mlsanityData to 14 Oct 2026

A three layer neural network can represent any multivariate function

arXiv 2012.03016 ↗First posted 5 Dec 2020cs.LG math.FA stat.MLcited by 10

Not on the map. Why?

Abstract (arXiv)

In 1987, Hecht-Nielsen showed that any continuous multivariate function can be implemented by a certain type three-layer neural network. This result was very much discussed in neural network literature. In this paper we prove that not only continuous functions but also all discontinuous functions can be implemented by such neural networks.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). First posted on arXiv 5 Dec 2020.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 1; 2022: 1; 2023: 2; 2024: 2; 2025: 2; 2026: 2.

10 papers.

  1. 2021Physics-enhanced deep surrogates for partial differential equationscited by 18
  2. 2022JAX-DIPS: Neural bootstrapping of finite discretization methods and application to elliptic problems with discontinuitiescited by 7
  3. 2023Conformalized Deep Splines for Optimal and Efficient Prediction Setscited by 5
  4. 2024On the Anatomy of Attentioncited by 3
  5. 2025Distance-Aware Error for Spline Networks: A Bottom-Up Approach to Uncertaintycited by 2
  6. 2023Data Topology-Dependent Upper Bounds of Neural Network Widthscited by 1
  7. 2024Generalizable autoregressive modeling of time series through functional narrativescited by 1
  8. 2025Kolmogorov GAM Networks are all you need!cited by 1
  9. 2026SharpNet: Enhancing MLPs to Represent Functions with Controlled Non-differentiabilitycited by 0
  10. 2026Structure-Preserving Reconstruction of Convex Lipschitz Functionals on Hilbert Spaces from Finite Samplescited by 0