Oscillatory neural dynamics improve long range communication in graphs
Oscillatory Neural Dynamics over Sheaves
Machine Learning
Summary
Graph neural networks struggle to pass information effectively between distant nodes. The authors introduce ONDA, which uses wave-like patterns and more complex data structures to help distant parts of a graph communicate better. This approach keeps the influence between faraway nodes alive over long distances. Their tests show ONDA outperforms previous methods, especially on challenging graphs and certain specialized tasks.
What this means in practice
- •For graph machine learning engineers: Enhance graph neural network models to improve message passing across distant nodes in complex graph datasets.
- •For network analysis developers: Build tools that detect and overcome communication bottlenecks in network structures using wave-based graph propagation.
Authors
Jan-Willem Van Looy, Alessandro Trenta, Alessio Gravina, Alessio Borgi, Ferdinando Zanchetta, Pietro Liò, Davide Bacciu, Rita Fioresi
Abstract
Effective long-range propagation remains a central challenge in graph neural networks, as increasing a model's propagation depth does not guarantee that distant nodes effectively influence each other. Sheaf neural networks enrich graph propagation through matrix-valued transport between stalks; still, this expressivity alone does not automatically imply effective long-range communication. We introduce ONDA, a long-range graph learning framework based on operator-valued information waves. Stalk-valued representations evolve through second-order dynamics governed by learned sheaf transport operators, combining wave-like propagation with expressive local geometry. We characterize long-range influence through a stalk-wise sensitivity analysis and show that the cross-influence never vanishes. Across long-range propagation, severe graph bottlenecks, graph transfer, and heterophilic benchmarks, ONDA consistently improves over scalar wave propagation, diffusive sheaf baselines, and state-of-the-art models, demonstrating the benefit of coupling wave dynamics with matrix-valued transport.