mlsanityData to 14 Oct 2026

On the Universal Approximation Property of Deep Fully Convolutional Neural Networks

arXiv 2211.14047 ↗First posted 25 Nov 2022cs.LG cs.CVcited by 7

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Abstract (arXiv)

We study the approximation of shift-invariant or equivariant functions by deep fully convolutional networks from the dynamical systems perspective. We prove that deep residual fully convolutional networks and their continuous-layer counterpart can achieve universal approximation of these symmetric functions at constant channel width. Moreover, we show that the same can be achieved by non-residual variants with at least 2 channels in each layer and convolutional kernel size of at least 2. In addition, we show that these requirements are necessary, in the sense that networks with fewer channels or smaller kernels fail to be universal approximators.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 26 of its 37 references that are in the map. First posted on arXiv 25 Nov 2022.

Builds on

26 of 37 references.

References · 26

  1. 2014Fully Convolutional Networks for Semantic Segmentationcited by 4,859
  2. 2018Neural Ordinary Differential Equationscited by 3,779
  3. 2015SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentationcited by 1,487
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  11. 2018Universality of Deep Convolutional Neural Networkscited by 176
  12. 2018Optimal approximation of continuous functions by very deep ReLU networkscited by 166
14 more
  1. 2020Deep Network Approximation for Smooth Functionscited by 164
  2. 2017Equivariance Through Parameter-Sharingcited by 141
  3. 2018Universal approximations of invariant maps by neural networkscited by 127
  4. 2019Deep Network Approximation Characterized by Number of Neuronscited by 122
  5. 2017Maximum Principle Based Algorithms for Deep Learningcited by 78
  6. 2019Deep Learning via Dynamical Systems: An Approximation Perspectivecited by 78
  7. 2019Approximation and Non-parametric Estimation of ResNet-type Convolutional Neural Networkscited by 40
  8. 2018Equivalence of approximation by convolutional neural networks and fully-connected networkscited by 38
  9. 2021Approximation and Learning with Deep Convolutional Models: a Kernel Perspectivecited by 31
  10. 2021Locality defeats the curse of dimensionality in convolutional teacher-student scenarioscited by 26
  11. 2021Eigenspace Restructuring: a Principle of Space and Frequency in Neural Networkscited by 17
  12. 2020Approximation in shift-invariant spaces with deep ReLU neural networkscited by 12
  13. 2021Approximation Theory of Convolutional Architectures for Time Series Modellingcited by 10
  14. 2022Deep Neural Network Approximation of Invariant Functions through Dynamical Systemscited by 9

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 1; 2025: 1; 2026: 2.

7 papers.

  1. 2023A Brief Survey on the Approximation Theory for Sequence Modellingcited by 15
  2. 2023Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrologycited by 11
  3. 2023On Enhancing Expressive Power via Compositions of Single Fixed-Size ReLU Networkcited by 6
  4. 2025A unified framework for establishing the universal approximation of transformer-type architecturescited by 2
  5. 2024Dynamic Universal Approximation Theory: The Basic Theory for Deep Learning-Based Computer Vision Modelscited by 0
  6. 2026Sharp Approximation Rates for Neural Networks with Affine Latent Parameterizationscited by 0
  7. 2026Rank and computation of the pathlifting Jacobian of a DAG ReLU networkcited by 0