[
    {
        "id": "osp-16637",
        "type": "article-journal",
        "title": "Oscillatory Neural Dynamics over Sheaves",
        "author": [
            {
                "family": "Van Looy",
                "given": "Jan-Willem"
            },
            {
                "family": "Trenta",
                "given": "Alessandro"
            },
            {
                "family": "Gravina",
                "given": "Alessio"
            },
            {
                "family": "Borgi",
                "given": "Alessio"
            },
            {
                "family": "Zanchetta",
                "given": "Ferdinando"
            },
            {
                "family": "Liò",
                "given": "Pietro"
            },
            {
                "family": "Bacciu",
                "given": "Davide"
            },
            {
                "family": "Fioresi",
                "given": "Rita"
            }
        ],
        "URL": "https://omanscience.com/en/articles/oscillatory-neural-dynamics-over-sheaves",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "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."
    }
]