mlsanityData to 14 Oct 2026

C1-approximation with rational functions and rational neural networks

arXiv 2508.19672 ↗First posted 27 Aug 2025cs.LG cs.IT cs.NAcited by 2

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Abstract (arXiv)

We show that suitably regular functions can be approximated in the C1-norm both with rational functions and rational neural networks, including approximation rates with respect to width and depth of the network, and degree of the rational functions. As consequence of our results, we further obtain C1-approximation results for rational neural networks with the EQL^div and ParFam architecture, both of which are important in particular in the context of symbolic regression for physical law learning.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 12 of its 27 references that are in the map. First posted on arXiv 27 Aug 2025.

Builds on

12 of 27 references.

References · 12

  1. 2018Learning Equations for Extrapolation and Controlcited by 156
  2. 2016Extrapolation and learning equationscited by 110
  3. 2019Error bounds for approximations with deep ReLU neural networks in Ws,p normscited by 95
  4. 2019Deep Neural Network Approximation Theorycited by 93
  5. 2020Rational neural networkscited by 75
  6. 2019Approximation spaces of deep neural networkscited by 51
  7. 2017Neural networks and rational functionscited by 40
  8. 2022Simultaneous approximation of a smooth function and its derivatives by deep neural networks with piecewise-polynomial activationscited by 29
  9. 2020Semiglobal optimal feedback stabilization of autonomous systems via deep neural network approximationcited by 10
  10. 2022A descent algorithm for the optimal control of ReLU neural network informed PDEs based on approximate directional derivativescited by 5
  11. 2024On uniqueness in structured model learningcited by 4
  12. 2022First-order conditions for the optimal control of learning-informed nonsmooth PDEscited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Symbolic recovery of PDEs from measurement datacited by 0
  2. 2026All you need is SAMPATcited by 0