We analyse the geometric instability of embeddings produced by graph neural networks (GNNs). Existing methods are only applicable for small graphs and lack context in the graph domain. We propose a simple, efficient and graph-native Graph Gram Index (GGI) to measure such instability which is invariant to permutation, orthogonal transformation, translation and order of evaluation. This allows us to study the varying instability behaviour of GNN embeddings on large graphs for both node classification and link prediction.

翻译：我们分析了图神经网络（GNN）所生成嵌入的几何不稳定性。现有方法仅适用于小规模图，且在图形域中缺乏上下文。我们提出了一种简单、高效且图原生的图格拉姆指数（GGI），用于衡量这种不稳定性，该指数对排列、正交变换、平移和评估顺序具有不变性。这使我们能够研究大图图上GNN嵌入在节点分类和链接预测任务中的不同不稳定性行为。