mlsanityData to 14 Oct 2026

P1-KAN: an effective Kolmogorov-Arnold network with application to hydraulic valley optimization

arXiv 2410.03801 ↗First posted 4 Oct 2024cs.LG cs.NE stat.MLcited by 3

Not on the map. Why?

Abstract (arXiv)

A new Kolmogorov-Arnold network (KAN) is proposed to approximate potentially irregular functions in high dimensions. We provide error bounds for this approximation, assuming that the Kolmogorov-Arnold expansion functions are sufficiently smooth. When the function is only continuous, we also provide universal approximation theorems. We show that it outperforms multilayer perceptrons in terms of accuracy and convergence speed. We also compare it with several proposed KAN networks: it outperforms all networks for irregular functions and achieves similar accuracy to the original spline-based KAN network for smooth functions. Finally, we compare some of the KAN networks in optimizing a French hydraulic valley.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 23 of its 41 references that are in the map. First posted on arXiv 4 Oct 2024.

Builds on

23 of 41 references.

References · 23

  1. 2016Gaussian Error Linear Units (GELUs)cited by 3,502
  2. 2024KAN: Kolmogorov-Arnold Networkscited by 649
  3. 2024U-KAN Makes Strong Backbone for Medical Image Segmentation and Generationcited by 179
  4. 2024Kolmogorov-Arnold Networks are Radial Basis Function Networkscited by 128
  5. 2024Wav-KAN: Wavelet Kolmogorov-Arnold Networkscited by 122
  6. 2024Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximationcited by 118
  7. 2024Kolmogorov-Arnold Networks (KANs) for Time Series Analysiscited by 98
  8. 2024DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problemscited by 84
  9. 2024Convolutional Kolmogorov-Arnold Networkscited by 77
  10. 2024KAN or MLP: A Fairer Comparisoncited by 73
  11. 2019Theoretical Issues in Deep Networks: Approximation, Optimization and Generalizationcited by 72
  12. 2024TKAN: Temporal Kolmogorov-Arnold Networkscited by 71
11 more
  1. 2024Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretabilitycited by 70
  2. 2024Kolmogorov-Arnold Transformercited by 56
  3. 2024BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networkscited by 46
  4. 2024Demonstrating the Efficacy of Kolmogorov-Arnold Networks in Vision Taskscited by 40
  5. 2024ReLU-KAN: New Kolmogorov-Arnold Networks that Only Need Matrix Addition, Dot Multiplication, and ReLUcited by 33
  6. 2021Neural networks-based algorithms for stochastic control and PDEs in financecited by 26
  7. 2024Exploring the Limitations of Kolmogorov-Arnold Networks in Classification: Insights to Software Training and Hardware Implementationcited by 22
  8. 2024CoxKAN: Kolmogorov-Arnold Networks for Interpretable, High-Performance Survival Analysiscited by 22
  9. 2024Reduced Effectiveness of Kolmogorov-Arnold Networks on Functions with Noisecited by 17
  10. 2024Higher-order-ReLU-KANs (HRKANs) for solving physics-informed neural networks (PINNs) more accurately, robustly and fastercited by 13
  11. 2021Reservoir optimization and Machine Learning methodscited by 4

Built on by

Cited by year (2026 to 14 Oct)

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

3 papers.

  1. 2025Input Convex Kolmogorov Arnold Networkscited by 5
  2. 2026Learning operators on labelled conditional distributions with applications to mean field control of non exchangeable systemscited by 3
  3. 2026Hyper Input Convex Neural Networks for Shape Constrained Learning and Optimal Transportcited by 2