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Transferability of Graph Neural Networks: an Extended Graphon Approach

arXiv 2109.10096 ↗First posted 21 Sep 2021cs.LG cs.NA math.NAcited by 51

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Abstract (arXiv)

We study spectral graph convolutional neural networks (GCNNs), where filters are defined as continuous functions of the graph shift operator (GSO) through functional calculus. A spectral GCNN is not tailored to one specific graph and can be transferred between different graphs. It is hence important to study the GCNN transferability: the capacity of the network to have approximately the same repercussion on different graphs that represent the same phenomenon. Transferability ensures that GCNNs trained on certain graphs generalize if the graphs in the test set represent the same phenomena as the graphs in the training set. In this paper, we consider a model of transferability based on graphon analysis. Graphons are limit objects of graphs, and, in the graph paradigm, two graphs represent the same phenomenon if both approximate the same graphon. Our main contributions can be summarized as follows: 1) we prove that any fixed GCNN with continuous filters is transferable under graphs that approximate the same graphon, 2) we prove transferability for graphs that approximate unbounded graphon shift operators, which are defined in this paper, and, 3) we obtain non-asymptotic approximation results, proving linear stability of GCNNs. This extends current state-of-the-art results which show asymptotic transferability for polynomial filters under graphs that approximate bounded graphons.

Key facts. Cited by 51 papers in the map (data through 7 Oct 2026). Builds on 18 of its 43 references that are in the map. First posted on arXiv 21 Sep 2021.

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18 of 43 references.

References · 18

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  3. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  4. 2016Geometric deep learning: going beyond Euclidean datacited by 1,042
  5. 2017CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filterscited by 203
  6. 2019Graph Neural Networks with convolutional ARMA filterscited by 185
  7. 2019Stability Properties of Graph Neural Networkscited by 125
  8. 2019Transferability of Spectral Graph Convolutional Neural Networkscited by 90
  9. 2020Graph Neural Networks: Architectures, Stability and Transferabilitycited by 79
  10. 2020Convergence and Stability of Graph Convolutional Networks on Large Random Graphscited by 75
  11. 2019Certifiable Robustness to Graph Perturbationscited by 62
  12. 2020Efficient Robustness Certificates for Discrete Data: Sparsity-Aware Randomized Smoothing for Graphs, Images and Morecited by 56
6 more
  1. 2020Graphon Signal Processingcited by 37
  2. 2021Interpretable Stability Bounds for Spectral Graph Filterscited by 28
  3. 2019On the Transferability of Spectral Graph Filterscited by 27
  4. 2020On the Stability of Graph Convolutional Neural Networks under Edge Rewiringcited by 25
  5. 2020Graphon Filters: Graph Signal Processing in the Limitcited by 16
  6. 2020Graph and graphon neural network stabilitycited by 15

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 5; 2023: 16; 2024: 11; 2025: 6; 2026: 12.

51 papers.

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  1. 2022Generalization Analysis of Message Passing Neural Networks on Large Random Graphscited by 58
  2. 2021Transferability Properties of Graph Neural Networkscited by 42
  3. 2022OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphscited by 38
  4. 2023A graphon-signal analysis of graph neural networkscited by 29
  5. 2023Fine-grained Expressivity of Graph Neural Networkscited by 25
  6. 2023HoloNets: Spectral Convolutions do extend to Directed Graphscited by 20
  7. 2023Limits, approximation and size transferability for GNNs on sparse graphs via graphopscited by 17
  8. 2023Graph Neural Tangent Kernel: Convergence on Large Graphscited by 16
  9. 2024Generalization Bounds for Message Passing Networks on Mixture of Graphonscited by 16
  10. 2024A Manifold Perspective on the Statistical Generalization of Graph Neural Networkscited by 16
  11. 2023Convergence of Message Passing Graph Neural Networks with Generic Aggregation On Large Random Graphscited by 9
  12. 2023Geometric Graph Filters and Neural Networks: Limit Properties and Discriminability Trade-offscited by 9
38 more
  1. 2024Learning on Large Graphs using Intersecting Communitiescited by 8
  2. 2024Generalization of Geometric Graph Neural Networks with Lipschitz Loss Functionscited by 6
  3. 2024Sparse Covariance Neural Networkscited by 6
  4. 2022Space-Time Graph Neural Networks with Stochastic Graph Perturbationscited by 5
  5. 2024Graph neural networks and non-commuting operatorscited by 5
  6. 2023Transferability of coVariance Neural Networks and Application to Interpretable Brain Age Prediction using Anatomical Featurescited by 4
  7. 2024Generalization of Graph Neural Networks is Robust to Model Mismatchcited by 4
  8. 2025Covariance Density Neural Networkscited by 3
  9. 2026Graph Signal Diffusion Models for Wireless Resource Allocationcited by 3
  10. 2022Unveiling the Sampling Density in Non-Uniform Geometric Graphscited by 2
  11. 2022Stable and Transferable Hyper-Graph Neural Networkscited by 2
  12. 2023Limitless stability for Graph Convolutional Networkscited by 2
  13. 2023Manifold Filter-Combine Networkscited by 2
  14. 2023Transferability of Graph Neural Networks using Graphon and Sampling Theoriescited by 2
  15. 2023A Local Graph Limits Perspective on Sampling-Based GNNscited by 2
  16. 2023On the Trade-Off between Stability and Representational Capacity in Graph Neural Networkscited by 2
  17. 2025Efficient Learning on Large Graphs using a Densifying Regularity Lemmacited by 2
  18. 2025The Graphon Limit Hypothesis: Understanding Neural Network Pruning via Infinite Width Analysiscited by 2
  19. 2023ResolvNet: A Graph Convolutional Network with multi-scale Consistencycited by 1
  20. 2024Transferable Graphical MARL for Real-Time Estimation in Dynamic Wireless Networkscited by 1
  21. 2025Towards Coordinate- and Dimension-Agnostic Machine Learning for Partial Differential Equationscited by 1
  22. 2026Manifold limit for the training of shallow graph convolutional neural networkscited by 1
  23. 2026Any-Dimensional Invariant Universalitycited by 1
  24. 2026DiPhon: Diffusion on Graphons for Scalable Graph Generationcited by 1
  25. 2026Any-Dimensional Learning by Samplingcited by 1
  26. 2023Local transfer learning from one data space to anothercited by 0
  27. 2023Spectral Convergence of Complexon Shift Operatorscited by 0
  28. 2024Perfect Recovery for Random Geometric Graph Matching with Shallow Graph Neural Networkscited by 0
  29. 2024Distributed Training of Large Graph Neural Networks with Variable Communication Ratescited by 0
  30. 2024A Review of Graph-Powered Data Quality Applications for IoT Monitoring Sensor Networkscited by 0
  31. 2025Graph Variate Neural Networkscited by 0
  32. 2025On the Convergence and Size Transferability of Continuous-depth Graph Neural Networkscited by 0
  33. 2026Decentralized Learning Strategies for Estimation Error Minimization with Graph Neural Networkscited by 0
  34. 2026Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNscited by 0
  35. 2026Learning to Approximate Uniform Facility Location via Graph Neural Networkscited by 0
  36. 2026Size Transferability of Graph Transformers with Convolutional Positional Encodingscited by 0
  37. 2026When Do Graph Foundation Models Transfer? A Data-Centric Theorycited by 0
  38. 2026Limit Analysis of Graph Neural Networks with Wireless Conflict Graphscited by 0

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