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:2510.20954v3 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2510.20954 arXiv-issued DOI via DataCite |
From: Roxanne Holden [view email]
[v1]
Thu, 23 Oct 2025 19:28:56 UTC (832 KB)
[v2]
Mon, 23 Feb 2026 23:49:09 UTC (895 KB)
[v3]
Sun, 24 May 2026 16:00:37 UTC (895 KB)
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