Renormalized Graph Representations for Node Classification

TL;DR

This paper explores how using renormalized, multi-scale graph representations improves node classification accuracy by capturing interactions at different scales, demonstrating the benefits of multi-resolution analysis in graph neural networks.

Contribution

It introduces a method to incorporate Laplacian renormalization group-based coarse-grained graph representations into node classification models, showing improved performance.

Findings

Models with multi-scale representations outperform single-scale models.

Using the characteristic scale graph improves test accuracy.

Multi-resolution approach captures interactions at different ranges.

Abstract

Graph neural networks process information on graphs represented at a given resolution scale. We analyze the effect of using different coarse-grained graph resolutions, obtained through the Laplacian renormalization group theory, on node classification tasks. At the theory's core is grouping nodes connected by significant information flow at a given time scale. Representations of the graph at different scales encode interaction information at different ranges. We specifically experiment using representations at the characteristic scale of the graph's mesoscopic structures. We provide the models with the original graph and the graph represented at the characteristic resolution scale and compare them to models that can only access the original graph. Our results showed that models with access to both the original graph and the characteristic scale graph can achieve statistically significant improvements in test accuracy.