Permutation equivariant neural networks employing parameter-sharing schemes have emerged as powerful models for leveraging a wide range of data symmetries, significantly enhancing the generalization and computational efficiency of the resulting models. Recently, Kolmogorov-Arnold Networks (KANs) have demonstrated promise through their improved interpretability and expressivity compared to traditional architectures based on MLPs. While equivariant KANs have been explored in recent literature for a few specific data types, a principled framework for applying them to data with permutation symmetries in a general context remains absent. This paper introduces Function Sharing KAN (FS-KAN), a principled approach to constructing equivariant and invariant KA layers for arbitrary permutation symmetry groups, unifying and significantly extending previous work in this domain. We derive the basic construction of these FS-KAN layers by generalizing parameter-sharing schemes to the Kolmogorov-Arnold setup and provide a theoretical analysis demonstrating that FS-KANs have the same expressive power as networks that use standard parameter-sharing layers, allowing us to transfer well-known and important expressivity results from parameter-sharing networks to FS-KANs. Empirical evaluations on multiple data types and symmetry groups show that FS-KANs exhibit superior data efficiency compared to standard parameter-sharing layers, by a wide margin in certain cases, while preserving the interpretability and adaptability of KANs, making them an excellent architecture choice in low-data regimes.
Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)
Department of Materials Science and Engineering, Delft University of Technology（材料科学与工程系，代尔夫特理工大学）；Department of Biomechanical Engineering, Delft University of Technology（生物机械工程系，代尔夫特理工大学）
The Thørväld Group（Thørväld集团）；Inria Paris-Rocquencourt（Inria巴黎-罗克昆court分部）；Rajiv Gandhi University Doimukh（拉贾戈夫德大学多伊穆克）；Tsinghua University（清华大学）；Palmer Research Laboratories（帕勒尔研究实验室）；The Kumquat Consortium（Kumquat consortium）
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学基础与前沿科学研究所）；Potsdam Institute for Climate Impact Research（波茨坦气候影响研究所）；Department of Physics, Humboldt University Berlin（柏林洪堡大学物理系）；Research Institute of Intelligent Complex Systems, Fudan University（复旦大学智能复杂系统研究所）；School of Physics, University of Electronic Science and Technology of China（电子科技大学物理学院）；Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China（电子科技大学教育部量子物理与光子量子信息重点实验室）；Non-classical Information Science Basic Discipline Research Center of Sichuan Province, University of Electronic Science and Technology of China（电子科技大学四川省非经典信息科学基础学科研究中心）
Kolmogorov-Arnold Networks for Personal Context Recognition on ExtraSensory
University of Information Technology, Ho Chi Minh City, Vietnam（胡志明市信息技术大学）；Vietnam National University Ho Chi Minh City, Ho Chi Minh City, Vietnam（越南国立大学胡志明市分校）
Kolmogorov-Arnold networks for metal surface defect classification
AGH University of Krakow（克拉科夫AGH大学）；Systems Research Institute, Polish Academy of Sciences（波兰科学院系统研究所）；University of Technology Sydney（悉尼科技大学）；Óbuda University（欧布达大学）；NASK National Research Institute（NASK国家研究院）
Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation
Indian Institute of Science Education and Research Mohali（印度科学教育与研究研究所莫哈利分校）；Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育与研究研究所蒂鲁文南特布勒姆分校）
PostHoc FREE Calibrating on Kolmogorov Arnold Networks
Institute for Clarity in Documentation（文献研究所）；Inria Paris-Rocquencourt（法国国家信息与自动化研究所巴黎-罗康校区）；Rajiv Gandhi University（拉吉夫·甘地大学）；Tsinghua University（清华大学）；Palmer Research Laboratories（帕尔默研究实验室）
Predictive Modeling of Flexible EHD Pumps using Kolmogorov-Arnold Networks
College of Mechanical Engineering, Chongqing University of Technology（重庆理工大学机械工程学院）；Nagoya University（名古屋大学）；Faculty of Engineering, Yamaguchi University（山口大学工程学院）
Kolmogorov Arnold networks (KAN) for aerodynamic prediction: a comparison with MLPs and GNNs
ETSIAE-UPM-School of Aeronautics, Universidad Politécnica de Madrid（马德里理工大学航空学院）；Center for Computational Simulation, Universidad Politécnica de Madrid（马德里理工大学计算模拟中心）；Institute for Cross-Disciplinary Physics and Complex Systems (IFISC, CSIC-UIB)（跨学科物理与复杂系统研究所（IFISC，CSIC-UIB））
A Practitioner's Guide to Kolmogorov-Arnold Networks
Department of Mathematics, Hong Kong Baptist University（香港 Baptist大学数学系）；Institution for Foundations of Data Science, Yale University（数据科学基础研究所，耶鲁大学）；Robotics and Technology of Computers Lab., Universidad de Sevilla（机器人与计算机技术实验室，塞维利亚大学）
KANGURA: Kolmogorov-Arnold Network-Based Geometry-Aware Learning with Unified Representation Attention for 3D Modeling of Complex Structures
Department of Electrical Engineering, Iran University of Science and Technology（伊朗科学技术大学电气工程系）；Department of Computer Engineering, Iran University of Science and Technology（伊朗科学技术大学计算机工程系）；Department of Industrial & Management Systems Engineering, West Virginia University（西弗吉尼亚大学工业与管理系统工程系）；H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology（佐治亚理工学院H.米尔顿·斯图尔特工业与系统工程学院）；Department of Computer Science, University of California, Davis（加州大学戴维斯分校计算机科学系）
Sinc Kolmogorov-Arnold network and its application for solving PDEs with singularities
Skolkovo Institute of Science and Technology（斯克洛夫科学与技术研究所）；Southern University of Science and Technology（南方科技大学）；International Center for Mathematics（国际数学中心）；National Center for Applied Mathematics Shenzhen (NCAMS)（深圳应用数学中心）
Physics Informed Kolmogorov-Arnold Neural Networks for Dynamical Analysis via Efficent-KAN and WAV-KAN
Indian Institute of Technology, Delhi（印度理工学院德里分校）；Indian Institute of Technology, Dhanbad（印度理工学院丹巴德分校）；Sun Moon University（日月大学）；Amrita Vishwa Vidyapeetham（阿米塔大学）；United States DEVCOM Army Research Laboratory（美国DEVCOM陆军研究实验室）；University of Massachusetts at Boston（马萨诸塞大学波士顿分校）；Tulane University（杜兰大学）
