Lost in Aggregation: On a Fundamental Expressivity Limit of Message-Passing Graph Neural Networks
arXiv:2603.14846v3 Announce Type: replace 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 aforeme
This research is emerging as the field of Graph Neural Networks matures, prompting deeper theoretical understanding of their fundamental limitations while they are extensively applied.
This paper highlights a fundamental expressivity limit in common Message-Passing Graph Neural Networks, which impacts their ability to distinguish between complex graph structures.
The understanding of MP-GNN limitations means future AI development will need to explore architectures beyond simple message-passing for tasks requiring high graph discrimination.
- · Researchers developing novel GNN architectures
- · AI fields requiring specialized graph analysis
- · Developers of algorithms that combine MP-GNNs with other techniques
- · Over-reliance on basic MP-GNNs for complex graph tasks
- · Companies investing solely in standard MP-GNN optimizations
The finding prompts research into more sophisticated GNN architectures that overcome these expressivity limits.
It could lead to a divergence in GNN applications, with basic MP-GNNs used for simpler tasks and advanced models for complex relational data.
This could accelerate the adoption of 'architecture search' and hybrid AI models for graph-based problems, impacting the overall AI development landscape.
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Read at arXiv cs.LG