Stability-Shaped Deep Graph Learning

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.

Machine Learning (cs.LG)

arXiv:2610.06344 [cs.LG]

(or arXiv:2610.06344v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.06344 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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