mlsanityData to 7 Oct 2026

Universal Approximation Theorem for Neural Networks

arXiv 2102.10993 ↗First posted 19 Feb 2021cs.LG cs.AIcited by 7

Not on the map. Why?

Abstract (arXiv)

Is there any theoretical guarantee for the approximation ability of neural networks? The answer to this question is the "Universal Approximation Theorem for Neural Networks". This theorem states that a neural network is dense in a certain function space under an appropriate setting. This paper is a comprehensive explanation of the universal approximation theorem for feedforward neural networks, its approximation rate problem (the relation between the number of intermediate units and the approximation error), and Barron space in Japanese.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 3 of its 27 references that are in the map. First posted on arXiv 19 Feb 2021.

Builds on

3 of 27 references.

References · 3

  1. 2016Error bounds for approximations with deep ReLU networkscited by 567
  2. 2015Neural Network with Unbounded Activation Functions is Universal Approximatorcited by 63
  3. 2019The Barron Space and the Flow-induced Function Spaces for Neural Network Modelscited by 39

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 1; 2024: 3; 2025: 1; 2026: 1.

7 papers.

  1. 2024fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functionscited by 60
  2. 2022A case study of spatiotemporal forecasting techniques for weather forecastingcited by 3
  3. 2025Neuronal Attention Circuit (NAC) for Representation Learningcited by 3
  4. 2023How important are specialized transforms in Neural Operators?cited by 2
  5. 2024Robust Noisy Label Learning via Two-Stream Sample Distillationcited by 1
  6. 2024LSTM Autoencoder-based Deep Neural Networks for Barley Genotype-to-Phenotype Predictioncited by 1
  7. 2026An End-to-End PyTorch Interface for Differentiable PDE Solvers: A RANS Model-Correction Studycited by 0