mlsanityData to 14 Oct 2026

Transferability Properties of Graph Neural Networks

arXiv 2112.04629 ↗First posted 9 Dec 2021cs.LG eess.SPcited by 43

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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.

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

28 of 54 references.

References · 28

  1. 2017Attention Is All You Needcited by 60,361
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  3. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,089
  4. 2016Geometric deep learning: going beyond Euclidean datacited by 1,048
  5. 2017Graph Signal Processing: Overview, Challenges and Applicationscited by 413
  6. 2019Stability Properties of Graph Neural Networkscited by 127
  7. 2020Graphon Neural Networks and the Transferability of Graph Neural Networkscited by 118
  8. 2018Convolutional Neural Network Architectures for Signals Supported on Graphscited by 95
  9. 2019Transferability of Spectral Graph Convolutional Neural Networkscited by 92
  10. 2020Convergence and Stability of Graph Convolutional Networks on Large Random Graphscited by 76
  11. 2020Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networkscited by 75
  12. 2013Discrete Signal Processing on Graphs: Frequency Analysiscited by 73
16 more
  1. 2019Learning Decentralized Controllers for Robot Swarms with Graph Neural Networkscited by 62
  2. 2021Transferability of Graph Neural Networks: an Extended Graphon Approachcited by 53
  3. 2020Graphon Signal Processingcited by 37
  4. 2019Stability of Graph Scattering Transformscited by 34
  5. 2017Rates of Convergence of Spectral Methods for Graphon Estimationcited by 28
  6. 2019On the Transferability of Spectral Graph Filterscited by 28
  7. 2021Interpretable Stability Bounds for Spectral Graph Filterscited by 28
  8. 2020On the Stability of Graph Convolutional Neural Networks under Edge Rewiringcited by 25
  9. 2017Centrality measures for graphons: Accounting for uncertainty in networkscited by 17
  10. 2020Graphon Filters: Graph Signal Processing in the Limitcited by 16
  11. 2019Invariance-Preserving Localized Activation Functions for Graph Neural Networkscited by 14
  12. 2020Graph Neural Networks for Decentralized Controllerscited by 14
  13. 2018Graphon Control of Large-scale Networks of Linear Systemscited by 11
  14. 2019The Graphon Fourier Transformcited by 10
  15. 2018Graphon games: A statistical framework for network games and interventionscited by 8
  16. 2020The Laplacian Spectrum of Large Graphs Sampled from Graphonscited by 8

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 5; 2023: 9; 2024: 11; 2025: 5; 2026: 13.

43 papers.

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  1. 2024Position: Graph Foundation Models are Already Herecited by 86
  2. 2022Generalization Analysis of Message Passing Neural Networks on Large Random Graphscited by 59
  3. 2023HoloNets: Spectral Convolutions do extend to Directed Graphscited by 20
  4. 2023When to Pre-Train Graph Neural Networks? From Data Generation Perspective!cited by 18
  5. 2023Limits, approximation and size transferability for GNNs on sparse graphs via graphopscited by 18
  6. 2024Generalization Bounds for Message Passing Networks on Mixture of Graphonscited by 17
  7. 2024A Manifold Perspective on the Statistical Generalization of Graph Neural Networkscited by 17
  8. 2023Graph Neural Tangent Kernel: Convergence on Large Graphscited by 16
  9. 2022Tangent Bundle Filters and Neural Networks: from Manifolds to Cellular Sheaves and Backcited by 9
  10. 2023Convergence of Message Passing Graph Neural Networks with Generic Aggregation On Large Random Graphscited by 9
  11. 2023Geometric Graph Filters and Neural Networks: Limit Properties and Discriminability Trade-offscited by 9
  12. 2023GRAPES: Learning to Sample Graphs for Scalable Graph Neural Networkscited by 7
31 more
  1. 2024Generalization of Geometric Graph Neural Networks with Lipschitz Loss Functionscited by 6
  2. 2022Training Graph Neural Networks on Growing Stochastic Graphscited by 5
  3. 2022A Spectral Analysis of Graph Neural Networks on Dense and Sparse Graphscited by 5
  4. 2024Graph neural networks and non-commuting operatorscited by 5
  5. 2024Generalization of Graph Neural Networks is Robust to Model Mismatchcited by 4
  6. 2023Transferability of Graph Neural Networks using Graphon and Sampling Theoriescited by 3
  7. 2026Any-Dimensional Invariant Universalitycited by 3
  8. 2022Unveiling the Sampling Density in Non-Uniform Geometric Graphscited by 2
  9. 2023A Local Graph Limits Perspective on Sampling-Based GNNscited by 2
  10. 2025Learning graphons from data: Random walks, transfer operators, and spectral clusteringcited by 2
  11. 2026Stability of Flow Models for Graph Signalscited by 2
  12. 2024Transferable Graphical MARL for Real-Time Estimation in Dynamic Wireless Networkscited by 1
  13. 2024Transfer Learning Under High-Dimensional Graph Convolutional Regression Model for Node Classificationcited by 1
  14. 2025From Small to Large: Generalization Bounds for Transformers on Variable-Size Inputscited by 1
  15. 2026Size-Transferability of Graph Transformers with Convolutional Positional Encodingscited by 1
  16. 2024Perfect Recovery for Random Geometric Graph Matching with Shallow Graph Neural Networkscited by 0
  17. 2024Sampling Transferable Graph Neural Networks with Limited Graph Informationcited by 0
  18. 2024A Review of Graph-Powered Data Quality Applications for IoT Monitoring Sensor Networkscited by 0
  19. 2025Landmark-Based Node Representations for Shortest Path Distance Approximations in Random Graphscited by 0
  20. 2025Graph Semi-Supervised Learning for Point Classification on Data Manifoldscited by 0
  21. 2025A Spectral Framework for Graph Neural Operators: Convergence Guarantees and Tradeoffscited by 0
  22. 2026Decentralized Learning Strategies for Estimation Error Minimization with Graph Neural Networkscited by 0
  23. 2026Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNscited by 0
  24. 2026Low-Complexity and Consistent Graphon Estimation from Multiple Networkscited by 0
  25. 2026Spectral Graph Sparsification Preserves Representation Geometry in Graph Neural Networkscited by 0
  26. 2026Graph Transfer Learning via Shared Latent Geometry: Theory and Applicationscited by 0
  27. 2026Limit Analysis of Graph Neural Networks with Wireless Conflict Graphscited by 0
  28. 2026Train Small, Deploy Large: Zero-Shot GNN Transfer Through Geometric Renormalizationcited by 0
  29. 2026Attention Graphons: A Graph Limit Perspective on Graph Transformerscited by 0
  30. 2026Fractional Laplace Neural Operators: Exact Architectures, an Expressivity Frontier at Criticality, and Certified Stability for Memory-Driven Network Dynamicscited by 0
  31. 2026Dimension-Free Scaling Laws for Size Generalization: An Exponential Separationcited by 0