Graph Representational Learning: When Does More Expressivity Hurt Generalization?

• URL: http://arxiv.org/abs/2505.11298v1
• Date: Fri, 16 May 2025 14:28:34 GMT
• Title: Graph Representational Learning: When Does More Expressivity Hurt Generalization?
• Authors: Sohir Maskey, Raffaele Paolino, Fabian Jogl, Gitta Kutyniok, Johannes F. Lutzeyer,
• Abstract summary: Graph Neural Networks (GNNs) are powerful tools for learning on structured data.<n>We introduce a family of premetrics that capture different degrees of structural similarity between graphs.<n>We derive generalization bounds that depend on the distance between training and test graphs, model complexity, and training set size.
• Score: 15.458310474570299
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Graph Neural Networks (GNNs) are powerful tools for learning on structured data, yet the relationship between their expressivity and predictive performance remains unclear. We introduce a family of premetrics that capture different degrees of structural similarity between graphs and relate these similarities to generalization, and consequently, the performance of expressive GNNs. By considering a setting where graph labels are correlated with structural features, we derive generalization bounds that depend on the distance between training and test graphs, model complexity, and training set size. These bounds reveal that more expressive GNNs may generalize worse unless their increased complexity is balanced by a sufficiently large training set or reduced distance between training and test graphs. Our findings relate expressivity and generalization, offering theoretical insights supported by empirical results.

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