Ramanujan Graph Rewiring with Non Negative Resistance Curvature

A new graph rewiring strategy called Ramanujan Propagation aims to fix a persistent bottleneck in Graph Neural Networks (GNNs) known as over-squashing, according to a preprint posted on arXiv [1]. GNNs learn from graph-structured data by passing messages along edges, but conventional methods compress information from exponentially large neighborhoods into fixed-size vectors, blocking long-range dependencies [1]. The paper, authored by Hugo Attali and submitted on June 19, 2026, introduces a technique that rewires input graphs using Ramanujan graphs — structures that guarantee non-negative resistance curvature [1]. This property mitigates over-squashing and allows information to flow more efficiently across the network [1]. The algorithmic framework constructs a rewired graph that preserves the original local connectivity while adding the curvature guarantees [1]. In experiments, Ramanujan Propagation outperformed nine state-of-the-art rewiring techniques, positioning Ramanujan graphs as a structural prior for scalable message passing [1]. The manuscript was updated to a second version on June 24, 2026, with the file size growing from 88 KB to 91 KB [1]. The work appears on arXiv, an open-access repository that hosts preprints across mathematics, physics, computer science, and related fields [6]. arXiv was founded in 1991 and now receives roughly 24,000 submissions per month [6]. The platform also supports arXivLabs, a framework launched in 2020 that lets community collaborators build experimental tools on top of the repository [5].