mlsanityData to 14 Oct 2026

Universal approximation results for neural networks with non-polynomial activation function over non-compact domains

arXiv 2410.14759 ↗First posted 18 Oct 2024stat.ML cs.LG cs.NEcited by 7

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Abstract (arXiv)

This paper extends the universal approximation property of single-hidden-layer feedforward neural networks beyond compact domains, which is of particular interest for the approximation within weighted Ck-spaces and weighted Sobolev spaces over unbounded domains. More precisely, by assuming that the activation function is non-polynomial, we establish universal approximation results within function spaces defined over non-compact subsets of a Euclidean space, including Lp-spaces, weighted Ck-spaces, and weighted Sobolev spaces, where the latter two include the approximation of the (weak) derivatives. Moreover, we provide some dimension-independent rates for approximating a function with sufficiently regular and integrable Fourier transform by neural networks with non-polynomial activation function.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 13 of its 62 references that are in the map. First posted on arXiv 18 Oct 2024.

Builds on

13 of 62 references.

References · 13

  1. 2019Universal Approximation with Deep Narrow Networkscited by 200
  2. 2017Optimal Approximation with Sparsely Connected Deep Neural Networkscited by 91
  3. 2021Sharp Bounds on the Approximation Rates, Metric Entropy, and n-widths of Shallow Neural Networkscited by 86
  4. 2015Neural Network with Unbounded Activation Functions is Universal Approximatorcited by 63
  5. 2021Universal Approximation Theorems for Differentiable Geometric Deep Learningcited by 41
  6. 2023Deep Network Approximation: Beyond ReLU to Diverse Activation Functionscited by 33
  7. 2016Risk Bounds for High-dimensional Ridge Function Combinations Including Neural Networkscited by 26
  8. 2022Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformercited by 22
  9. 2019Differentiable reservoir computingcited by 20
  10. 2023Global universal approximation of functional input maps on weighted spacescited by 19
  11. 2023Rates of Approximation by ReLU Shallow Neural Networkscited by 12
  12. 2019Uniform error estimates for artificial neural network approximations for heat equationscited by 11
1 more
  1. 2023Noncompact uniform universal approximationcited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 4; 2026: 2.

7 papers.

  1. 2024Solving stochastic partial differential equations using neural networks in the Wiener chaos expansioncited by 6
  2. 2026Any-Dimensional Invariant Universalitycited by 3
  3. 2025Distributionally Robust Deep Q-Learningcited by 1
  4. 2025Neural Measures for learning distributions of Random PDEscited by 1
  5. 2025Approximation rates of quantum neural networks for periodic functions via Jackson's inequalitycited by 1
  6. 2025Distributionally robust approximation property of neural networkscited by 0
  7. 2026Neural operators approximate strongly continuous convex monotone semigroupscited by 0