# Transferability Properties of Graph Neural Networks

arXiv: https://arxiv.org/abs/2112.04629 · HTML: https://mlsanity.com/paper/2112.04629/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 54 references that are in the map.
- First posted on arXiv 9 Dec 2021.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [Graphon Neural Networks and the Transferability of Graph Neural Networks](https://mlsanity.com/paper/2006.03548/) (2020)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [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)
- [Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks](https://mlsanity.com/paper/2003.03777/) (2020)
- [Discrete Signal Processing on Graphs: Frequency Analysis](https://mlsanity.com/paper/1307.0468/) (2013)
- [Learning Decentralized Controllers for Robot Swarms with Graph Neural Networks](https://mlsanity.com/paper/1903.10527/) (2019)
- [Transferability of Graph Neural Networks: an Extended Graphon Approach](https://mlsanity.com/paper/2109.10096/) (2021)
- [Graphon Signal Processing](https://mlsanity.com/paper/2003.05030/) (2020)
- [Stability of Graph Scattering Transforms](https://mlsanity.com/paper/1906.04784/) (2019)
- [Rates of Convergence of Spectral Methods for Graphon Estimation](https://mlsanity.com/paper/1709.03183/) (2017)
- [On the Transferability of Spectral Graph Filters](https://mlsanity.com/paper/1901.10524/) (2019)
- [Interpretable Stability Bounds for Spectral Graph Filters](https://mlsanity.com/paper/2102.09587/) (2021)
- [On the Stability of Graph Convolutional Neural Networks under Edge Rewiring](https://mlsanity.com/paper/2010.13747/) (2020)
- [Centrality measures for graphons: Accounting for uncertainty in networks](https://mlsanity.com/paper/1707.09350/) (2017)
- [Graphon Filters: Graph Signal Processing in the Limit](https://mlsanity.com/paper/2003.02099/) (2020)
- [Invariance-Preserving Localized Activation Functions for Graph Neural Networks](https://mlsanity.com/paper/1903.12575/) (2019)
- [Graph Neural Networks for Decentralized Controllers](https://mlsanity.com/paper/2003.10280/) (2020)
- [Graphon Control of Large-scale Networks of Linear Systems](https://mlsanity.com/paper/1807.03412/) (2018)
- [The Graphon Fourier Transform](https://mlsanity.com/paper/1910.10195/) (2019)
- [Graphon games: A statistical framework for network games and interventions](https://mlsanity.com/paper/1802.00080/) (2018)
- [The Laplacian Spectrum of Large Graphs Sampled from Graphons](https://mlsanity.com/paper/2004.09177/) (2020)

