ONDA paper couples oscillatory dynamics with sheaves to fix long-range propagation in GNNs
burny_tech · x · 2026-10-27
A new arXiv paper, Oscillatory Neural Dynamics over Sheaves, introduces ONDA, targeting the long-standing GNN problem that deeper propagation doesn't guarantee distant nodes actually influence each other.
- Building on sheaf neural networks (matrix-valued transport between stalks), ONDA evolves stalk-valued representations via second-order oscillatory dynamics governed by learned sheaf transport operators—wave-like propagation with expressive local geometry
- A stalk-wise sensitivity analysis shows cross-influence never vanishes
- Across long-range propagation, severe graph bottlenecks, graph transfer, and heterophilic benchmarks, ONDA consistently beats scalar wave propagation, diffusive sheaf baselines, and state-of-the-art models
Authors include Pietro Liò, Davide Bacciu, et al.
Related event: ONDA: Oscillatory Neural Dynamics Tackle Long-Range Propagation in GNNs(2 posts)→
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