Universal Approximation

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Kolmogorov-Arnold Classifier Systems as Universal Approximators
Sep 29, 2026Hiroki Shiraishi, Hisao Ishibuchi, Masaya NakataUniversal Approximation
Graduate School of Engineering Science, Yokohama National University, Yokohama 240-8501, Japan · Digital Healthcare Research Department, Hitachi, Ltd., Tokyo 185-8601, Japan · Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China +1
Universal Approximation of Measure-to-Measure Operators by Pushforwards
Sep 28, 2026Takashi Furuya, Nicholas H. Nelsen, Frank ColeTransformer Universal Approximation
Doshisha University, RIKEN AIP · UT Austin · UCLA
Kolmogorov--Arnold stability for discontinuous functions
Sep 7, 2026Sviatoslav V. DzhenzherAdversarial Robustness Kolmogorov-Arnold Networks
Moscow Institute of Physics and Technology 141701, Institutskii lane, 9, Dolgoprudny, Russia.
A Single Atom in Front of a Mirror is a Universal Reservoir Computer
Aug 11, 2026Peter J. Ehlers, Phi Hung Nguyen, Kanu Sinha +4Reservoir Computing Universal Approximation
Wyant College of Optical Sciences, University of Arizona, Tucson, AZ, USA · Department of Physics, University of Arizona, Tucson, AZ, USA · School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, Australia
Universal Function Approximation via Diffractive Optical Processors: Physical Limits, Error Bounds, and Learnability
Aug 5, 2026Md Sadman Sakib Rahman, Che-Yung Shen, Aydogan OzcanUniversal Approximation Photonic Computing
Electrical and Computer Engineering Department, University of California, Los Angeles, CA, 90095, USA · Bioengineering Department, University of California, Los Angeles, CA, 90095, USA · California NanoSystems Institute (CNSI), University of California, Los Angeles, CA, 90095, USA
Minimum Block Width for Universal Approximation by Residual Neural Networks with Inner Width One
Jul 6, 2026Qi Zhou, Xuan Zhou, Xiao-Song YangReLU Neural Networks Residual Learning
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, P.R. China. · Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, P.R. China.
Algorithmic Foundations of Deep Learning: Complexity-Theoretic Rates and a Characterization of Universal Approximation
Jun 25, 2026Anastasis Kratsios, Simone Brugiapaglia, Bum Jun Kim +2Universal Approximation Neural Network Approximation Theory
McMaster University & Vector Institute, Toronto, ON, Canada · Concordia University, Montréal, QC, Canada · University of Tokyo, Tokyo, Japan +2
EML Trees Are Universal Approximators
Jun 22, 2026Joe Germany, Elie Abdo, Joseph BakarjiUniversal Approximation Neural Network Approximation Theory
Department of Mathematics American University of Beirut Beirut, Lebanon · Department of Mechanical Engineering American University of Beirut Beirut, Lebanon
Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System
Jun 18, 2026Zhiwen Yu, Derong Yang, Liujian Zhang +5PDE Solving Universal Approximation
School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China · Peng Cheng Laboratory, Shenzhen 518000, China · School of Future Technology, South China University of Technology, Guangzhou 510006, China +2
Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy
Jun 15, 2026Baicheng Li, Haizhao Yang, Shijun ZhangNeural Network Activation Functions Universal Approximation
Department of Mathematics, University of Maryland, College Park, MD, USA · Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China
Weighted universal approximation of differentiable maps on infinite-dimensional manifolds
Jun 8, 2026Philipp Schmocker, Josef TeichmannUniversal Approximation Neural Network Approximation Theory
Expressive Power of Floating-Point Neural Networks with Arbitrary Reduction Orders and Inexact Activation Implementations
May 27, 2026Yeachan Park, Geonho Hwang, Wonyeol Lee +1Neural Network Activation Functions Universal Approximation
Any-Dimensional Invariant Universality
May 22, 2026Shengtai Yao, Eitan Levin, Mateo DíazUniversal Approximation Neural Network Approximation Theory
Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218, USA. · Department of Computing and Mathematical Sciences, Caltech, Pasadena, CA 91125, USA.
Approximation Theory for Neural Networks: Old and New
May 20, 2026Soumendu Sundar Mukherjee, Himasish TalukdarUniversal Approximation Neural Network Approximation Theory
Statistics and Mathematics Unit, Indian Statistical Institute, Kolkata
Embedding Dimension Lower Bounds for Universality of Deep Sets and Janossy Pooling
May 8, 2026Ali Syed, Aditya Nambiar, Jonathan W. SiegelRepresentation Learning Deep Sets
Department of Mathematics Texas A&M University College Station, TX 77843
Progressive Approximation in Deep Residual Networks: Theory and Validation
Apr 27, 2026Wei Wang, Xiao-Yong Wei, Qing LiEfficient Neural Network Inference Residual Learning
Department of Computing, the Hong Kong Polytechnic University.
Necessary and sufficient conditions for universality of Kolmogorov-Arnold networks
Apr 26, 2026Vugar IsmailovKolmogorov-Arnold Networks Universal Approximation
Global universal approximation with Brownian signatures
Dec 18, 2025Mihriban Ceylan, David J. PrömelUniversal Approximation
Autonomous-Flow-Based Generation
Date pendingHossein Rouhvarzi, Anastasis KratsiosUniversal Approximation Continuous Normalizing Flows
McMaster University and the Vector Institute Department of Mathematics 1280 Main Street West, Hamilton, Ontario, L8S 4K1, Canada

Sep 29, 2026, cs.LGJ/K move · Enter open · S save

Kolmogorov-Arnold Classifier Systems as Universal Approximators

Hiroki Shiraishi, Hisao Ishibuchi, Masaya Nakata

Graduate School of Engineering Science, Yokohama National University, Yokohama 240-8501, Japan · Digital Healthcare Research Department, Hitachi, Ltd., Tokyo 185-8601, Japan · Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China+1

Universal Approximation

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As the input dimension

n

grows, rule-based machine learning, such as Learning Classifier Systems (LCSs), faces a fundamental scalability bottleneck for function approximation: both rule count and parameter count grow exponentially with

n

. Traditional LCSs partition the

n

-dimensional input space directly, requiring

\mathcal{O}(m^n)

rules for adequate coverage, where

m

is the per-variable resolution. This article breaks from this paradigm by reorganizing rules dimension-wise, guided by the Kolmogorov-Arnold representation theorem: any continuous

n

-dimensional function can be expressed as a finite superposition of one-dimensional functions. The proposed Kolmogorov-Arnold Classifier System (KACS) decomposes the target function into one-dimensional subproblems and assigns a dedicated ruleset to each, reducing the worst-case rule count from

\mathcal{O}(m^n)

\mathcal{O}(mn^2)

and replacing

n

-dimensional local models with one-dimensional models requiring only two parameters per rule, independent of

n

. We also provide the first constructive proof that an LCS, namely KACS, is a universal approximator for continuous functions on compact domains. Evaluated against a direct

n

-dimensional input space partitioning approach under otherwise identical conditions, KACS achieves competitive accuracy in many settings while using only 2% to 40% of the parameters. Our implementation is available at https://github.com/YNU-NakataLab/KACS.

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