Catastrophic forgetting remains the central obstacle in continual learning (CL): parameters shared across tasks interfere with one another, and existing regularization methods such as EWC and SI apply uniform penalties without awareness of which input region a parameter serves. We propose KAN-CL, a continual learning framework that exploits the compact-support spline parameterization of Kolmogorov-Arnold Networks (KANs) to perform importance-weighted anchoring at per-knot granularity. Deployed as a classification head on a convolutional backbone with standard EWC regularization on the backbone (bbEWC) KAN-CL achieves forgetting reductions of 88% and 93% over a head-only KAN baseline on Split-CIFAR-10/5T and Split-CIFAR-100/10T respectively, while matching or exceeding the accuracy of all baselines on both benchmarks. We further provide a Neural Tangent Kernel (NTK) analysis showing that KAN's spline locality induces a structural rank deficit in the cross-task NTK, yielding a forgetting bound that holds even in the feature-learning regime. These results establish that combining an architecture with natural parameter locality (KAN head) with a complementary backbone regularizer (bbEWC) yields a compositional and principled approach to catastrophic forgetting.
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）
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）
Massachusetts Institute of Technology（麻省理工学院）；The NSF Institute for Artificial Intelligence and Fundamental Interactions（NSF人工智能与基本相互作用研究所）；California Institute of Technology（加州理工学院）
University of Twente（特文特大学）；Leiden University（莱顿大学）
There is a longstanding debate whether the Kolmogorov-Arnold representation theorem can explain the use of more than one hidden layer in neural networks. The Kolmogorov-Arnold representation decomposes a multivariate function into an interior and an outer function and therefore has indeed a similar structure as a neural network with two hidden layers. But there are distinctive differences. One of the main obstacles is that the outer function depends on the represented function and can be wildly varying even if the represented function is smooth. We derive modifications of the Kolmogorov-Arnold…
HKAN: Hierarchical Kolmogorov-Arnold Network without Backpropagation
the Faculty of Electrical Engineering, Czestochowa University of Technology（捷斯托霍瓦技术大学电子工程系）；the Faculty of Mathematics and Computer Science, University of Lodz（罗兹大学数学与计算机科学系）；the Centre for Data Analysis, Modelling and Computational Sciences (CAMINO), University of Lodz（罗兹大学数据分析、建模与计算科学中心）
Columbia University（哥伦比亚大学）；National University of Singapore（新加坡国立大学）
We prove a theorem concerning the approximation of multivariate functions by deep ReLU networks, for which the curse of the dimensionality is lessened. Our theorem is based on a constructive proof of the Kolmogorov--Arnold superposition theorem, and on a subset of multivariate continuous functions whose outer superposition functions can be efficiently approximated by deep ReLU networks.
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）
Department of Physics and Engineering Physics, Tulane University（Tulane 大学物理与工程物理系）；Institute of Applied Geosciences, Karlsruhe Institute of Technology（卡尔斯鲁厄技术大学应用地球科学研究所）
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）
DAE-KAN: A Kolmogorov-Arnold Network Model for High-Index Differential-Algebraic Equations
School of Computer Science and Cyber Engineering, Guangzhou University（广州大学计算机科学与网络工程学院）；Huangpu Research School of Guangzhou University（广州大学黄埔研究学院）；Department of Mathematics, Morgan State University（摩根州立大学数学系）；Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR)（高性能计算研究所（IHPC），科技研究局（A*STAR））；Centre for Frontier AI Research (CFAR), Agency for Science, Technology and Research (A*STAR)（前沿人工智能研究中心（CFAR），科技研究局（A*STAR））
AR-KAN: Autoregressive-Weight-Enhanced Kolmogorov-Arnold Network for Time Series Forecasting
School of Information Science and Engineering, Southeast University（东南大学信息科学与工程学院）；School of Economics and Management, Southeast University（东南大学经济管理学院）
