Geometric instability of graph neural networks on large graphs

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

Geometric instability of graph neural networks on large graphs

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arxiv 2308.10099 v2 pith:J5NADQR4 submitted 2023-08-19 cs.LG cs.SI

Emily Morris , Haotian Shen , Weiling Du , Muhammad Hamza Sajjad , Borun Shi This is my paper · ORCID

classification cs.LGcs.SI

keywords graphinstabilitygraphsembeddingsgeometriclargenetworksneural

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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.

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