Geometric instability of graph neural networks on large graphs

Borun Shi, Emily Morris, Haotian Shen, Weiling Du, Muhammad Hamza Sajjad

Keywords: embedding instability, geometric instability, large graphs, graph neural networks

TL;DR: We propose a simple and efficient method to show the geometric instability of embeddings produced by GNNs.

Abstract: 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.

Submission Type: Extended abstract (max 4 main pages).

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Submission Number: 51