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.
Keywords
Publication details
- Journal
- Not available
- Open access
- Green open access
Cite this article
APA 7
Van Looy, J. W., Trenta, A., Gravina, A., Borgi, A., Zanchetta, F., Liò, P., Bacciu, D., & Fioresi, R. (2026). Oscillatory Neural Dynamics over Sheaves. https://omanscience.com/en/articles/oscillatory-neural-dynamics-over-sheaves
MLA 9
Van Looy, Jan-Willem, et al. "Oscillatory Neural Dynamics over Sheaves." https://omanscience.com/en/articles/oscillatory-neural-dynamics-over-sheaves.
Chicago (author–date)
Van Looy, Jan-Willem, Alessandro Trenta, Alessio Gravina, Alessio Borgi, Ferdinando Zanchetta, Pietro Liò, Davide Bacciu, and Rita Fioresi. 2026. "Oscillatory Neural Dynamics over Sheaves." https://omanscience.com/en/articles/oscillatory-neural-dynamics-over-sheaves.
Harvard
Van Looy, J. W., Trenta, A., Gravina, A., Borgi, A., Zanchetta, F., Liò, P., Bacciu, D. and Fioresi, R. (2026) 'Oscillatory Neural Dynamics over Sheaves', Available at: https://omanscience.com/en/articles/oscillatory-neural-dynamics-over-sheaves.
Vancouver
Van Looy JW, Trenta A, Gravina A, Borgi A, Zanchetta F, Liò P, et al. Oscillatory Neural Dynamics over Sheaves. https://omanscience.com/en/articles/oscillatory-neural-dynamics-over-sheaves
IEEE
J. W. Van Looy, A. Trenta, A. Gravina, A. Borgi, F. Zanchetta, P. Liò, D. Bacciu, and R. Fioresi, "Oscillatory Neural Dynamics over Sheaves," https://omanscience.com/en/articles/oscillatory-neural-dynamics-over-sheaves.