本文探索了具有分段线性函数的 Kolmogorov Arnold Networks (KANs) 与 ReLU networks 之间的联系，并提供了两者相互转换的完全显式构造方法。
摘要：
Kolmogorov-Arnold Networks 是一种新的神经网络架构家族，有望克服维度灾难并具有可解释性优势 (arXiv:2404.19756)。在本文中，我们探索了具有分段线性（一元实）函数的 Kolmogorov Arnold Networks (KANs) 与 ReLU networks 之间的联系。我们提供了完全显式的构造，以将分段线性 KAN 转换为 ReLU network，反之亦然。
英文摘要：
Kolmogorov-Arnold Networks are a new family of neural network architectures which holds promise for overcoming the curse of dimensionality and has interpretability benefits (arXiv:2404.19756). In this paper, we explore the connection between Kolmogorov Arnold Networks (KANs) with piecewise linear (univariate real) functions and ReLU networks. We provide completely explicit constructions to convert a piecewise linear KAN into a ReLU network and vice versa.
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.
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）
ReLU-KAN: New Kolmogorov-Arnold Networks that Only Need Matrix Addition, Dot Multiplication, and ReLU
University of South China（南华大学）；Paris Elite Institute of Technology, Shanghai Jiao Tong University（上海交通大学巴黎卓越工程师学院）；University of Science and Technology Beijing（北京科技大学）；Dalian University of Technology（大连理工大学）
针对 KAN 因 B 样条基函数导致 GPU 并行效率低的问题，本文提出仅用 ReLU 与逐点乘法的 ReLU-KAN，在 4 层网络上较传统 KAN 提速 20 倍，并保持更稳定训练、更强拟合及抗遗忘特性。
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…
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）
