Stability-Shaped Deep Graph Learning

Junyou Zhu; Langzhou He; Fenying Cai; Christian Nauck; Ping Xiong; Chao Gao; Philip S. Yu; Klaus-Robert Müller; Jürgen Kurths; Frank Hellmann

arXiv · 2610.06344

Stability-Shaped Deep Graph Learning

Junyou Zhu·Langzhou He·Fenying Cai·Christian Nauck·Ping Xiong·Chao Gao·Philip S. Yu·Klaus-Robert Müller·Jürgen Kurths·Frank Hellmann

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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.

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BibTeX RIS

Junyou Zhu, Langzhou He, Fenying Cai, Christian Nauck, Ping Xiong, Chao Gao, Philip S. Yu, Klaus-Robert Müller, Jürgen Kurths, Frank Hellmann. 2026-10-05. Stability-Shaped Deep Graph Learning. https://arxiv.org/abs/2610.06344

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