mlsanityData to 7 Oct 2026

Barron Space for Graph Convolution Neural Networks

arXiv 2311.02838 ↗First posted 6 Nov 2023stat.ML cs.LG eess.SPcited by 1

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Abstract (arXiv)

Graph convolutional neural network (GCNN) operates on graph domain and it has achieved a superior performance to accomplish a wide range of tasks. In this paper, we introduce a Barron space of functions on a compact domain of graph signals. We prove that the proposed Barron space is a reproducing kernel Banach space, it can be decomposed into the union of a family of reproducing kernel Hilbert spaces with neuron kernels, and it could be dense in the space of continuous functions on the domain. Approximation property is one of the main principles to design neural networks. In this paper, we show that outputs of GCNNs are contained in the Barron space and functions in the Barron space can be well approximated by outputs of some GCNNs in the integrated square and uniform measurements. We also estimate the Rademacher complexity of functions with bounded Barron norm and conclude that functions in the Barron space could be learnt from their random samples efficiently.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 31 of its 71 references that are in the map. First posted on arXiv 6 Nov 2023.

Builds on

31 of 71 references.

References · 31

  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. 2018Graph Neural Networks: A Review of Methods and Applicationscited by 1,571
  5. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,097
  6. 2016Geometric deep learning: going beyond Euclidean datacited by 1,042
  7. 2017Graph Signal Processing: Overview, Challenges and Applicationscited by 409
  8. 2020A Survey of Convolutional Neural Networks: Analysis, Applications, and Prospectscited by 396
  9. 2015Recent Advances in Convolutional Neural Networkscited by 360
  10. 2014Breaking the Curse of Dimensionality with Convex Neural Networkscited by 329
  11. 2016Learning Convolutional Neural Networks for Graphscited by 314
  12. 2014Graph-based Anomaly Detection and Description: A Surveycited by 182
19 more
  1. 2019Universal Invariant and Equivariant Graph Neural Networkscited by 182
  2. 2018Adaptive Graph Convolutional Neural Networkscited by 155
  3. 2018Rademacher Complexity for Adversarially Robust Generalizationcited by 132
  4. 2021Optimal Approximation Rate of ReLU Networks in terms of Width and Depthcited by 95
  5. 2020Graph signal processing for machine learning: A review and new perspectivescited by 73
  6. 2013Discrete Signal Processing on Graphs: Frequency Analysiscited by 72
  7. 2020Representation formulas and pointwise properties for Barron functionscited by 62
  8. 2022Graph Filters for Signal Processing and Machine Learning on Graphscited by 53
  9. 2021Understanding neural networks with reproducing kernel Banach spacescited by 50
  10. 2021Characterization of the Variation Spaces Corresponding to Shallow Neural Networkscited by 48
  11. 2021Reproducing Kernel Hilbert Space, Mercer's Theorem, Eigenfunctions, Nystr"om Method, and Use of Kernels in Machine Learning: Tutorial and Surveycited by 36
  12. 2019On Reproducing Kernel Banach Spaces: Generic Definitions and Unified Framework of Constructionscited by 29
  13. 2016Stationary signal processing on graphscited by 28
  14. 2021On the Universality of Graph Neural Networks on Large Random Graphscited by 26
  15. 2023Nonparametric regression using over-parameterized shallow ReLU neural networkscited by 24
  16. 2023Optimal rates of approximation by shallow ReLUk neural networks and applications to nonparametric regressioncited by 15
  17. 2020Graph Signal Processing and Deep Learning: Convolution, Pooling, and Topologycited by 11
  18. 2022Graph Fourier transform based on singular value decomposition of directed Laplaciancited by 4
  19. 2020Polynomial graph filter of multiple shifts and distributed implementation of inverse filteringcited by 3

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