A Spectral Theory of Normalized Corrected GNN Propagation

Qihan Chen; Wei Li; Meng Qin; Jianfeng Hou

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arXiv · 2606.23572

A Spectral Theory of Normalized Corrected GNN Propagation

Qihan Chen·Wei Li·Meng Qin·Jianfeng Hou

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Abstract

We develop a spectral theory for \emph{normalized corrected GNN propagation}. The object of study is the symmetric normalized adjacency with its degree-stationary component removed, matching the normalization used by standard GCN-style models while isolating the stationary direction most directly tied to oversmoothing. The central theoretical question is whether this corrected normalized operator preserves class-discriminative signal after many propagation layers. Our main result is a high-probability exact-recovery theorem for the binary Contextual Stochastic Block Model after $k=O(\log n)$ propagation steps in the dense polylogarithmic regime $p\ge C\log^B n/n$, for any fixed $B>4$, under explicit graph-signal and feature-SNR conditions. We also establish a multi-class partial recovery theorem showing contraction toward class centers for most nodes. Synthetic and real node-classification experiments are included as empirical checks of the theory's predicted dependence on depth, graph signal, and feature noise.

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Qihan Chen, Wei Li, Meng Qin, Jianfeng Hou. 2026-06-22. A Spectral Theory of Normalized Corrected GNN Propagation. https://arxiv.org/abs/2606.23572

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