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Related papers: Geometric Kolmogorov-Arnold Superposition Theorem

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Kolmogorov-Arnold Networks (KANs) have emerged as a promising alternative to traditional Multi-Layer Perceptrons (MLPs), offering enhanced interpretability and a solid mathematical foundation. However, their parameter efficiency remains a…

Machine Learning · Computer Science 2025-10-09 Di Zhang

The Kolmogorov-Arnold (KA) representation theorem constructs universal, but highly non-smooth inner functions (the first layer map) in a single (non-linear) hidden layer neural network. Such universal functions have a distinctive local…

Machine Learning · Computer Science 2025-12-03 Michael H. Freedman , Michael Mulligan

We present a novel approach for verifying properties of Kolmogorov-Arnold Networks (KANs), a class of neural networks characterized by nonlinear, univariate activation functions typically implemented as piecewise polynomial splines or…

Machine Learning · Computer Science 2026-02-09 Noah Schwartz , Chandra Kanth Nagesh , Sriram Sankaranarayanan , Ramneet Kaur , Tuhin Sahai , Susmit Jha

Uncovering physical laws from experimental data is a fundamental goal of theoretical physics. In this work, we apply the spline-based, interpretable Kolmogorov-Arnold Network (KAN) to explore the algebraic structure underlying the baryon…

High Energy Physics - Phenomenology · Physics 2026-01-06 Jian-Yao He , Xun Chen , Xiao-Yan Zhu , Wen Luo

Kolmogorov-Arnold networks (KANs) as an alternative to multi-layer perceptrons (MLPs) are a recent development demonstrating strong potential for data-driven modeling. This work applies KANs as the backbone of a neural ordinary differential…

Machine Learning · Computer Science 2024-09-23 Benjamin C. Koenig , Suyong Kim , Sili Deng

Kolmogorov-Arnold Networks (KANs) have shown potential as an alternative to Multi-Layer Perceptrons (MLPs) in neural networks, providing universal function approximation with fewer parameters and reduced memory usage. In this paper, we…

Machine Learning · Computer Science 2024-09-04 Victor Augusto Kich , Jair Augusto Bottega , Raul Steinmetz , Ricardo Bedin Grando , Ayano Yorozu , Akihisa Ohya

Kolmogorov-Arnold Networks or KANs have shown the ability to outperform classical Deep Neural Networks, while using far fewer trainable parameters for regression problems on scientific domains. Even more powerful has been their…

Function approximation using Haar basis systems offers an efficient implementation when compressed via Patricia trees while retaining the flexibility of wavelets for both global and local fitting. However, like B-spline-based…

Machine Learning · Computer Science 2026-02-05 Susumu Katayama

This study explores the application of Kolmogorov-Arnold Networks (KANs) in predicting nuclear binding energies, leveraging their ability to decompose complex multi-parameter systems into simpler univariate functions. By utilizing data from…

Nuclear Theory · Physics 2025-02-10 Hao Liu , Jin Lei , Zhongzhou Ren

The prediction of quantum dynamical responses lies at the heart of modern physics. Yet, modeling these time-dependent behaviors remains a formidable challenge because quantum systems evolve in high-dimensional Hilbert spaces, often…

Machine Learning · Computer Science 2025-09-24 Abhijit Sen , Illya V. Lukin , Kurt Jacobs , Lev Kaplan , Andrii G. Sotnikov , Denys I. Bondar

Kolmogorov Arnold Networks (KANs) are neural architectures inspired by the Kolmogorov Arnold representation theorem that leverage B Spline parameterizations for flexible, locally adaptive function approximation. Although KANs can capture…

Machine Learning · Computer Science 2025-03-04 Wenhao Liang , Wei Emma Zhang , Lin Yue , Miao Xu , Olaf Maennel , Weitong Chen

We explain how to use Kolmogorov Superposition Theorem (KST) to break the curse of dimensionality when approximating a dense class of multivariate continuous functions. We first show that there is a class of functions called…

Numerical Analysis · Mathematics 2025-10-06 Ming-Jun Lai , Zhaiming Shen

Kolmogorov-Arnold Networks (KAN) has recently attracted significant attention as a promising alternative to traditional Multi-Layer Perceptrons (MLP). Despite their theoretical appeal, KAN require validation on large-scale benchmark…

Machine Learning · Computer Science 2024-09-12 Chang Dong , Liangwei Zheng , Weitong Chen

Modern machine learning, grounded in the Universal Approximation Theorem, has achieved significant success in the study of phase transitions in both equilibrium and non-equilibrium systems. However, identifying the critical points of…

Statistical Mechanics · Physics 2025-03-25 Dian Xu , Shanshan Wang , Wei Li , Weibing Deng , Feng Gao , Jianmin Shen

Kolmogorov Arnold Networks (KANs) are recent architectural advancement in neural computation that offer a mathematically grounded alternative to standard neural networks. This study presents an empirical evaluation of KANs in context of…

Machine Learning · Computer Science 2025-07-21 Pankaj Yadav , Vivek Vijay

Deep learning methods have been widely used as an end-to-end modeling strategy of electrical energy systems because of their conveniency and powerful pattern recognition capability. However, due to the "closed-box" nature, deep learning…

Signal Processing · Electrical Eng. & Systems 2026-05-12 Zhenghao Zhou , Yiyan Li , Zelin Guo , Zheng Yan , Mo-Yuen Chow

Kolmogorov-Arnold Networks (KANs) have been recently proposed as a machine learning framework that is more interpretable and controllable than the multi-layer perceptron. Various network architectures have been proposed within the KAN…

Machine Learning · Computer Science 2025-02-21 Tatiana Boura , Stasinos Konstantopoulos

Sets represent a fundamental abstraction across many types of data. To handle the unordered nature of set-structured data, models such as DeepSets and PointNet rely on fixed, non-learnable pooling operations (e.g., sum or max) -- a design…

Machine Learning · Computer Science 2026-02-06 Tomas Tokar , Scott Sanner

The research undertakes a comprehensive comparative analysis of Kolmogorov-Arnold Networks (KAN) and Multi-Layer Perceptrons (MLP), highlighting their effectiveness in solving essential computational challenges like nonlinear function…

Machine Learning · Computer Science 2026-01-16 Aradhya Gaonkar , Nihal Jain , Vignesh Chougule , Nikhil Deshpande , Sneha Varur , Channabasappa Muttal

The discovery of high-performance thermoelectric materials requires models that are both accurate and interpretable. Traditional machine learning approaches, while effective at property prediction, often act as black boxes and provide…

Materials Science · Physics 2025-12-15 Marco Fronzi , Michael J. Ford , Kamal Singh Nayal , Olexandr Isayev , Catherine Stampfl