# A Survey on Kolmogorov-Arnold Network

arXiv: https://arxiv.org/abs/2411.06078 · HTML: https://mlsanity.com/paper/2411.06078/

## Key facts

- Cited by 68 papers in the map (data through 14 Oct 2026).
- Builds on 79 of its 135 references that are in the map.
- First posted on arXiv 9 Nov 2024.

## Builds on (most cited first, 30 of 79)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation](https://mlsanity.com/paper/1609.08144/) (2016)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Efficient Processing of Deep Neural Networks: A Tutorial and Survey](https://mlsanity.com/paper/1703.09039/) (2017)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [A Simple Way to Initialize Recurrent Networks of Rectified Linear Units](https://mlsanity.com/paper/1504.00941/) (2015)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [Wav-KAN: Wavelet Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.12832/) (2024)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks](https://mlsanity.com/paper/2406.02917/) (2024)
- [Kolmogorov-Arnold Networks (KANs) for Time Series Analysis](https://mlsanity.com/paper/2405.08790/) (2024)
- [The Kolmogorov-Arnold representation theorem revisited](https://mlsanity.com/paper/2007.15884/) (2020)
- [Convolutional Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.13155/) (2024)
- [TKAN: Temporal Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.07344/) (2024)
- [Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretability](https://mlsanity.com/paper/2406.02496/) (2024)
- [fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions](https://mlsanity.com/paper/2406.07456/) (2024)
- [KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physics](https://mlsanity.com/paper/2407.04192/) (2024)
- [GKAN: Graph Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.06470/) (2024)
- [A Temporal Kolmogorov-Arnold Transformer for Time Series Forecasting](https://mlsanity.com/paper/2406.02486/) (2024)
- [Error bounds for deep ReLU networks using the Kolmogorov--Arnold superposition theorem](https://mlsanity.com/paper/1906.11945/) (2019)
- [KAGNNs: Kolmogorov-Arnold Networks meet Graph Learning](https://mlsanity.com/paper/2406.18380/) (2024)
- [Kolmogorov-Arnold Network for Satellite Image Classification in Remote Sensing](https://mlsanity.com/paper/2406.00600/) (2024)
- [BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.11173/) (2024)

## Built on by (most cited first, 30 of 68)

- [A Practitioner's Guide to Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2510.25781/) (2025)
- [KANEL'E: Kolmogorov-Arnold Networks for Efficient LUT-based Evaluation](https://mlsanity.com/paper/2512.12850/) (2025)
- [Kolmogorov Arnold Neural Interpolator for Downscaling and Correcting Meteorological Fields from In-Situ Observations](https://mlsanity.com/paper/2501.14404/) (2025)
- [Medical Image Classification with KAN-Integrated Transformers and Dilated Neighborhood Attention](https://mlsanity.com/paper/2502.13693/) (2025)
- [asKAN: Active Subspace embedded Kolmogorov-Arnold Network](https://mlsanity.com/paper/2504.04669/) (2025)
- [Physics-informed time series analysis with Kolmogorov-Arnold Networks under Ehrenfest constraints](https://mlsanity.com/paper/2509.18483/) (2025)
- [Leveraging KANs for Expedient Training of Multichannel MLPs via Preconditioning and Geometric Refinement](https://mlsanity.com/paper/2505.18131/) (2025)
- [Free-RBF-KAN: Kolmogorov-Arnold Networks with Adaptive Radial Basis Functions for Efficient Function Learning](https://mlsanity.com/paper/2601.07760/) (2026)
- [Gated QKAN-FWP: Scalable Quantum-inspired Sequence Learning](https://mlsanity.com/paper/2605.06734/) (2026)
- [KANs for Computer Vision: An Experimental Study](https://mlsanity.com/paper/2411.18224/) (2024)
- [AF-KAN: Activation Function-Based Kolmogorov-Arnold Networks for Efficient Representation Learning](https://mlsanity.com/paper/2503.06112/) (2025)
- [A Unified Benchmark of Federated Learning with Kolmogorov-Arnold Networks for Medical Imaging](https://mlsanity.com/paper/2504.19639/) (2025)
- [Interpretable Clinical Classification with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2509.16750/) (2025)
- [SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networks](https://mlsanity.com/paper/2603.18548/) (2026)
- [Geometric Kolmogorov-Arnold Superposition Theorem](https://mlsanity.com/paper/2502.16664/) (2025)
- [X-KAN: Optimizing Local Kolmogorov-Arnold Networks via Evolutionary Rule-Based Machine Learning](https://mlsanity.com/paper/2505.14273/) (2025)
- [QuadKAN: KAN-Enhanced Quadruped Motion Control via End-to-End Reinforcement Learning](https://mlsanity.com/paper/2508.19153/) (2025)
- [SechKAN: Kolmogorov-Arnold Networks with Hyperbolic Secant Functions](https://mlsanity.com/paper/2607.18290/) (2026)
- [Kolmogorov-Arnold Network for Remote Sensing Image Semantic Segmentation](https://mlsanity.com/paper/2501.07390/) (2025)
- [Efficiency Bottlenecks of Convolutional Kolmogorov-Arnold Networks: A Comprehensive Scrutiny with ImageNet, AlexNet, LeNet and Tabular Classification](https://mlsanity.com/paper/2501.15757/) (2025)
- [Low Tensor-Rank Adaptation of Kolmogorov--Arnold Networks](https://mlsanity.com/paper/2502.06153/) (2025)
- [Kolmogorov-Arnold Network for Transistor Compact Modeling](https://mlsanity.com/paper/2503.15209/) (2025)
- [Variational Kolmogorov-Arnold Network](https://mlsanity.com/paper/2507.02466/) (2025)
- [Bridging KAN and MLP: MJKAN, a Hybrid Architecture with Both Efficiency and Expressiveness](https://mlsanity.com/paper/2507.04690/) (2025)
- [Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2508.00247/) (2025)
- [Lookup multivariate Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2509.07103/) (2025)
- [Uncertainty Quantification for Scientific Machine Learning using Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KAN)](https://mlsanity.com/paper/2512.05306/) (2025)
- [Learning Nonlinear Heterogeneity in Physical Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2601.15340/) (2026)
- [Optimization, Generalization and Differential Privacy Bounds for Gradient Descent on Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2601.22409/) (2026)
- [SurvKAN: A Fully Parametric Survival Model Based on Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2602.02179/) (2026)

## Abstract (arXiv)

This systematic review explores the theoretical foundations, evolution, applications, and future potential of Kolmogorov-Arnold Networks (KAN), a neural network model inspired by the Kolmogorov-Arnold representation theorem. KANs distinguish themselves from traditional neural networks by using learnable, spline-parameterized functions instead of fixed activation functions, allowing for flexible and interpretable representations of high-dimensional functions. This review details KAN's architectural strengths, including adaptive edge-based activation functions that improve parameter efficiency and scalability in applications such as time series forecasting, computational biomedicine, and graph learning. Key advancements, including Temporal-KAN, FastKAN, and Partial Differential Equation (PDE) KAN, illustrate KAN's growing applicability in dynamic environments, enhancing interpretability, computational efficiency, and adaptability for complex function approximation tasks. Additionally, this paper discusses KAN's integration with other architectures, such as convolutional, recurrent, and transformer-based models, showcasing its versatility in complementing established neural networks for tasks requiring hybrid approaches. Despite its strengths, KAN faces computational challenges in high-dimensional and noisy data settings, motivating ongoing research into optimization strategies, regularization techniques, and hybrid models. This paper highlights KAN's role in modern neural architectures and outlines future directions to improve its computational efficiency, interpretability, and scalability in data-intensive applications.