arXiv:2510.20954v3 Announce Type: replace-cross Abstract: Graphons, as limits of graph sequences, provide an operator-theoretic framework for analyzing the asymptotic behavior of graph neural operators. Spectral convergence of sampled graphs to graphons induces convergence of the corresponding neural operators, enabling transferability analyses of graph neural networks (GNNs). This paper develops a unified spectral framework that brings together convergence results under different assumptions on the underlying graphon, including no regularity, global Lipschitz continuity, and piecewise-Lipschi
The accelerating development of graph neural networks for complex data structures necessitates foundational advancements in theoretical understanding and performance guarantees.
This research provides a rigorous mathematical framework for understanding and assuring the behavior of GNNs, crucial for their reliable application in critical AI systems.
A unified spectral framework for Graph Neural Operators offers convergence guarantees, which will enable more robust and predictable GNN development.
- · AI researchers
- · GNN developers
- · Companies using AI for complex data analytics
- · Developers of ad-hoc GNN solutions without theoretical grounding
Improved stability and predictability of Graph Neural Networks for real-world applications.
Accelerated deployment of GNNs in areas requiring high reliability, such as drug discovery or logistics optimization.
Enhanced trust in AI systems built with GNNs, potentially broadening their adoption across sensitive industries.
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Read at arXiv cs.LG