Geometric instability of graph neural networks on large graphs

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 invaria...

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Bibliographic Details
Published in:arXiv.org 2023-11
Main Authors: Morris, Emily, Shen, Haotian, Du, Weiling, Muhammad Hamza Sajjad, Shi, Borun
Format: Article
Language:English
Subjects:
Graph neural networks
Graphs
Permutations
Stability
Stability analysis
Online Access:Get full text
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Summary: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.
ISSN:2331-8422