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. Approximation Rates for Metaplectic Neural Networks

    Aug 9, 2026Ahmed Abdeljawad, Marcello Carioni, Elena CorderoShallow Neural NetworksNeural Network Approximation Theory

    Johann Radon Institute of Computational and Applied Mathematics (RICAM) Austrian Academy of Sciences Altenberger Straße 69, A-4040 Linz, Austria · Department of Applied Mathematics University of Twente 7500AE Enschede, The Netherlands · Dipartimento di Matematica Università degli Studi di Torino via Carlo Alberto 10, 10123 Torino, Italy

  2. A cylindrical neural approximation theorem for conditional laws of McKean-Vlasov equations with common noise

    Aug 8, 2026Nacira Agram, Reda Hmioui, Jan RemsMean-Field TheoryNeural Network Approximation Theory

    Department of Mathematics, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden. · Digital Futures, Sweden. · Grenoble INP – Ensimag, Université Grenoble Alpes, Grenoble, France. +1

  3. Optimal Neural Network Approximation via Empirical Least Squares with Deterministic Samples

    Aug 7, 2026Xinliang Liu, Tong Mao, Jinchao XuNeural PDE SolversReLU Neural Networks

    School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China · Shenzhen Loop Area Institute, Shenzhen 518000, P. R. China

  4. Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces

    Aug 5, 2026Khemraj Shukla, George Em KarniadakisPDE Operator LearningNeural Network Approximation Theory

    Division of Applied Mathematics, Brown University Providence, Rhode Island 02912, USA

  5. Do Neural Networks Really Beat the Curse of Dimensionality? A Bit-Complexity View

    Aug 2, 2026Tong Mao, Jinchao XuNeural Network Approximation Theory

    King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia

  6. Fractional Parabolic Partial Differential Equations in Anisotropic Spectral Barron Spaces: Regularity and Neural Approximation

    Jul 30, 2026Jae-Hwan Choi, Hyojae Lim, Jinsol Seo +2Neural PDE SolversPDE Solving

  7. Error Analysis of Neural-Network-Based Engression

    Jul 30, 2026Juntong Chen, Zijian Guo, Xinwei ShenConditional Distribution EstimationNeural Network Approximation Theory

    School of Mathematical Sciences, Xiamen University · Center for Data Science, Zhejiang University · Department of Statistics, University of Washington

  8. Universality and Approximation Rates of Graph Neural Networks with Random Features

    Jul 29, 2026Lukas Gonon, Thilo Meyer-Brandis, Niklas WeberGraph Neural NetworksEquivariant Neural Networks

    School of Computer Science University of St. Gallen St. Gallen, 9000, Switzerland · Department of Mathematics LMU Munich Munich, 80333, Germany

  9. Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks

    Jul 28, 2026Yunwei Ren, Zihao Wang, Jason D. LeeBoolean Function LearningNeural Network Approximation Theory

    Princeton University · Stanford University · University of California, Berkeley

  10. Operator Neural Jump ODEs: L2L^2-optimal prediction in function spaces

    Jul 25, 2026Florian Krach, Oliver Löthgren, Josef TeichmannTime Series ForecastingNeural Network Approximation Theory

    Department of Mathematics ETH Zurich

  11. Shallower ReLU Network Representations via Exact Linear Algebra

    Jul 22, 2026Kilian Rueß, Gennadiy Averkov, Florestan Brunck +7Shallow Neural NetworksReLU Neural Networks

    University of Technology Nuremberg · Brandenburg University of Technology Cottbus–Senftenberg · University of Copenhagen +3

  12. Local Stability and Gaussian Smoothing of Quantized Neural Networks

    Jul 22, 2026Sergey Salishev, Anton Makarov, Oleg GranichinNeural Network Activation FunctionsNeural Network Approximation Theory

    St. Petersburg State University, 199034, Saint Petersburg, Russia

  13. Boundary-Adapted PINNs for Elliptic Dirichlet Problems: H2(Ω)H^2(Ω) A Priori Error Bounds with Application to Mean Escape Time Computation

    Jul 21, 2026Nathanael Tepakbong, Jun Fan, Xiang Zhou +1PDE SolvingNeural Network Approximation Theory

    Department of Data Science, City University of Hong Kong · Department of Mathematics, Hong Kong Baptist University · Department of Mathematics, City University of Hong Kong +1

  14. Neural network realization of binary refinement iterates via a two-chart atlas selector

    Jul 21, 2026Tsogtgerel GantumurReLU Neural NetworksNeural Network Approximation Theory

