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[2510.20954] A Spectral Framework for Graph Neural Operators: Convergence Guarantees and Tradeoffs
Summary
This paper presents a spectral framework for analyzing graph neural operators, focusing on convergence guarantees and tradeoffs under various assumptions about graphons.
Why It Matters
Understanding the convergence of graph neural networks (GNNs) is crucial for their application in real-world scenarios. This framework allows researchers to compare different convergence results, enhancing the reliability and transferability of GNNs across diverse datasets.
Key Takeaways
- Introduces a unified spectral framework for graph neural operators.
- Establishes convergence guarantees under various assumptions on graphons.
- Enables direct comparison of convergence rates and tradeoffs.
- Demonstrates empirical results on both synthetic and real-world graphs.
- Enhances understanding of GNN transferability across different contexts.
Statistics > Machine Learning arXiv:2510.20954 (stat) [Submitted on 23 Oct 2025 (v1), last revised 23 Feb 2026 (this version, v2)] Title:A Spectral Framework for Graph Neural Operators: Convergence Guarantees and Tradeoffs Authors:Roxanne Holden, Luana Ruiz View a PDF of the paper titled A Spectral Framework for Graph Neural Operators: Convergence Guarantees and Tradeoffs, by Roxanne Holden and 1 other authors View PDF HTML (experimental) 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-Lipschitz continuity. The framework places these results in a common operator setting, enabling direct comparison of their assumptions, convergence rates, and tradeoffs. We further illustrate the empirical tightness of these rates on synthetic and real-world graphs. Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG); Signal Processing (eess.SP) Cite as: arXiv:2510.20954 [stat.ML] (or arXiv:2510.20954v2 [stat.ML] for this version) https://doi.org/10.48550/arXiv.2510.20954 Focus to learn mor...