# Generalization Bounds and Model Complexity for Kolmogorov-Arnold Networks

arXiv: https://arxiv.org/abs/2410.08026 · HTML: https://mlsanity.com/paper/2410.08026/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 53 references that are in the map.
- First posted on arXiv 10 Oct 2024.

## Builds on (most cited first, 30 of 41)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [The generalization error of random features regression: Precise asymptotics and double descent curve](https://mlsanity.com/paper/1908.05355/) (2019)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [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)
- [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)
- [DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problems](https://mlsanity.com/paper/2405.19143/) (2024)
- [Convolutional Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.13155/) (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)
- [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)
- [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)
- [Enhancing Graph Collaborative Filtering with FourierKAN Feature Transformation](https://mlsanity.com/paper/2406.01034/) (2024)
- [Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2407.17611/) (2024)
- [KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Search](https://mlsanity.com/paper/2406.17630/) (2024)
- [Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomials](https://mlsanity.com/paper/2406.02583/) (2024)
- [rKAN: Rational Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.14495/) (2024)
- [Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems](https://mlsanity.com/paper/2406.19662/) (2024)
- [Unveiling the Power of Wavelets: A Wavelet-based Kolmogorov-Arnold Network for Hyperspectral Image Classification](https://mlsanity.com/paper/2406.07869/) (2024)
- [Suitability of KANs for Computer Vision: A preliminary investigation](https://mlsanity.com/paper/2406.09087/) (2024)
- [Kolmogorov-Arnold Graph Neural Networks](https://mlsanity.com/paper/2406.18354/) (2024)
- [A Benchmarking Study of Kolmogorov-Arnold Networks on Tabular Data](https://mlsanity.com/paper/2406.14529/) (2024)

## Built on by (most cited first, 11 of 11)

- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [PointNet with KAN versus PointNet with MLP for 3D Classification and Segmentation of Point Sets](https://mlsanity.com/paper/2410.10084/) (2024)
- [Initialization Schemes for Kolmogorov-Arnold Networks: An Empirical Study](https://mlsanity.com/paper/2509.03417/) (2025)
- [Improving Memory Efficiency for Training KANs via Meta Learning](https://mlsanity.com/paper/2506.07549/) (2025)
- [Optimization, Generalization and Differential Privacy Bounds for Gradient Descent on Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2601.22409/) (2026)
- [KANFIS: A Neuro-Symbolic Framework for Interpretable and Uncertainty-Aware Learning](https://mlsanity.com/paper/2602.03034/) (2026)
- [Hardware-Oriented Inference Complexity of Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2604.03345/) (2026)
- [KAPLAN: Kolmogorov-Arnold Prognostic Learnable Activation Networks for Survival Analysis](https://mlsanity.com/paper/2605.23082/) (2026)
- [Non-Crossing Deep Quantile Regression for Distributional Survival Prediction](https://mlsanity.com/paper/2608.16864/) (2026)
- [Stability-Constrained Approximation in Spline KANs: Exact Layer Balancing and Budget-Compatible Saturation](https://mlsanity.com/paper/2609.17619/) (2026)
- [Fisher Simplicity in Kolmogorov-Arnold Networks and Multilayer Perceptrons](https://mlsanity.com/paper/2609.32503/) (2026)

## Abstract (arXiv)

Kolmogorov-Arnold Network (KAN) is a network structure recently proposed by Liu et al. (2024) that offers improved interpretability and a more parsimonious design in many science-oriented tasks compared to multi-layer perceptrons. This work provides a rigorous theoretical analysis of KAN by establishing generalization bounds for KAN equipped with activation functions that are either represented by linear combinations of basis functions or lying in a low-rank Reproducing Kernel Hilbert Space (RKHS). In the first case, the generalization bound accommodates various choices of basis functions in forming the activation functions in each layer of KAN and is adapted to different operator norms at each layer. For a particular choice of operator norms, the bound scales with the l1 norm of the coefficient matrices and the Lipschitz constants for the activation functions, and it has no dependence on combinatorial parameters (e.g., number of nodes) outside of logarithmic factors. Moreover, our result does not require the boundedness assumption on the loss function and, hence, is applicable to a general class of regression-type loss functions. In the low-rank case, the generalization bound scales polynomially with the underlying ranks as well as the Lipschitz constants of the activation functions in each layer. These bounds are empirically investigated for KANs trained with stochastic gradient descent on simulated and real data sets. The numerical results demonstrate the practical relevance of these bounds.