Curse of Dimensionality

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9 papers2 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

Kolmogorov-Arnold Networks: Curse of Dimensionality and Structural Bias
Oct 15, 2026Yunhao Ni, Yuxin Guo, Jie Luo +2Curse of Dimensionality Kolmogorov-Arnold Networks
State Key Laboratory of Complex and Critical Software Environment, Beihang University, Beijing, China · Hangzhou International Innovation Institute, Beihang University, Hangzhou, China
Kolmogorov-Arnold Classifier Systems as Universal Approximators
Sep 29, 2026Hiroki Shiraishi, Hisao Ishibuchi, Masaya NakataUniversal Approximation Function 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
Residual neural networks overcome the curse of dimensionality for semilinear heat equations
Sep 3, 2026Ilkhom Mukhammadiev, Diyora SalimovaNeural PDE Solvers PDE Solving
Department of Applied Mathematics, University of Freiburg, Germany
Why Large Language Models Fail at Tabular Prediction
Aug 3, 2026Marta Garnelo, Wojciech M. CzarneckiLLM Evaluation Tabular Classification
Fundamental Technologies
Do Neural Networks Really Beat the Curse of Dimensionality? A Bit-Complexity View
Aug 2, 2026Tong Mao, Jinchao XuCurse of Dimensionality Neural Network Approximation Theory
King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia
Mitigating the Curse of Dimensionality in Uniform Convergence of Deep Neural Networks via Smooth Activations
Jun 4, 2026Yizhe Ding, Runze Li, Jia Liu +1ReLU Neural Networks Curse of Dimensionality
Department of Statistics, The Pennsylvania State University
Support-Conditioned Flow Matching Is Kernel Smoothing
May 13, 2026Daniel Matsui SmolaFlow Matching Cross-Attention
Department of Computer Science University of Washington Seattle, WA
Sparse-Aware Neural Networks for Nonlinear Functionals: Mitigating the Exponential Dependence on Dimension
Apr 8, 2026Jianfei Li, Shuo Huang, Han Feng +2Curse of Dimensionality Neural Network Approximation Theory
Department of Mathematics, Ludwig-Maximilians-Universität München (LMU Munich), Akademiestr. 7, 80799 München · Department of Mathematics, City University of Hong Kong, Hong Kong, China · School of Mathematics and Statistics, The University of Sydney, Sydney, New South Wales 2006, Australia +3
Localized Diffusion Models
May 7, 2025Georg A. Gottwald, Shuigen Liu, Youssef Marzouk +2Curse of Dimensionality Score-Based Generative Modeling
School of Mathematics and Statistics, The University of Sydney · Department of Mathematics, National University of Singapore · Laboratory for Information and Decision Systems, Massachusetts Institute of Technology +1

Oct 15, 2026J/K move · Enter open · S save

Kolmogorov-Arnold Networks: Curse of Dimensionality and Structural Bias

Yunhao Ni, Yuxin Guo, Jie Luo, Wenjun Wu+1

State Key Laboratory of Complex and Critical Software Environment, Beihang University, Beijing, China · Hangzhou International Innovation Institute, Beihang University, Hangzhou, China

Curse of Dimensionality Kolmogorov-Arnold Networks Neural Network Approximation Theory Neural Network Generalization Multilayer Perceptrons

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Kolmogorov-Arnold networks (KANs) have a dimension-independent approximation exponent when the target admits a sufficiently smooth representation by univariate edge functions. We ask whether this favorable scaling belongs to the architecture or to the assumed target class. For arbitrary-depth standard spline-KANs, we prove a worst-case lower bound on isotropic Sobolev balls: below a dimension-independent accuracy threshold, the required number of spline coefficients grows at least exponentially with input dimension. Existing composition-matched MLP results, by contrast, show that favorable exponents on low-arity targets are not exclusive to KANs. We also revisit empirical comparisons. On four scaling-law targets, spline-KAN approximants constructed from known decompositions transfer exactly to MLPs with the cubic ReLU activation

σ(x)=(\max\{0,x\})^3

, although their full dense parameter counts are larger. In controlled ridge-profile scans, KANs have a strong advantage when each nonlinear component depends on one input coordinate. When a component couples multiple input coordinates, this advantage may narrow sharply. At tight budgets, interacting targets often favor MLPs. In the random-label test on MNIST, ReLU-MLPs fit the randomized training labels more efficiently than spline-only KANs. Together, these results locate favorable scaling in target structure and a compatible inductive bias, not a general KAN-specific escape from the curse of dimensionality.