A Short Note on Upper Bounds for Graph Neural Operator Convergence Rate
arXiv:2510.20954v1 Announce Type: new
Abstract: Graphons, as limits of graph sequences, provide a framework for analyzing the asymptotic behavior of graph neural operators. Spectral convergence of sampled graphs to graphons yields operator-level convergence rates, enabling transferability analyses of GNNs. This note summarizes known bounds under no assumptions, global Lipschitz continuity, and piecewise-Lipschitz continuity, highlighting tradeoffs between assumptions and rates, and illustrating their empirical tightness on synthetic and real data.
Abstract: Graphons, as limits of graph sequences, provide a framework for analyzing the asymptotic behavior of graph neural operators. Spectral convergence of sampled graphs to graphons yields operator-level convergence rates, enabling transferability analyses of GNNs. This note summarizes known bounds under no assumptions, global Lipschitz continuity, and piecewise-Lipschitz continuity, highlighting tradeoffs between assumptions and rates, and illustrating their empirical tightness on synthetic and real data.
Roxanne Holden, Luana Ruiz
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