Alessio Borgi

Alessio Borgi

PhD in Graph Neural Networks and Generative AI 👨🏻‍💻🤖

Oscillatory Neural Dynamics over Sheaves

Published in arXiv preprint arXiv:2610.10018, 2026

Overview

Increasing a graph neural network’s propagation depth expands its receptive field, but does not guarantee that distant nodes effectively influence one another. Cellular sheaves enrich local communication through learned matrix-valued transport between stalks; expressive transport alone, however, does not ensure useful long-range propagation.

ONDA couples this learned transport geometry with second-order oscillatory dynamics. Restriction maps shape how signals transform across edges, while wave-like evolution helps those signals remain influential over depth. The model also supports learned dissipation and forcing to adapt its dynamics to the task.

Key Contributions

  • A sheaf neural architecture that combines learned matrix-valued transport with oscillatory propagation.
  • A stalk-wise sensitivity analysis showing that a nontrivial source-to-target response does not converge to zero in the fixed, conservative, self-adjoint setting, with a corresponding discrete result under a step-size stability condition.
  • Strong results on ECHO-Synth shortest-path and eccentricity prediction, Barbell bottlenecks, and graph transfer up to 50 hops, alongside competitive performance on heterophilic benchmarks.

Resources

Recommended citation: Van Looy, J.-W.; Trenta, A.; Gravina, A.; Borgi, A.; Zanchetta, F.; Liò, P.; Bacciu, D.; Fioresi, R. (2026). "Oscillatory Neural Dynamics over Sheaves." arXiv:2610.10018.
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