## Built on by (most cited first, 30 of 43)

- [Position: Graph Foundation Models are Already Here](https://mlsanity.com/paper/2402.02216/) (2024)
- [Generalization Analysis of Message Passing Neural Networks on Large Random Graphs](https://mlsanity.com/paper/2202.00645/) (2022)
- [HoloNets: Spectral Convolutions do extend to Directed Graphs](https://mlsanity.com/paper/2310.02232/) (2023)
- [When to Pre-Train Graph Neural Networks? From Data Generation Perspective!](https://mlsanity.com/paper/2303.16458/) (2023)
- [Limits, approximation and size transferability for GNNs on sparse graphs via graphops](https://mlsanity.com/paper/2306.04495/) (2023)
- [Generalization Bounds for Message Passing Networks on Mixture of Graphons](https://mlsanity.com/paper/2404.03473/) (2024)
- [A Manifold Perspective on the Statistical Generalization of Graph Neural Networks](https://mlsanity.com/paper/2406.05225/) (2024)
- [Graph Neural Tangent Kernel: Convergence on Large Graphs](https://mlsanity.com/paper/2301.10808/) (2023)
- [Tangent Bundle Filters and Neural Networks: from Manifolds to Cellular Sheaves and Back](https://mlsanity.com/paper/2210.15058/) (2022)
- [Convergence of Message Passing Graph Neural Networks with Generic Aggregation On Large Random Graphs](https://mlsanity.com/paper/2304.11140/) (2023)
- [Geometric Graph Filters and Neural Networks: Limit Properties and Discriminability Trade-offs](https://mlsanity.com/paper/2305.18467/) (2023)
- [GRAPES: Learning to Sample Graphs for Scalable Graph Neural Networks](https://mlsanity.com/paper/2310.03399/) (2023)
- [Generalization of Geometric Graph Neural Networks with Lipschitz Loss Functions](https://mlsanity.com/paper/2409.05191/) (2024)
- [Training Graph Neural Networks on Growing Stochastic Graphs](https://mlsanity.com/paper/2210.15567/) (2022)
- [A Spectral Analysis of Graph Neural Networks on Dense and Sparse Graphs](https://mlsanity.com/paper/2211.03231/) (2022)
- [Graph neural networks and non-commuting operators](https://mlsanity.com/paper/2411.04265/) (2024)
- [Generalization of Graph Neural Networks is Robust to Model Mismatch](https://mlsanity.com/paper/2408.13878/) (2024)
- [Transferability of Graph Neural Networks using Graphon and Sampling Theories](https://mlsanity.com/paper/2307.13206/) (2023)
- [Any-Dimensional Invariant Universality](https://mlsanity.com/paper/2605.23156/) (2026)
- [Unveiling the Sampling Density in Non-Uniform Geometric Graphs](https://mlsanity.com/paper/2210.08219/) (2022)
- [A Local Graph Limits Perspective on Sampling-Based GNNs](https://mlsanity.com/paper/2310.10953/) (2023)
- [Learning graphons from data: Random walks, transfer operators, and spectral clustering](https://mlsanity.com/paper/2507.18147/) (2025)
- [Stability of Flow Models for Graph Signals](https://mlsanity.com/paper/2607.07510/) (2026)
- [Transferable Graphical MARL for Real-Time Estimation in Dynamic Wireless Networks](https://mlsanity.com/paper/2404.03227/) (2024)
- [Transfer Learning Under High-Dimensional Graph Convolutional Regression Model for Node Classification](https://mlsanity.com/paper/2405.16672/) (2024)
- [From Small to Large: Generalization Bounds for Transformers on Variable-Size Inputs](https://mlsanity.com/paper/2512.12805/) (2025)
- [Size-Transferability of Graph Transformers with Convolutional Positional Encodings](https://mlsanity.com/paper/2602.15239/) (2026)
- [Perfect Recovery for Random Geometric Graph Matching with Shallow Graph Neural Networks](https://mlsanity.com/paper/2402.07340/) (2024)
- [Sampling Transferable Graph Neural Networks with Limited Graph Information](https://mlsanity.com/paper/2410.16593/) (2024)
- [A Review of Graph-Powered Data Quality Applications for IoT Monitoring Sensor Networks](https://mlsanity.com/paper/2410.21006/) (2024)

## Abstract (arXiv)

Graph neural networks (GNNs) are composed of layers consisting of graph convolutions and pointwise nonlinearities. Due to their invariance and stability properties, GNNs are provably successful at learning representations from data supported on moderate-scale graphs. However, they are difficult to learn on large-scale graphs. In this paper, we study the problem of training GNNs on graphs of moderate size and transferring them to large-scale graphs. We use graph limits called graphons to define limit objects for graph filters and GNNs -- graphon filters and graphon neural networks (WNNs) -- which we interpret as generative models for graph filters and GNNs. We then show that graphon filters and WNNs can be approximated by graph filters and GNNs sampled from them on weighted and stochastic graphs. Because the error of these approximations can be upper bounded, by a triangle inequality argument we can further bound the error of transferring a graph filter or a GNN across graphs. Our results show that (i) the transference error decreases with the graph size, and (ii) that graph filters have a transferability-discriminability tradeoff that in GNNs is alleviated by the scattering behavior of the nonlinearity. These findings are demonstrated empirically in a movie recommendation problem and in a decentralized control task.