[
    {
        "id": "osp-17060",
        "type": "article-journal",
        "title": "Stability-Shaped Deep Graph Learning",
        "author": [
            {
                "family": "Zhu",
                "given": "Junyou"
            },
            {
                "family": "He",
                "given": "Langzhou"
            },
            {
                "family": "Cai",
                "given": "Fenying"
            },
            {
                "family": "Nauck",
                "given": "Christian"
            },
            {
                "family": "Xiong",
                "given": "Ping"
            },
            {
                "family": "Gao",
                "given": "Chao"
            },
            {
                "family": "Yu",
                "given": "Philip S."
            },
            {
                "family": "Müller",
                "given": "Klaus-Robert"
            },
            {
                "family": "Kurths",
                "given": "Jürgen"
            },
            {
                "family": "Hellmann",
                "given": "Frank"
            }
        ],
        "URL": "https://omanscience.com/ar/articles/stability-shaped-deep-graph-learning",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "abstract": "In deep graph neural networks, increasing depth enlarges the receptive field but often leads to over-smoothing, where node representations tend to align. We develop a unified, mode-wise stability framework for deep GNN propagation that provides a principled characterization of over-smoothing. By interpreting layer depth as time and layer updates as graph-coupled dynamics, over-smoothing can be understood as an undesirable dynamical synchronization of features, for which the master stability curve provides a theoretical tool to assess the stability of synchrony. Guided by this theory, we further propose Stability-Shaped Deep Graph Learning (SDGL) to mitigate over-smoothing in deep GNNs. SDGL has two complementary instantiations: one induces controlled Turing instability to replace synchronization with spatial pattern formation, and the other maintains stable near-critical propagation. Experiments on diverse node- and graph-level benchmarks demonstrate the improved depth scaling and consistent accuracy gains over strong baselines, including graphs exhibiting long-range dependencies."
    }
]