用李雅普诺夫稳定性理论设计神经控制器，提升GNN测试时的特征重建效果。
Control the GNN: Utilizing Neural Controller with Lyapunov Stability for Test-Time Feature Reconstruction
- 将GNN视为控制系统，以神经控制器动态调整测试阶段节点特征。
- 理论保证预测值在测试时渐近逼近真实值，提升模型鲁棒性。
- 适用于分布偏移严重的图数据场景，尤其适合对可靠性要求高的应用。
图神经网络（GNN）的性能易受训练与测试样本分布差异的影响。已有研究尝试在不修改模型参数的前提下，通过测试阶段重构节点特征来缓解分布偏移问题，但缺乏对测试时预测值与真实值之间接近程度的理论分析。本文提出一种基于李雅普诺夫稳定性理论的新颖节点特征重建方法。具体而言，将GNN在测试阶段建模为控制系统，将节点特征视为控制变量，并设计一个满足李雅普诺夫稳定性准则的神经控制器，以确保预测值在测试过程中逐步逼近真实值。我们在多个数据集上进行了大量实验，验证了该方法的有效性，显著提升了模型性能。
原文摘要 · Abstract (English)
The performance of graph neural networks (GNNs) is susceptible to discrepancies between training and testing sample distributions. Prior studies have attempted to mitigating the impact of distribution shift by reconstructing node features during the testing phase without modifying the model parameters. However, these approaches lack theoretical analysis of the proximity between predictions and ground truth at test time. In this paper, we propose a novel node feature reconstruction method grounded in Lyapunov stability theory. Specifically, we model the GNN as a control system during the testing phase, considering node features as control variables. A neural controller that adheres to the Lyapunov stability criterion is then employed to reconstruct these node features, ensuring that the predictions progressively approach the ground truth at test time. We validate the effectiveness of our approach through extensive experiments across multiple datasets, demonstrating significant performance improvements.
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