mlsanityData to 14 Oct 2026

Input Convex Kolmogorov Arnold Networks

arXiv 2505.21208 ↗First posted 27 May 2025stat.ML cs.LG math.OCcited by 5

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Abstract (arXiv)

This article presents an input convex neural network architecture using Kolmogorov-Arnold networks (ICKAN). Two specific networks are presented: the first is based on a low-order, linear-by-part, representation of functions, and a universal approximation theorem is provided. The second is based on cubic splines, for which only numerical results support convergence. We demonstrate on simple tests that these networks perform competitively with classical input convex neural networks (ICNNs). In a second part, we use the networks to solve some optimal transport problems needing a convex approximation of functions and demonstrate their effectiveness. Comparisons with ICNNs show that cubic ICKANs produce results similar to those of classical ICNNs.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 21 of its 36 references that are in the map. First posted on arXiv 27 May 2025.

Builds on

21 of 36 references.

References · 21

  1. 2024KAN: Kolmogorov-Arnold Networkscited by 649
  2. 2016Input Convex Neural Networkscited by 414
  3. 2019Optimal transport mapping via input convex neural networkscited by 206
  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. 2019Wasserstein-2 Generative Networkscited by 97
  8. 2021Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmarkcited by 96
  9. 2018Optimal Control Via Neural Networks: A Convex Approachcited by 85
  10. 2019Theoretical Issues in Deep Networks: Approximation, Optimization and Generalizationcited by 72
  11. 2021Plugin Estimation of Smooth Optimal Transport Mapscited by 68
  12. 2020Learned convex regularizers for inverse problemscited by 55
9 more
  1. 2024BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networkscited by 46
  2. 2019Learning Convex Optimization Control Policiescited by 31
  3. 2019Concentration bounds for linear Monge mapping estimation and optimal transport domain adaptationcited by 17
  4. 2019Max-Affine Regression: Provable, Tractable, and Near-Optimal Statistical Estimationcited by 15
  5. 2025Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)cited by 13
  6. 2020Input Convex Neural Networks for Optimal Voltage Regulationcited by 7
  7. 2022The GroupMax neural network approximation of convex functionscited by 5
  8. 2023Max-affine regression via first-order methodscited by 3
  9. 2024P1-KAN: an effective Kolmogorov-Arnold network with application to hydraulic valley optimizationcited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 5.

5 papers.

  1. 2026Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material modelscited by 6
  2. 2026Hyper Input Convex Neural Networks for Shape Constrained Learning and Optimal Transportcited by 2
  3. 2026SOC-ICNN: From Polyhedral to Conic Geometry for Learning Convex Surrogate Functionscited by 1
  4. 2026Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networkscited by 1
  5. 2026Saddle Networks: Structure-Preserving Architectures for Convex-Concave Functionscited by 0