# Transferability of Graph Neural Networks using Graphon and Sampling Theories

arXiv: https://arxiv.org/abs/2307.13206 · HTML: https://mlsanity.com/paper/2307.13206/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 63 references that are in the map.
- First posted on arXiv 25 Jul 2023.

## Builds on (most cited first, 27 of 27)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [A Survey of Graph Neural Networks for Recommender Systems: Challenges, Methods, and Directions](https://mlsanity.com/paper/2109.12843/) (2021)
- [Graphon Neural Networks and the Transferability of Graph Neural Networks](https://mlsanity.com/paper/2006.03548/) (2020)
- [Transferability of Spectral Graph Convolutional Neural Networks](https://mlsanity.com/paper/1907.12972/) (2019)
- [Convergence and Stability of Graph Convolutional Networks on Large Random Graphs](https://mlsanity.com/paper/2006.01868/) (2020)
- [Transferability of Graph Neural Networks: an Extended Graphon Approach](https://mlsanity.com/paper/2109.10096/) (2021)
- [Content-Based Citation Recommendation](https://mlsanity.com/paper/1802.08301/) (2018)
- [Transferability Properties of Graph Neural Networks](https://mlsanity.com/paper/2112.04629/) (2021)
- [Stochastic blockmodel approximation of a graphon: Theory and consistent estimation](https://mlsanity.com/paper/1311.1731/) (2013)
- [Exponential Convergence of the Deep Neural Network Approximation for Analytic Functions](https://mlsanity.com/paper/1807.00297/) (2018)
- [Graphon Signal Processing](https://mlsanity.com/paper/2003.05030/) (2020)
- [The game theoretic p-Laplacian and semi-supervised learning with few labels](https://mlsanity.com/paper/1711.10144/) (2017)
- [Learning by Transference: Training Graph Neural Networks on Growing Graphs](https://mlsanity.com/paper/2106.03693/) (2021)
- [Graphon Filters: Graph Signal Processing in the Limit](https://mlsanity.com/paper/2003.02099/) (2020)
- [Graph and graphon neural network stability](https://mlsanity.com/paper/2010.12529/) (2020)
- [Learning Sparse Graphon Mean Field Games](https://mlsanity.com/paper/2209.03880/) (2022)
- [Convolutional Neural Networks on Manifolds: From Graphs and Back](https://mlsanity.com/paper/2210.00376/) (2022)
- [Band-limited Training and Inference for Convolutional Neural Networks](https://mlsanity.com/paper/1911.09287/) (2019)
- [Graphon Pooling in Graph Neural Networks](https://mlsanity.com/paper/2003.01795/) (2020)
- [Structured Citation Trend Prediction Using Graph Neural Networks](https://mlsanity.com/paper/2104.02562/) (2021)
- [Subsampling Sparse Graphons Under Minimal Assumptions](https://mlsanity.com/paper/1907.12528/) (2019)
- [Training Graph Neural Networks by Graphon Estimation](https://mlsanity.com/paper/2109.01918/) (2021)
- [Theoretical guarantees for the advantage of GNNs over NNs in generalizing bandlimited functions on Euclidean cubes](https://mlsanity.com/paper/2206.05904/) (2022)
- [Stochastic Block Smooth Graphon Model](https://mlsanity.com/paper/2203.13304/) (2022)

## Built on by (most cited first, 3 of 3)

- [Learning graphons from data: Random walks, transfer operators, and spectral clustering](https://mlsanity.com/paper/2507.18147/) (2025)
- [The Graphon Limit Hypothesis: Understanding Neural Network Pruning via Infinite Width Analysis](https://mlsanity.com/paper/2510.17515/) (2025)
- [Algorithmic Foundations of Deep Learning: Complexity-Theoretic Rates and a Characterization of Universal Approximation](https://mlsanity.com/paper/2606.26705/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) have become powerful tools for processing graph-based information in various domains. A desirable property of GNNs is transferability, where a trained network can swap in information from a different graph without retraining and retain its accuracy. A recent method of capturing transferability of GNNs is through the use of graphons, which are symmetric, measurable functions representing the limit of large dense graphs. In this work, we contribute to the application of graphons to GNNs by presenting an explicit two-layer graphon neural network (WNN) architecture. We prove its ability to approximate bandlimited graphon signals within a specified error tolerance using a minimal number of network weights. We then leverage this result, to establish the transferability of an explicit two-layer GNN over all sufficiently large graphs in a convergent sequence. Our work addresses transferability between both deterministic weighted graphs and simple random graphs and overcomes issues related to the curse of dimensionality that arise in other GNN results. The proposed WNN and GNN architectures offer practical solutions for handling graph data of varying sizes while maintaining performance guarantees without extensive retraining.