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

  15. Functional Equivalence and Geometric Diversity in Neural Network Approximations: An Empirical Characterization

    Jul 21, 2026Anuragine S A, Prem JagadeesanMultilayer PerceptronsNeural Representation Geometry

    Amrita School of Artificial Intelligence Amrita Vishwa Vidyapeetham, Coimbatore, India

  16. Expressivity of Shallow Neural Networks Over Finite Fields

    Jul 19, 2026Maksym Zubkov, Carol Wu, Shiwei Yang +2Shallow Neural NetworksPolynomial Neural Networks

    Department of Mathematics, University of British Columbia, 1984 Mathematics Rd, Vancouver, V6T 1Z2, BC, Canada

  17. Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning

    Jul 17, 2026Ronald KatendePrimal-Dual OptimizationNeural PDE Solvers

    Department of Mathematics Kabale University Kikungiri Hill, Katuna Road, Kabale, Uganda

  18. NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes

    Jul 15, 2026Anastasis Kratsios, Giulia Livieri, Philipp SchmockerNeural Network Approximation TheoryNeural Operators

  19. Approximation of solutions of parameter-dependent problems by residual neural networks

    Jul 15, 2026Ana CarpioNeural Surrogate ModelingNeural Network Optimization

    Universidad Complutense de Madrid, Spain

  20. Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width

    Jul 12, 2026Yanming Lai, Defeng Sun, Yang WangReLU Neural NetworksNeural Network Approximation Theory

    Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, China · Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong, China

  21. All you need is SAMPAT

    Jul 10, 2026Jayadeva, Madhur AswaniShallow Neural NetworksInterpretable ML

    Department of Electrical Engineering, Indian Institute of Technology, Delhi

  22. An optimal control approach for neural network architecture adaptation with a posteriori error estimation

    Jul 8, 2026C G Krishnanunni, Thomas Scott, Tan Bui-ThanhNeural Network Approximation Theory

    Department of Aerospace Engineering & Engineering Mechanics, UT Austin · Oden Institute for Computational Engineering and Sciences, UT Austin.

  23. On Explicit Super-Expressive Approximation for Neural Networks

    Jul 7, 2026Feng-Lei Fan, Ze-Yu Li, Chen-Yu Wang +1Neural Network Approximation TheoryNeural Network Expressivity

    Department of Data Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Kowloon, Hong Kong. · Department of Mathematics, Chinese University of Hong Kong, University Avenue, Shatin, N.T., Hong Kong. · School of Civil Engineering and Architecture, Guangxi Minzu University, Nanning 530006, China.

  24. A Function-Space Dichotomy for Compositional Learning: Exponential Sub-Optimality of the Neural Tangent Kernel

    Jul 7, 2026Arkaprabha Ganguli, Emil ConstantinescuNeural Network GeneralizationKernel Regression

    Mathematics & Computer Science Division, Argonne National Laboratory, Lemont, IL, USA

  25. Deep Neural Variation Spaces: A Unifying Perspective on Depth and Complexity

    Jul 6, 2026Julia Nakhleh, Robert D. NowakReLU Neural NetworksNeural Network Approximation Theory

    Department of Computer Science · University of Wisconsin-Madison · Department of Electrical & Computer Engineering

  26. Minimum Block Width for Universal Approximation by Residual Neural Networks with Inner Width One

    Jul 6, 2026Qi Zhou, Xuan Zhou, Xiao-Song YangReLU Neural NetworksResidual 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.

  27. A Unified Framework for Quantized and Continuous Strong Lottery Tickets

    Jul 4, 2026Aakash Kumar, Emanuele NataleNeural Network Approximation TheoryNeural Network Quantization

    COATI, CNRS, Inria, I3S, Université Coté d’Azur, France

  28. Foundations of Equivariant Deep Learning: Unifying Graph and Sheaf Neural Networks

    Jul 4, 2026Yoshihiro MaruyamaGraph Neural NetworksEquivariant Neural Networks

    Department of Mathematical and Information Sciences, Kyoto University, Kyoto, Japan.

  29. LRX-PINN: A Layer-Resolving XNet Physics-Informed Neural Network with Integrated Cauchy Activations for Convection-Dominated Problems

    Jul 4, 2026Zihao Guo, Xin Li, Zhihong XiaNeural PDE SolversPDE Solving

    Institute for Advanced Research, Great Bay University, Dongguan, China · College of Computer Science and Technology, Dongguan University of Technology, Dongguan, China · Department of Mathematics, Northwestern University, Evanston, USA

  30. Rethinking Neural Nonlinearity as Gating

    Jul 3, 2026Muhammad Sabih, Frank Hannig, Jürgen TeichNeural Network Activation FunctionsNeural Network Approximation Theory

    Department of Computer Science, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Germany