Neural Network Approximation Theory

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15 papers in the last four weeks, up 15% on the four weeks before. 0.1% of all new papers.

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  1. Exact ReLU realization of tensor-product refinement iterates

    May 5, 2026Tsogtgerel GantumurReLU Neural NetworksNeural Network Approximation Theory

    McGill University, Montréal, QC, Canada · National University of Mongolia, Ulaanbaatar, Mongolia · Mongolian Academy of Sciences, Institute of Mathematics and Digital Technology

  2. Simultaneous CNN Approximation on Manifolds with Applications to Boundary Value Problems

    May 5, 2026Hanfei Zhou, Lei ShiPDE SolvingNeural Network Approximation Theory

    School of Mathematical Sciences, Fudan University, Shanghai, 200433, China · Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai, 200433, China

  3. Parametrizing Convex Sets Using Sublinear Neural Networks

    May 5, 2026Eloi MartinetNeural Network Approximation Theory

    Institute for Mathematics, University of Würzburg Germany

  4. Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation

    May 4, 2026Nicole HaoFourier Neural OperatorPDE Solving

    Department of Mathematics, Cornell University

  5. Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle

    May 4, 2026Filippo Giovagnini, Sotirios Kotitsas, Marco RomitoNeural Network Approximation TheoryWasserstein Distance

  6. ParaRNN: An Interpretable and Parallelizable Recurrent Neural Network for Time-Dependent Data

    May 4, 2026Yuxi Cai, Lan Li, Feiqing Huang +1Interpretable MLRecurrent Neural Networks

    Department of Statistics and Actuarial Science, University of Hong Kong

  7. Floating-Point Networks with Automatic Differentiation Can Represent Almost All Floating-Point Functions and Their Gradients

    May 3, 2026Sejun Park, Yeachan Park, Geonho HwangAutomatic DifferentiationNeural Network Approximation Theory

    Department of Artificial Intelligence, Korea University, Seoul, 02841, Republic of Korea · Department of Mathematics and Statistics, Sejong University, Seoul, 05006, Republic of Korea · Department of Mathematical Sciences, Gwangju Institute of Science and Technology, Gwangju, 61005, Republic of Korea

  8. Exact Loop Controllers for ReLU Realization of Homogeneous Curve Refinements

    May 3, 2026Boldsaikhan Bolorkhuu, Tsogtgerel GantumurReLU Neural NetworksNeural Network Approximation Theory

    1McGill University · 2National University of Mongolia · Institute of Mathematics and Digital Technology, Mongolian Academy of Sciences

  9. Hyper Input Convex Neural Networks for Shape Constrained Learning and Optimal Transport

    Apr 29, 2026Shayan Hundrieser, Insung Kong, Johannes Schmidt-HieberInput Convex Neural NetworksNeural Network Approximation Theory

    *Department of Applied Mathematics, University of Twente, Enschede, The Netherlands

  10. Layer-wise Lipschitz-Product Control for Deep Kolmogorov--Arnold Network Representations of Compositionally Structured Functions

    Apr 29, 2026Aleksander TankmanKolmogorov-Arnold NetworksNeural Network Approximation Theory

    Fivestar Europe OÜ, Tallinn, Estonia

  11. Transformer Approximations from ReLUs

    Apr 27, 2026Jerry Yao-Chieh Hu, Mingcheng Lu, Yi-Chen Lee +1Softmax AttentionNeural Network Approximation Theory

    Center for Foundation Models and Generative AI, Northwestern University, Evanston, IL 60208, USA · Department of Computer Science, Northwestern University, Evanston, IL 60208, USA · Department of Physics, National Taiwan University, Taipei 10617, Taiwan +1

  12. Progressive Approximation in Deep Residual Networks: Theory and Validation

    Apr 27, 2026Wei Wang, Xiao-Yong Wei, Qing LiEfficient Neural Network InferenceResidual Learning

    Department of Computing, the Hong Kong Polytechnic University.

  13. Necessary and sufficient conditions for universality of Kolmogorov-Arnold networks

    Apr 26, 2026Vugar IsmailovKolmogorov-Arnold NetworksUniversal Approximation

  14. Explicit integral representations and quantitative bounds for two-layer ReLU networks

    Apr 25, 2026Anthony LeeReLU Neural NetworksReproducing Kernel Hilbert Spaces

    School of Mathematics, University of Bristol

  15. SOC-ICNN: From Polyhedral to Conic Geometry for Learning Convex Surrogate Functions

    Apr 24, 2026Kang Liu, Jianchen Hu, Wei PengNeural Surrogate ModelingInput Convex Neural Networks

