arXiv:2512.19332v2 Announce Type: replace Abstract: We study the numerical and Boolean expressiveness of MPLang, a declarative language that captures the computation of graph neural networks (GNNs) through linear message passing and activation functions. We begin with A-MPLang, the fragment without activation functions, and give a characterization of its expressive power in terms of walk-summed features. For bounded activation functions, we show that (under mild conditions) all eventually constant activations yield the same expressive power - numerical and Boolean - and that it subsumes previo
This research provides a theoretical understanding of Graph Neural Networks (GNNs), a key component in advanced AI, at a time when their practical application and development are rapidly expanding.
A deeper theoretical understanding of GNNs' expressive power aids in designing more effective and predictable AI systems, impacting fields from drug discovery to social network analysis.
The characterization of GNN expressiveness, particularly regarding activation functions, potentially refines the development and deployment strategies for complex AI models.
- · AI researchers
- · Machine learning framework developers
- · Sectors using GNNs for complex data analysis
- · Developers relying on trial-and-error GNN design
Improved design principles for Graph Neural Networks could emerge, leading to more robust and powerful models.
Enhanced GNN capabilities could accelerate discoveries in materials science, drug development, and complex system modeling.
More explainable and predictable GNNs might reduce the 'black box' problem in certain AI applications, fostering greater trust and adoption.
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Read at arXiv cs.LG