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arXiv · 2603.14846

Lost in Aggregation: On a Fundamental Expressivity Limit of Message-Passing Graph Neural Networks

Eran Rosenbluth
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Abstract

We define an information-complexity property for aggregation functions, capturing a vast range of practical aggregations, and prove that any Message-Passing Graph Neural Network (MP-GNN) model with such aggregations induces only a polynomial number of equivalence classes on all graphs - while the number of non-isomorphic graphs is super-exponential (in number of vertices). Adding a familiar perspective, we observe that merely 2 iterations of Color Refinement (CR) induce at least an exponential number of equivalence classes, making the aforementioned MP-GNNs relatively infinitely weaker. Previous studies state that sum-aggregation MP-GNNs match full CR however they consider a weak, 'non-uniform', notion of distinguishing-power where each graph size may require a different MP-GNN to distinguish graphs up to that size. Our results concern both distinguishing between non-equivariant vertices and distinguishing between non-isomorphic graphs.

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BibTeXRIS

Eran Rosenbluth. 2026-03-16. Lost in Aggregation: On a Fundamental Expressivity Limit of Message-Passing Graph Neural Networks. https://arxiv.org/abs/2603.14846

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