mitigates oversquashing and oversmoothing in GNNs.

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.