SAGMAN：流形上图神经网络的稳定性分析
SAGMAN: Stability Analysis of Graph Neural Networks on the Manifolds
AI总结：
针对图神经网络对输入图结构和节点特征变化敏感、稳定性难评估的问题，提出谱框架SAGMAN，结合保距离图降维方法评估GNN节点稳定性，可扩展至推荐系统，还能用于提升GNN稳定性与对抗攻击研究。
摘要：
现代图神经网络（GNN）可能对输入图结构和节点特征的变化较为敏感，有可能导致不可预测的行为与性能下降。在本研究中，我们提出了名为SAGMAN的谱框架，用于检验GNN的稳定性。该框架评估由GNN的非线性映射在输入与输出流形之间引发的距离畸变：若输入流形上的两个邻近节点（经GNN模型）被映射到输出流形上的两个相距较远的节点，则意味着距离畸变大，GNN的稳定性较差。我们提出了一种保距离的图降维（GDR）方法，该方法利用谱图嵌入和概率图模型（PGM）构建低维的输入/输出基于图的流形，以开展有意义的稳定性分析。我们的实证评估表明，SAGMAN能够有效评估每个节点在受到各类边或特征扰动时的稳定性，为GNN稳定性评估提供了一种可扩展的方法，还可延伸应用于推荐系统领域。此外，我们还展示了其在下游任务中的效用，尤其是在提升GNN稳定性和助力对抗性定向攻击方面。
英文摘要：
Modern graph neural networks (GNNs) can be sensitive to changes in the input graph structure and node features, potentially resulting in unpredictable behavior and degraded performance. In this work, we introduce a spectral framework known as SAGMAN for examining the stability of GNNs. This framework assesses the distance distortions that arise from the nonlinear mappings of GNNs between the input and output manifolds: when two nearby nodes on the input manifold are mapped (through a GNN model) to two distant ones on the output manifold, it implies a large distance distortion and thus a poor GNN stability. We propose a distance-preserving graph dimension reduction (GDR) approach that utilizes spectral graph embedding and probabilistic graphical models (PGMs) to create low-dimensional input/output graph-based manifolds for meaningful stability analysis. Our empirical evaluations show that SAGMAN effectively assesses the stability of each node when subjected to various edge or feature perturbations, offering a scalable approach for evaluating the stability of GNNs, extending to applications within recommendation systems. Furthermore, we illustrate its utility in downstream tasks, notably in enhancing GNN stability and facilitating adversarial targeted attacks.
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