SAGMAN: Stability Analysis of Graph Neural Networks (GNNs) on the Manifolds

Wuxinlin Cheng, Chenhui Deng, Ali Aghdaei, Zhiru Zhang, Zhuo Feng

Keywords: Manifolds, Stability, Graph Neural Networks

Abstract: Graph neural networks (GNNs) are highly effective at tasks that involve analyzing graph-structured data, such as predicting protein interactions, modeling social networks, and identifying communities within graphs. However, modern GNNs can be sensitive to changes in the input graph structure and node features, leading to unpredictable behavior and degraded performance. In this work, we introduce a spectral framework (SAGMAN) for analyzing the stability of GNNs. SAGMAN quantifies the stability of each node by examining the distance mapping distortions (DMDs) on the input/output manifolds: when two nearby nodes on the input manifold are mapped (through a GNN model) to two distant nodes (data samples) on the output manifold, it implies a large DMD and thus poor GNN stability. To create low-dimensional input/output manifolds for meaningful DMD estimations while exploiting both the input graph topology and node features, we propose a spectral sparsification framework for estimating probabilistic graphical models (PGMs) such that the constructed input/output graph structures can well preserve pair-wise distances on the manifolds. Our empirical evaluations show that SAGMAN can effectively reveal each node's stability under various edge/feature perturbations, offering a scalable approach for assessing the stability of GNNs.

Primary Area: optimization

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Submission Number: 7179