mlsanityData to 13 Oct 2026

Weighted Sobolev Approximation Rates for Neural Networks on Unbounded Domains

arXiv 2411.04108 ↗First posted 6 Nov 2024cs.LG math.FA stat.MLcited by 5

Not on the map. Why?

Abstract (arXiv)

In this work, we consider the approximation capabilities of shallow neural networks in weighted Sobolev spaces for functions in the spectral Barron space. The existing literature already covers several cases, in which the spectral Barron space can be approximated well, i.e., without curse of dimensionality, by shallow networks and several different classes of activation function. The limitations of the existing results are mostly on the error measures that were considered, in which the results are restricted to Sobolev spaces over a bounded domain. We will here treat two cases that extend upon the existing results. Namely, we treat the case with bounded domain and Muckenhoupt weights and the case, where the domain is allowed to be unbounded and the weights are required to decay. We first present embedding results for the more general weighted Fourier-Lebesgue spaces in the weighted Sobolev spaces and then we establish asymptotic approximation rates for shallow neural networks that come without curse of dimensionality.

Key facts. Cited by 5 papers in the map (data through 13 Oct 2026). Builds on 17 of its 46 references that are in the map. First posted on arXiv 6 Nov 2024.

Builds on

17 of 46 references.

References · 17

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5 more
  1. 2019Approximation capabilities of neural networks on unbounded domainscited by 7
  2. 2023Weighted variation spaces and approximation by shallow ReLU networkscited by 7
  3. 2023Noncompact uniform universal approximationcited by 7
  4. 2022Lp sampling numbers for the Fourier-analytic Barron spacecited by 6
  5. 2023Space-Time Approximation with Shallow Neural Networks in Fourier Lebesgue spacescited by 5

Built on by

Cited by year (2026 to 13 Oct)

Citing papers per year: 2025: 3; 2026: 2.

5 papers.

  1. 2025Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Datacited by 2
  2. 2025Time-Frequency Analysis for Neural Networkscited by 2
  3. 2025Approximation Capabilities of Feedforward Neural Networks with GELU Activationscited by 2
  4. 2026Any-Dimensional Invariant Universalitycited by 2
  5. 2026Approximation Rates for Metaplectic Neural Networkscited by 0