Problem
Research questions and friction points this paper is trying to address.
Deep Graph Neural Networks
Over-smoothing
Node Representations
Dynamical Synchronization
Stability-Shaped Deep Graph Learning
🤖 AI Summary
This study addresses the over-smoothing problem in deep graph neural networks (GNNs), where increasing depth impairs the modeling of long-range dependencies. To overcome this limitation, this work proposes a unified dynamical framework grounded in pattern stability that formulates feature propagation as a dynamic synchronization process, leveraging the master stability function to elucidate feature alignment mechanisms. The core innovation lies in replacing conventional synchronized states with controlled Turing instability or near-critically stable propagation, thereby reshaping the learning paradigm of deep GNNs from a dynamical systems perspective. Extensive evaluations on node- and graph-level benchmarks demonstrate that the proposed approach significantly enhances depth scalability while maintaining high accuracy on long-range dependency tasks, consistently outperforming existing baselines.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Over-smoothing
Master Stability Curve
Turing Instability
Graph Neural Networks
Dynamical Synchronization
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