# Reduced Effectiveness of Kolmogorov-Arnold Networks on Functions with Noise

arXiv: https://arxiv.org/abs/2407.14882 · HTML: https://mlsanity.com/paper/2407.14882/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 33 references that are in the map.
- First posted on arXiv 20 Jul 2024.

## Builds on (most cited first, 19 of 19)

- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (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)
- [Kolmogorov-Arnold Networks (KANs) for Time Series Analysis](https://mlsanity.com/paper/2405.08790/) (2024)
- [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)
- [KAGNNs: Kolmogorov-Arnold Networks meet Graph Learning](https://mlsanity.com/paper/2406.18380/) (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)
- [ReLU-KAN: New Kolmogorov-Arnold Networks that Only Need Matrix Addition, Dot Multiplication, and ReLU](https://mlsanity.com/paper/2406.02075/) (2024)
- [GraphKAN: Enhancing Feature Extraction with Graph Kolmogorov Arnold Networks](https://mlsanity.com/paper/2406.13597/) (2024)
- [Predictive Modeling of Flexible EHD Pumps using Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.07488/) (2024)
- [How to Learn More? Exploring Kolmogorov-Arnold Networks for Hyperspectral Image Classification](https://mlsanity.com/paper/2406.15719/) (2024)
- [Diffusion Representation for Asymmetric Kernels](https://mlsanity.com/paper/2401.12251/) (2024)

## Built on by (most cited first, 17 of 17)

- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [On the expressiveness and spectral bias of KANs](https://mlsanity.com/paper/2410.01803/) (2024)
- [Multifidelity Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2410.14764/) (2024)
- [Exploring Kolmogorov-Arnold Networks for Interpretable Time Series Classification](https://mlsanity.com/paper/2411.14904/) (2024)
- [KAN versus MLP on Irregular or Noisy Functions](https://mlsanity.com/paper/2408.07906/) (2024)
- [Rethinking the Function of Neurons in KANs](https://mlsanity.com/paper/2407.20667/) (2024)
- [KAN we improve on HEP classification tasks? Kolmogorov-Arnold Networks applied to an LHC physics example](https://mlsanity.com/paper/2408.02743/) (2024)
- [ChemKANs for Combustion Chemistry Modeling and Acceleration](https://mlsanity.com/paper/2504.12580/) (2025)
- [P1-KAN: an effective Kolmogorov-Arnold network with application to hydraulic valley optimization](https://mlsanity.com/paper/2410.03801/) (2024)
- [Efficiency Bottlenecks of Convolutional Kolmogorov-Arnold Networks: A Comprehensive Scrutiny with ImageNet, AlexNet, LeNet and Tabular Classification](https://mlsanity.com/paper/2501.15757/) (2025)
- [HKAN: Hierarchical Kolmogorov-Arnold Network without Backpropagation](https://mlsanity.com/paper/2501.18199/) (2025)
- [AR-KAN: Autoregressive-Weight-Enhanced Kolmogorov-Arnold Network for Time Series Forecasting](https://mlsanity.com/paper/2509.02967/) (2025)
- [Algorithms and data structures for automatic precision estimation of neural networks](https://mlsanity.com/paper/2509.24607/) (2025)
- [Optimized Piecewise Affine Abstractions of Neural Networks with Learnable Activation Functions](https://mlsanity.com/paper/2602.06737/) (2026)
- [Autocorrelation Reintroduces Spectral Bias in KANs for Time Series Forecasting](https://mlsanity.com/paper/2604.23518/) (2026)
- [KAN-MLP-Mixer: A comprehensive investigation of the usage of Kolmogorov-Arnold Networks (KANs) for improving IMU-based Human Activity Recognition](https://mlsanity.com/paper/2605.19031/) (2026)

## Abstract (arXiv)

It has been observed that even a small amount of noise introduced into the dataset can significantly degrade the performance of KAN. In this brief note, we aim to quantitatively evaluate the performance when noise is added to the dataset. We propose an oversampling technique combined with denoising to alleviate the impact of noise. Specifically, we employ kernel filtering based on diffusion maps for pre-filtering the noisy data for training KAN network. Our experiments show that while adding i.i.d. noise with any fixed SNR, when we increase the amount of training data by a factor of r, the test-loss (RMSE) of KANs will exhibit a performance trend like test-loss ~ O(r^-frac12) as r→ +∞. We conclude that applying both oversampling and filtering strategies can reduce the detrimental effects of noise. Nevertheless, determining the optimal variance for the kernel filtering process is challenging, and enhancing the volume of training data substantially increases the associated costs, because the training dataset needs to be expanded multiple times in comparison to the initial clean data. As a result, the noise present in the data ultimately diminishes the effectiveness of Kolmogorov-Arnold networks.