# KAN versus MLP on Irregular or Noisy Functions

arXiv: https://arxiv.org/abs/2408.07906 · HTML: https://mlsanity.com/paper/2408.07906/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 52 references that are in the map.
- First posted on arXiv 15 Aug 2024.

## Builds on (most cited first, 30 of 31)

- [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)
- [KAN or MLP: A Fairer Comparison](https://mlsanity.com/paper/2407.16674/) (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)
- [Kolmogorov-Arnold Network for Satellite Image Classification in Remote Sensing](https://mlsanity.com/paper/2406.00600/) (2024)
- [KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Search](https://mlsanity.com/paper/2406.17630/) (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)
- [Exploring the Limitations of Kolmogorov-Arnold Networks in Classification: Insights to Software Training and Hardware Implementation](https://mlsanity.com/paper/2407.17790/) (2024)
- [How to Learn More? Exploring Kolmogorov-Arnold Networks for Hyperspectral Image Classification](https://mlsanity.com/paper/2406.15719/) (2024)
- [Reduced Effectiveness of Kolmogorov-Arnold Networks on Functions with Noise](https://mlsanity.com/paper/2407.14882/) (2024)
- [DropKAN: Regularizing KANs by masking post-activations](https://mlsanity.com/paper/2407.13044/) (2024)
- [COEFF-KANs: A Paradigm to Address the Electrolyte Field with KANs](https://mlsanity.com/paper/2407.20265/) (2024)
- [DKL-KAN: Scalable Deep Kernel Learning using Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2407.21176/) (2024)
- [RPN: Reconciled Polynomial Network Towards Unifying PGMs, Kernel SVMs, MLP and KAN](https://mlsanity.com/paper/2407.04819/) (2024)
- [Diffusion Representation for Asymmetric Kernels](https://mlsanity.com/paper/2401.12251/) (2024)
- [From Black Box to Clarity: AI-Powered Smart Grid Optimization with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2408.04063/) (2024)
- [KAN based Autoencoders for Factor Models](https://mlsanity.com/paper/2408.02694/) (2024)

## Built on by (most cited first, 7 of 7)

- [Color Matching Using Hypernetwork-Based Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2503.11781/) (2025)
- [Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learning](https://mlsanity.com/paper/2603.23854/) (2026)
- [Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learning](https://mlsanity.com/paper/2504.15240/) (2025)
- [Multilevel Training for Kolmogorov Arnold Networks](https://mlsanity.com/paper/2603.04827/) (2026)
- [AR-KAN: Autoregressive-Weight-Enhanced Kolmogorov-Arnold Network for Time Series Forecasting](https://mlsanity.com/paper/2509.02967/) (2025)
- [Optimized Piecewise Affine Abstractions of Neural Networks with Learnable Activation Functions](https://mlsanity.com/paper/2602.06737/) (2026)
- [Sample-Efficiency of Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2610.10627/) (2026)

## Abstract (arXiv)

In this paper, we compare the performance of Kolmogorov-Arnold Networks (KAN) and Multi-Layer Perceptron (MLP) networks on irregular or noisy functions. We control the number of parameters and the size of the training samples to ensure a fair comparison. For clarity, we categorize the functions into six types: regular functions, continuous functions with local non-differentiable points, functions with jump discontinuities, functions with singularities, functions with coherent oscillations, and noisy functions. Our experimental results indicate that KAN does not always perform best. For some types of functions, MLP outperforms or performs comparably to KAN. Furthermore, increasing the size of training samples can improve performance to some extent. When noise is added to functions, the irregular features are often obscured by the noise, making it challenging for both MLP and KAN to extract these features effectively. We hope these experiments provide valuable insights for future neural network research and encourage further investigations to overcome these challenges.