← Back to all news
arXiv Machine Learning By Jan-Willem Van Looy, Alessandro Trenta, Alessio Gravina, Alessio Borgi, Ferdinando Zanchetta, Pietro Li\`o, Davide Bacciu, Rita Fioresi

Oscillatory Neural Dynamics over Sheaves

Read the original on arXiv Machine Learning →

The paper introduces ONDA, a graph learning framework that uses operator‑valued information waves to enable effective long‑range propagation in graph neural networks. ONDA evolves stalk‑valued representations through second‑order dynamics governed by learned sheaf transport operators, combining wave‑like propagation with expressive local geometry. Experiments on challenging benchmarks show that ONDA consistently outperforms scalar wave propagation, diffusive sheaf baselines, and state‑of‑the‑art models, demonstrating the advantage of coupling wave dynamics with matrix‑valued transport.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

Related stories

arXiv Machine Learning
Jun 2

Graph Navier Stokes Networks

arXiv:2605. 21247v3 Announce Type: replace Abstract: Graph Neural Networks (GNNs) have emerged as a cornerstone of deep learning, with most existing methods rooted in graph signal processing and diffusion equations to model message passing.

By Zexing Zhao, Guangsi Shi, Yu Gong, Tianyu Wang, Shirui Pan, Hongye Cheng, Yuxiao Li
diffusionbenchmarks
More like this →
arXiv Machine Learning
Oct 3

Information propagation dynamics in Deep Graph Networks

The paper explores how information propagates in Deep Graph Networks (DGNs) for both static and dynamic graphs, treating DGNs as dynamical systems. It presents new architectures that better preserve long‑term node dependencies and learn complex spatio‑temporal patterns from irregular, sparsely sampled dynamic graphs. The work combines theoretical analysis with empirical results to demonstrate the effectiveness of these designs.

By Alessio Gravina
More like this →
arXiv Machine Learning
Jun 2

Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning

arXiv:2604. 20308v2 Announce Type: replace Abstract: Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued representations that capture relationships between directions-such as how atomic orientations covary in a molecule.

By Yuhan Peng, Junwen Dong, Yuzhi Zeng, Hao Li, Ce Ju, Huitao Feng, Diaaeldin Taha, Anna Wienhard, Kelin Xia
benchmarks
More like this →