    School of Future Technology Xi’an Jiaotong University Xi’an, China · School of Future Technology School of Automation Science and Engineering Xi’an Jiaotong University Xi’an, China · School of Automation Science and Engineering Xi’an Jiaotong University Xi’an, China

  16. Scale-Parameter Selection in Gaussian Kolmogorov-Arnold Networks

    Apr 23, 2026Amir Noorizadegan, Sifan WangKolmogorov-Arnold NetworksNeural Network Approximation Theory

    Department of Mathematics, Hong Kong Baptist University, Hong Kong SAR, China · Institution for Foundations of Data Science, Yale University, New Haven, CT 06520, USA

  17. Layer-wise Geometric Approximation Rates for Deep Networks

    Apr 22, 2026Shijun Zhang, Zuowei Shen, Yuesheng XuNeural Network Approximation TheoryNeural Network Expressivity

    Department of Applied Mathematics Hong Kong Polytechnic University · Department of Mathematics National University of Singapore · Department of Mathematics and Statistics Old Dominion University

  18. Neural Shape Operator Surrogates -- Expression Rate Bounds

    Apr 20, 2026Helmut Harbrecht, Christoph SchwabPDE Operator LearningNeural Network Approximation Theory

  19. Closing the Theory-Practice Gap in Spiking Transformers via Effective Dimension

    Apr 17, 2026Dongxin Guo, Jikun Wu, Siu Ming YiuSpiking TransformersTransformer Attention

    *The University of Hong Kong, Hong Kong, China · †Brain Investing Limited, Hong Kong, China

  20. Implicit Neural Representations: A Signal Processing Perspective

    Apr 16, 2026Dhananjaya Jayasundara, Vishal M. PatelImplicit Neural RepresentationsSpectral Bias

    Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD 21218 USA

  21. Equivalence of approximation by networks of single- and multi-spike neurons

    Mar 13, 2026Dominik Dold, Philipp Christian PetersenSpiking Neural NetworksNeural Network Approximation Theory

  22. Rational Neural Networks have Expressivity Advantages

    Feb 12, 2026Maosen Tang, Alex TownsendNeural Network Activation FunctionsNeural Network Approximation Theory

    Center for Applied Mathematics, Cornell University, United States · Department of Mathematics, Cornell University, United States

  23. Clifford Kolmogorov-Arnold Networks

    Feb 5, 2026Matthias Wolff, Francesco Alesiani, Christof Duhme +1Kolmogorov-Arnold NetworksNeural Network Approximation Theory

    Data Science Div. NEC Labs Europe Heidelberg, Germany

  24. Geometry-Preserving Neural Architectures on Manifolds with Boundary

    Feb 3, 2026Karthik Elamvazhuthi, Shiba Biswal, Kian Rosenblum +4Geometric Representation LearningNeural Network Approximation Theory

    Los Alamos National Laboratory · Boston College

  25. Agile Reinforcement Learning through Separable Neural Architecture and Applications

    Jan 30, 2026Rajib Mostakim, Reza T. Batley, Sourav SahaRL ControlNeural Network Approximation Theory

    Department of Mechanical Engineering, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh · Kevin T. Crofton Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA

  26. Linearized subspace refinement framework to expose hidden accuracy in trained neural networks

    Jan 20, 2026Wenbo Cao, Weiwei ZhangNeural Network OptimizationNeural Network Approximation Theory

    Institute of AI for Industries, Chinese Academy of Sciences, Nanjing 211135, China · Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China · School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China +2

  27. The Alexander-Hirschowitz theorem for neurovarieties

    Nov 24, 2025A. Massarenti, M. MellaPolynomial Neural NetworksParameter Identifiability

  28. On the Dimension-Free Approximation of Deep Neural Networks for Symmetric Korobov Functions

    Nov 16, 2025Yulong Lu, Tong Mao, Jinchao Xu +1Neural Network GeneralizationNeural Network Approximation Theory

    School of Mathematics, University of Minnesota, Minneapolis, 55455, MN, USA · Computer, Electrical and Mathematical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia · School of Mathematics, Georgia Institute of Technology, Atlanta, 30332, GA, USA

  29. DFNN: A Deep Fréchet Neural Network Framework for Learning Metric-Space-Valued Responses

    Oct 20, 2025Kyum Kim, Yaqing Chen, Paromita DubeyNeural Network GeneralizationNeural Network Approximation Theory

    Rutgers University · University of Southern California

  30. Configuration-Dependent Lower Bounds for Approximation by Shallow ReLUk^k Networks on the Sphere

    Oct 5, 2025Tong Mao, Jinchao XuShallow Neural NetworksNeural Network Approximation Theory

    Shenzhen Loop Area Institute, Shenzhen 518000, P. R. China · King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia.