mlsanityData to 14 Oct 2026

A Practitioner's Guide to Kolmogorov-Arnold Networks

arXiv 2510.25781 ↗First posted 28 Oct 2025cs.LG cs.AI cs.NAcited by 18

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Abstract (arXiv)

Kolmogorov-Arnold Networks (KANs), whose design is inspired-rather than dictated-by the Kolmogorov superposition theorem, have emerged as a structured alternative to MLPs. This review provides a systematic and comprehensive overview of the rapidly expanding KAN literature. The review is organized around three core themes: (i) clarifying the relationships between KANs and Kolmogorov superposition theory (KST), MLPs, and classical kernel methods; (ii) analyzing basis functions as a central design axis; and (iii) summarizing recent advances in accuracy, efficiency, regularization, and convergence. Finally, we provide a practical "Choose-Your-KAN" guide and outline open research challenges and future directions. The accompanying GitHub repository serves as a structured reference for ongoing KAN research.

Key facts. Cited by 18 papers in the map (data through 14 Oct 2026). Builds on 34 of its 153 references that are in the map. First posted on arXiv 28 Oct 2025.

Builds on

34 of 153 references.

References · 34

  1. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,621
  2. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,200
  3. 2020Sharpness-Aware Minimization for Efficiently Improving Generalizationcited by 1,417
  4. 2018On the Spectral Bias of Neural Networkscited by 1,341
  5. 2024KAN: Kolmogorov-Arnold Networkscited by 649
  6. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 634
  7. 2019DeepXDE: A deep learning library for solving differential equationscited by 619
  8. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 608
  9. 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 548
  10. 2019Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networkscited by 368
  11. 2018Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problemscited by 147
  12. 2021Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equationscited by 145
22 more
  1. 2021Parallel Physics-Informed Neural Networks via Domain Decompositioncited by 112
  2. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 104
  3. 2024DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problemscited by 84
  4. 2023Tackling the Curse of Dimensionality with Physics-Informed Neural Networkscited by 79
  5. 2024PirateNets: Physics-informed Deep Learning with Residual Adaptive Networkscited by 72
  6. 2024A Survey on Kolmogorov-Arnold Networkcited by 68
  7. 2024Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networkscited by 67
  8. 2024KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physicscited by 59
  9. 2025Optimizing the Optimizer for Physics-Informed Neural Networks and Kolmogorov-Arnold Networkscited by 42
  10. 2024Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networkscited by 38
  11. 2024KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Searchcited by 37
  12. 2022ExSpliNet: An interpretable and expressive spline-based neural networkcited by 33
  13. 2023On the Kolmogorov neural networkscited by 19
  14. 2024FC-KAN: Function Combinations in Kolmogorov-Arnold Networkscited by 19
  15. 2022A physics-informed deep neural network for surrogate modeling in classical elasto-plasticitycited by 15
  16. 2024PowerMLP: An Efficient Version of KANcited by 14
  17. 2024Deep Learning Alternatives of the Kolmogorov Superposition Theoremcited by 12
  18. 2025Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEscited by 11
  19. 2024Multifidelity Kolmogorov-Arnold Networkscited by 9
  20. 2024Learnable Activation Functions in Physics-Informed Neural Networks for Solving Partial Differential Equationscited by 7
  21. 2023Power-Enhanced Residual Network for Function Approximation and Physics-Informed Inverse Problemscited by 5
  22. 2024Stable Weight Updating: A Key to Reliable PDE Solutions Using Deep Learningcited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 17.

18 papers.

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  1. 2026Gated QKAN-FWP: Scalable Quantum-inspired Sequence Learningcited by 4
  2. 2026SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networkscited by 3
  3. 2026Making Gaussian Kolmogorov-Arnold Networks Reliable and Accuratecited by 3
  4. 2026SechKAN: Kolmogorov-Arnold Networks with Hyperbolic Secant Functionscited by 2
  5. 2026Tackling Failure Modes of PINNs and PIKANs Using Conflict-Free Gradientscited by 2
  6. 2025MINPO: Memory-Informed Neural Pseudo-Operator to Resolve Nonlocal Spatiotemporal Dynamicscited by 1
  7. 2026A Dynamic Framework for Grid Adaptation in Kolmogorov-Arnold Networkscited by 1
  8. 2026Empirical Stability Analysis of Kolmogorov-Arnold Networks in Hard-Constrained Recurrent Physics-Informed Discoverycited by 1
  9. 2026Multilevel Training for Kolmogorov Arnold Networkscited by 1
  10. 2026Hardware-Oriented Inference Complexity of Kolmogorov-Arnold Networkscited by 1
  11. 2026Partition-of-Unity Gaussian Kolmogorov-Arnold Networkscited by 1
  12. 2026Necessary and sufficient conditions for universality of Kolmogorov-Arnold networkscited by 0
6 more
  1. 2026Adaptive RBF-KAN: A Comparative Evaluation of Dynamic Shape Parameters in Kolmogorov-Arnold Networkscited by 0
  2. 2026From Handcrafted Features to Functional Edge Learning: Evolution of EEG Seizure Detection Frameworkscited by 0
  3. 2026Kolmogorov--Arnold Networks for Small Language Modelscited by 0
  4. 2026Complementary Matrix-Gated QKAN Fast-Weight Programmers for Quantum Dynamics Forecastingcited by 0
  5. 2026An Embedded RISC-V Evaluation of Kolmogorov--Arnold Networks in Hard-Constrained Recurrent Physics-Informed Modelscited by 0
  6. 2026Low-Rank Kolmogorov-Arnold Generator Flows for Interpretable Operator Learningcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025GS-KAN: Parameter-Efficient Kolmogorov-Arnold Networks via Sprecher-Type Shared Basis Functions
  2. 2025Approximation Rates in Besov Norms and Sample-Complexity of Kolmogorov-Arnold Networks with Residual Connections
  3. 2025Geometric Kolmogorov-Arnold Superposition Theorem
  4. 2025QuantKAN: A Unified Quantization Framework for Kolmogorov Arnold Networks
  5. 2026KANtize: Exploring Low-bit Quantization of Kolmogorov-Arnold Networks for Efficient Inference
  6. 2026FuncCode: Compressing Kolmogorov--Arnold Networks in Function Space with Hardware-Aware Quantization
  7. 2026SparseKAN: Compressing Kolmogorov--Arnold Networks Across Basis Functions, Neurons, and Bits
  8. 2025Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks