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 framework targeting different tasks and application domains, including sequence processing.
This paper proposes seqKAN, a new KAN architecture for sequence processing. Although multiple sequence processing KAN architectures have already been proposed, we argue that seqKAN is more faithful to the core concept of the KAN framework. Furthermore, we empirically demonstrate that it achieves better results.
The empirical evaluation is performed on generated data from a complex physics problem on an interpolation and an extrapolation task. Using this dataset we compared seqKAN against a prior KAN network for timeseries prediction, recurrent deep networks, and symbolic regression. seqKAN substantially outperforms all architectures, particularly on the extrapolation dataset, while also being the most transparent.
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）
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）
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）
Department of Computer, Control and Management Engineering, Sapienza University of Rome（西帕辛扎大学罗马分校计算机、控制与管理工程系）；Department of Life Science Informatics and Data Science, B-IT, LIMES Program Unit Chemical Biology and Medicinal Chemistry, Rheinische Friedrich-Wilhelms-Universität, Bonn, Germany（波恩德国莱茵-威斯巴登大学生命科学信息技术与数据科学系）；Lamarr Institute for Machine Learning and Artificial Intelligence, Bonn, Germany（波恩德国拉马尔机器学习与人工智能研究所）
Learning the Basis: A Kolmogorov-Arnold Network Approach Embedding Green's Function Priors
Key Laboratory of Universal Wireless Communication, Ministry of Education, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications（信息与通信工程学院，北京邮电大学，教育部无线通信重点实验室）；Department of Informatics and Telecommunications, National and Kapodistrian University of Athens（信息与电信学院，希腊国家与卡波迪斯蒂亚纳大学）；telecommunication company in Stockholm, Sweden（瑞典斯德哥尔摩的一家电信公司）；School of Computing, Engineering and Mathematical Sciences, La Trobe University（计算、工程与数学科学学院，拉特罗布大学）
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…
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.
Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks
Tsinghua University（清华大学）；Bauhaus-Universität Weimar（魏玛包豪斯大学）；CNPC Engineering Technology RD Company Limited（中国石油集团工程技术研究院有限公司）；Queensland University of Technology（昆士兰科技大学）；Leibniz University Hannover（汉诺威莱布尼茨大学）
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）
