On the Relationship Between Robustness and Expressivity of Graph Neural Networks

On the Relationship Between Robustness and Expressivity of Graph Neural Networks

Abstract

We investigate the vulnerability of Graph Neural Networks (GNNs) to bit-flip attacks (BFAs) by introducing an analytical framework to study the influence of architectural features, graph properties, and their interaction. The expressivity of GNNs refers to their ability to distinguish non-isomorphic graphs and depends on the encoding of node neighborhoods. We examine the vulnerability of neural multiset functions commonly used for this purpose and establish formal criteria to characterize a GNN’s susceptibility to losing expressivity due to BFAs. This enables an analysis of the impact of homophily, graph structural variety, feature encoding, and activation functions on GNN robustness. We derive theoretical bounds for the number of bit flips required to degrade GNN expressivity on a dataset, identifying ReLU-activated GNNs operating on highly homophilous graphs with low-dimensional or one-hot encoded features as particularly susceptible. Empirical results using ten real-world datasets confirm the statistical significance of our key theoretical insights and offer actionable results to mitigate BFA risks in expressivity-critical applications.

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Authors
  • Kummer, Lorenz
  • Gansterer, Wilfried
  • Kriege, Nils M.
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Shortfacts
Category
Paper in Conference Proceedings or in Workshop Proceedings (Paper)
Event Title
The 28th International Conference on Artificial Intelligence and Statistics (AISTATS)
Divisions
Data Mining and Machine Learning
Theory and Applications of Algorithms
Event Location
Mai Khao, Thailand
Event Type
Conference
Event Dates
03.05.-05.05.2025
Series Name
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics
ISSN/ISBN
2640-3498
Page Range
1243-1251,
Date
3 May 2025
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