Ramanujan Graph Rewiring with Non Negative Resistance Curvature
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Effective Resistance Rewiring: A Simple Topological Correction for Over-Squashing
Graph Neural Networks struggle to capture long-range dependencies due to over-squashing, where information from exponentially growing neighborhoods must pass through a small number of structural bottlenecks. While recent…
Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvature
Graph Neural Networks (GNNs) had been demonstrated to be inherently susceptible to the problems of over-smoothing and over-squashing. These issues prohibit the ability of GNNs to model complex graph interactions by limit…
The Effectiveness of Curvature-Based Rewiring and the Role of Hyperparameters in GNNs Revisited
Message passing is the dominant paradigm in Graph Neural Networks (GNNs). The efficiency of message passing, however, can be limited by the topology of the graph. This happens when information is lost during propagation …
Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvature
While Graph Neural Networks (GNNs) have been successfully leveraged for learning on graph-structured data across domains, several potential pitfalls have been described recently. Those include the inability to accurately…
Understanding over-squashing and bottlenecks on graphs via curvature
Most graph neural networks (GNNs) use the message passing paradigm, in which node features are propagated on the input graph. Recent works pointed to the distortion of information flowing from distant nodes as a factor l…
Node Classification