Ramanujan Graph Rewiring with Non Negative Resistance Curvature

2026-06-19

AI Summary

This work addresses the over-squashing problem in graph neural networks, which severely hinders the learning of long-range dependencies. The authors propose a novel rewiring strategy based on Ramanujan graphs, uniquely integrating Ramanujan graph theory with non-negative resistance curvature to optimize global information propagation pathways while preserving local connectivity. This approach introduces a theoretically grounded topological prior into graph neural networks. Experimental results demonstrate that the method significantly outperforms nine state-of-the-art rewiring techniques across multiple benchmarks, effectively mitigating over-squashing and enhancing both the model’s capacity to capture long-range dependencies and its overall performance.

Abstract

Graph Neural Networks (GNNs) have emerged as a powerful paradigm for learning on graph-structured data by iteratively propagating and aggregating information across edges. However, conventional message passing schemes often suffer from over-squashing, whereby exponentially large neighborhoods are compressed into fixed-dimensional embeddings, impeding effective long-range dependency learning. In this work, we introduce Ramanujan Propagation, a graph rewiring strategy that leverages Ramanujan graphs to alleviate topological bottlenecks in GNNs. We first establish that suitably chosen Ramanujan graphs guarantee non-negative resistance curvature, which mitigates over-squashing and facilitates efficient information flow. We then propose an algorithmic framework to construct a Ramanujan rewired graph that preserves the local connectivity of the original graph. Our experiments demonstrate that our method outperforms nine state-of-the-art rewiring techniques. These results establish Ramanujan graphs as a rigorous structural prior for scalable, topology-aware message passing in GNNs.

Problem

• over-squashing
• Graph Neural Networks
• long-range dependency
• message passing
• graph topology

Innovation

• Ramanujan graphs
• graph rewiring
• over-squashing
• resistance curvature
• graph neural networks