A Short Note on Upper Bounds for Graph Neural Operator Convergence Rate
This work provides incremental insights into the theoretical analysis of graph neural networks, aiding researchers in understanding convergence properties for transferability.
The paper summarizes known upper bounds for the convergence rate of graph neural operators under different continuity assumptions, highlighting tradeoffs and demonstrating empirical tightness on synthetic and real data.
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.