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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.20954 |
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| _version_ | 1866910251473698816 |
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| author | Holden, Roxanne Ruiz, Luana |
| author_facet | Holden, Roxanne Ruiz, Luana |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20954 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Spectral Framework for Graph Neural Operators: Convergence Guarantees and Tradeoffs Holden, Roxanne Ruiz, Luana Machine Learning Signal Processing 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. |
| title | A Spectral Framework for Graph Neural Operators: Convergence Guarantees and Tradeoffs |
| topic | Machine Learning Signal Processing |
| url | https://arxiv.org/abs/2510.20954 |