mlsanityData to 14 Oct 2026

EML Trees Are Universal Approximators

arXiv 2606.23179 ↗First posted 22 Jun 2026cs.LG cs.NA cs.NEcited by 1

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Abstract (arXiv)

The recently introduced EML (Exp-Minus-Log) function acts as continuous analogue of NAND gates, providing a compositional building block capable of representing elementary functions. In this work, we study the expressive power of tree-structured compositions of EML functions. We show that such trees enjoy a universal approximation property for functions in Wk, ∞ for k ∈ mathbb N, drawing on classical neural network approximation arguments while exploiting the ability to explicitly construct EML trees that mimic polynomial representations. We further propose a learning algorithm for EML-type trees equipped with fitting parameters, and demonstrate its feasibility in practical optimization problems. Our results establish EML trees as a theoretically grounded framework for function approximation.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 22 of its 34 references that are in the map. First posted on arXiv 22 Jun 2026.

Builds on

22 of 34 references.

References · 22

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  3. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
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10 more
  1. 2019Error bounds for approximations with deep ReLU neural networks in Ws,p normscited by 95
  2. 2021On the approximation of functions by tanh neural networkscited by 81
  3. 2022Generic bounds on the approximation error for physics-informed (and) operator learningcited by 65
  4. 2021Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEscited by 57
  5. 2024On the expressiveness and spectral bias of KANscited by 37
  6. 2025Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networkscited by 20
  7. 2023Neural Oscillators are Universalcited by 16
  8. 2025Common Task Framework For a Critical Evaluation of Scientific Machine Learning Algorithmscited by 13
  9. 2025The Seismic Wavefield Common Task Frameworkcited by 6
  10. 2026All elementary functions from a single binary operatorcited by 5

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Diversity of EML-type operatorscited by 0