# A Spectral Framework for Graph Neural Operators: Convergence Guarantees and Tradeoffs

arXiv: https://arxiv.org/abs/2510.20954 · HTML: https://mlsanity.com/paper/2510.20954/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 20 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Builds on (most cited first, 11 of 11)

- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [A Survey of Graph Neural Networks for Social Recommender Systems](https://mlsanity.com/paper/2212.04481/) (2022)
- [Transferability Properties of Graph Neural Networks](https://mlsanity.com/paper/2112.04629/) (2021)
- [A Consistent Histogram Estimator for Exchangeable Graph Models](https://mlsanity.com/paper/1402.1888/) (2014)
- [Graphon Signal Processing](https://mlsanity.com/paper/2003.05030/) (2020)
- [A graphon-signal analysis of graph neural networks](https://mlsanity.com/paper/2305.15987/) (2023)
- [Rates of Convergence of Spectral Methods for Graphon Estimation](https://mlsanity.com/paper/1709.03183/) (2017)
- [Centrality measures for graphons: Accounting for uncertainty in networks](https://mlsanity.com/paper/1707.09350/) (2017)
- [The Laplacian Spectrum of Large Graphs Sampled from Graphons](https://mlsanity.com/paper/2004.09177/) (2020)
- [Recent Developments in GNNs for Drug Discovery](https://mlsanity.com/paper/2506.01302/) (2025)

## Abstract (arXiv)

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.