mlsanityData to 7 Oct 2026

Transferability of Spectral Graph Convolutional Neural Networks

arXiv 1907.12972 ↗First posted 30 Jul 2019cs.LG stat.MLcited by 90

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Abstract (arXiv)

This paper focuses on spectral graph convolutional neural networks (ConvNets), where filters are defined as elementwise multiplication in the frequency domain of a graph. In machine learning settings where the dataset consists of signals defined on many different graphs, the trained ConvNet should generalize to signals on graphs unseen in the training set. It is thus important to transfer ConvNets between graphs. Transferability, which is a certain type of generalization capability, can be loosely defined as follows: if two graphs describe the same phenomenon, then a single filter or ConvNet should have similar repercussions on both graphs. This paper aims at debunking the common misconception that spectral filters are not transferable. We show that if two graphs discretize the same "continuous" space, then a spectral filter or ConvNet has approximately the same repercussion on both graphs. Our analysis is more permissive than the standard analysis. Transferability is typically described as the robustness of the filter to small graph perturbations and re-indexing of the vertices. Our analysis accounts also for large graph perturbations. We prove transferability between graphs that can have completely different dimensions and topologies, only requiring that both graphs discretize the same underlying space in some generic sense.

Key facts. Cited by 90 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 Jul 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 13; 2022: 23; 2023: 22; 2024: 12; 2025: 8; 2026: 12.

90 papers.

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  1. 2022Not too little, not too much: a theoretical analysis of graph (over)smoothingcited by 106
  2. 2021MagNet: A Neural Network for Directed Graphscited by 104
  3. 2022Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networkscited by 94
  4. 2024GFT: Graph Foundation Model with Transferable Tree Vocabularycited by 82
  5. 2022Theory of Graph Neural Networks: Representation and Learningcited by 60
  6. 2022Generalization Analysis of Message Passing Neural Networks on Large Random Graphscited by 58
  7. 2021Scalable and Adaptive Graph Neural Networks with Self-Label-Enhanced trainingcited by 54
  8. 2021Transferability of Graph Neural Networks: an Extended Graphon Approachcited by 51
  9. 2021Transferability Properties of Graph Neural Networkscited by 42
  10. 2022OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphscited by 38
  11. 2022Generalised Implicit Neural Representationscited by 31
  12. 2024Towards Graph Foundation Models: Learning Generalities Across Graphs via Task-Treescited by 30
38 more
  1. 2023A graphon-signal analysis of graph neural networkscited by 29
  2. 2022MSGNN: A Spectral Graph Neural Network Based on a Novel Magnetic Signed Laplaciancited by 28
  3. 2021On the Universality of Graph Neural Networks on Large Random Graphscited by 26
  4. 2023A Survey on Spectral Graph Neural Networkscited by 26
  5. 2021Learning by Transference: Training Graph Neural Networks on Growing Graphscited by 22
  6. 2025Relational Deep Learning: Challenges, Foundations and Next-Generation Architecturescited by 22
  7. 2023Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Backcited by 21
  8. 2023HoloNets: Spectral Convolutions do extend to Directed Graphscited by 20
  9. 2022Understanding Non-linearity in Graph Neural Networks from the Bayesian-Inference Perspectivecited by 19
  10. 2021Stability of Graph Convolutional Neural Networks to Stochastic Perturbationscited by 18
  11. 2021Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networkscited by 18
  12. 2022Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networkscited by 18
  13. 2022MentorGNN: Deriving Curriculum for Pre-Training GNNscited by 18
  14. 2023When to Pre-Train Graph Neural Networks? From Data Generation Perspective!cited by 17
  15. 2023Limits, approximation and size transferability for GNNs on sparse graphs via graphopscited by 17
  16. 2024Subgraph Pooling: Tackling Negative Transfer on Graphscited by 17
  17. 2021Graph Neural Networks: Methods, Applications, and Opportunitiescited by 16
  18. 2023Graph Neural Tangent Kernel: Convergence on Large Graphscited by 16
  19. 2023Approximately Equivariant Graph Networkscited by 16
  20. 2024Generalization Bounds for Message Passing Networks on Mixture of Graphonscited by 16
  21. 2024A Manifold Perspective on the Statistical Generalization of Graph Neural Networkscited by 16
  22. 2022Convolutional Neural Networks on Manifolds: From Graphs and Backcited by 13
  23. 2023What functions can Graph Neural Networks compute on random graphs? The role of Positional Encodingcited by 11
  24. 2022Graph-Time Convolutional Neural Networks: Architecture and Theoretical Analysiscited by 10
  25. 2021Stability of Neural Networks on Manifolds to Relative Perturbationscited by 9
  26. 2022The Manifold Scattering Transform for High-Dimensional Point Cloud Datacited by 9
  27. 2022Tangent Bundle Filters and Neural Networks: from Manifolds to Cellular Sheaves and Backcited by 9
  28. 2023Convergence of Message Passing Graph Neural Networks with Generic Aggregation On Large Random Graphscited by 9
  29. 2023Geometric Graph Filters and Neural Networks: Limit Properties and Discriminability Trade-offscited by 9
  30. 2021Stability to Deformations of Manifold Filters and Manifold Neural Networkscited by 8
  31. 2022Convergence of Invariant Graph Networkscited by 8
  32. 2021Node-Variant Graph Filters in Graph Neural Networkscited by 7
  33. 2023Zero-One Laws of Graph Neural Networkscited by 7
  34. 2023State of the Art and Potentialities of Graph-level Learningcited by 6
  35. 2024Sparse Covariance Neural Networkscited by 6
  36. 2022Learning Stochastic Graph Neural Networks with Constrained Variancecited by 5
  37. 2022Space-Time Graph Neural Networks with Stochastic Graph Perturbationscited by 5
  38. 2023Stability of Graph Convolutional Neural Networks through the lens of small perturbation analysiscited by 5

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