{"total":84,"rows":[{"id":"2101.12365","title":"Sharp Bounds on the Approximation Rates, Metric Entropy, and $n$-widths of Shallow Neural Networks","created":"2021-01-29","cited_by_count":86,"area":null},{"id":"2211.14400","title":"Optimal Approximation Rates for Deep ReLU Neural Networks on Sobolev and Besov Spaces","created":"2022-11-25","cited_by_count":51,"area":null},{"id":"2106.15002","title":"Characterization of the Variation Spaces Corresponding to Shallow Neural Networks","created":"2021-06-28","cited_by_count":48,"area":null},{"id":"2109.08844","title":"Near-Minimax Optimal Estimation With Shallow ReLU Neural Networks","created":"2021-09-18","cited_by_count":41,"area":null},{"id":"2410.01803","title":"On the expressiveness and spectral bias of KANs","created":"2024-10-02","cited_by_count":37,"area":null},{"id":"2106.08900","title":"Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality","created":"2021-06-14","cited_by_count":34,"area":null},{"id":"2102.02336","title":"On the Approximation Power of Two-Layer Networks of Random ReLUs","created":"2021-02-03","cited_by_count":29,"area":null},{"id":"2206.09527","title":"Simultaneous approximation of a smooth function and its derivatives by deep neural networks with piecewise-polynomial activations","created":"2022-06-20","cited_by_count":29,"area":null},{"id":"2305.18475","title":"Approximation Rate of the Transformer Architecture for Sequence Modeling","created":"2023-05-29","cited_by_count":28,"area":null},{"id":"2304.06094","title":"Energy-guided Entropic Neural Optimal Transport","created":"2023-04-12","cited_by_count":26,"area":null},{"id":"2106.07539","title":"On the Representation of Solutions to Elliptic PDEs in Barron Spaces","created":"2021-06-14","cited_by_count":25,"area":null},{"id":"2306.08321","title":"Nonparametric regression using over-parameterized shallow ReLU neural networks","created":"2023-06-14","cited_by_count":24,"area":null},{"id":"2107.00896","title":"Theory of Deep Convolutional Neural Networks III: Approximating Radial Functions","created":"2021-07-02","cited_by_count":22,"area":null},{"id":"2105.01228","title":"A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schr\\\"odinger Eigenvalue Problems","created":"2021-05-04","cited_by_count":19,"area":null},{"id":"2101.01708","title":"A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations","created":"2021-01-05","cited_by_count":18,"area":null},{"id":"2102.01621","title":"Depth separation beyond radial functions","created":"2021-02-02","cited_by_count":18,"area":null},{"id":"2109.00190","title":"Approximation Properties of Deep ReLU CNNs","created":"2021-09-01","cited_by_count":15,"area":null},{"id":"2304.01561","title":"Optimal rates of approximation by shallow ReLU$^k$ neural networks and applications to nonparametric regression","created":"2023-04-04","cited_by_count":15,"area":null},{"id":"2302.07937","title":"The Expressive Power of Tuning Only the Normalization Layers","created":"2023-02-15","cited_by_count":13,"area":null},{"id":"2308.05509","title":"On the Optimal Expressive Power of ReLU DNNs and Its Application in Approximation with Kolmogorov Superposition Theorem","created":"2023-08-10","cited_by_count":13,"area":null},{"id":"2105.04156","title":"ReLU Deep Neural Networks from the Hierarchical Basis Perspective","created":"2021-05-10","cited_by_count":12,"area":null},{"id":"2210.13601","title":"Active Learning for Single Neuron Models with Lipschitz Non-Linearities","created":"2022-10-24","cited_by_count":12,"area":null},{"id":"2307.12461","title":"Rates of Approximation by ReLU Shallow Neural Networks","created":"2023-07-24","cited_by_count":12,"area":null},{"id":"2402.08082","title":"Score-based generative models break the curse of dimensionality in learning a family of sub-Gaussian probability distributions","created":"2024-02-12","cited_by_count":12,"area":"diffusion"},{"id":"2307.15285","title":"Optimal Approximation of Zonoids and Uniform Approximation by Shallow Neural Networks","created":"2023-07-28","cited_by_count":11,"area":null},{"id":"2101.03906","title":"Scaling Up Bayesian Uncertainty Quantification for Inverse Problems using Deep Neural Networks","created":"2021-01-11","cited_by_count":10,"area":null},{"id":"2309.16200","title":"Max-Sliced Mutual Information","created":"2023-09-28","cited_by_count":10,"area":null},{"id":"2112.12555","title":"Optimal learning of high-dimensional classification problems using deep neural networks","created":"2021-12-23","cited_by_count":9,"area":null},{"id":"2210.14184","title":"Learning Ability of Interpolating Deep Convolutional Neural Networks","created":"2022-10-25","cited_by_count":9,"area":null},{"id":"2305.00608","title":"Differentiable Neural Networks with RePU Activation: with Applications to Score Estimation and Isotonic Regression","created":"2023-05-01","cited_by_count":9,"area":null},{"id":"2312.16483","title":"Expressivity and Approximation Properties of Deep Neural Networks with ReLU$^k$ Activation","created":"2023-12-27","cited_by_count":9,"area":null},{"id":"2205.14421","title":"Approximation of Functionals by Neural Network without Curse of Dimensionality","created":"2022-05-28","cited_by_count":8,"area":null},{"id":"2304.04443","title":"Approximation of Nonlinear Functionals Using Deep ReLU Networks","created":"2023-04-10","cited_by_count":8,"area":null},{"id":"2404.18769","title":"Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks","created":"2024-04-29","cited_by_count":8,"area":null},{"id":"2209.08399","title":"Approximation results for Gradient Descent trained Shallow Neural Networks in $1d$","created":"2022-09-17","cited_by_count":7,"area":null},{"id":"2307.15772","title":"Weighted variation spaces and approximation by shallow ReLU networks","created":"2023-07-28","cited_by_count":7,"area":null},{"id":"2403.08121","title":"Early Directional Convergence in Deep Homogeneous Neural Networks for Small Initializations","created":"2024-03-12","cited_by_count":7,"area":null},{"id":"2208.07605","title":"$L^p$ sampling numbers for the Fourier-analytic Barron space","created":"2022-08-16","cited_by_count":6,"area":null},{"id":"2210.09041","title":"Approximation analysis of CNNs from a feature extraction view","created":"2022-10-14","cited_by_count":6,"area":null},{"id":"2408.10996","title":"Approximation Rates for Shallow ReLU$^k$ Neural Networks on Sobolev Spaces via the Radon Transform","created":"2024-08-20","cited_by_count":6,"area":null},{"id":"2508.05141","title":"Deep Neural Networks with General Activations: Super-Convergence in Sobolev Norms","created":"2025-08-07","cited_by_count":6,"area":null},{"id":"2206.05669","title":"Universality and approximation bounds for echo state networks with random weights","created":"2022-06-12","cited_by_count":5,"area":null},{"id":"2312.08461","title":"Space-Time Approximation with Shallow Neural Networks in Fourier Lebesgue spaces","created":"2023-12-13","cited_by_count":5,"area":null},{"id":"2406.02529","title":"ReLUs Are Sufficient for Learning Implicit Neural Representations","created":"2024-06-04","cited_by_count":5,"area":null},{"id":"2110.08996","title":"Finding Everything within Random Binary Networks","created":"2021-10-18","cited_by_count":4,"area":null},{"id":"2112.14877","title":"A Unified and Constructive Framework for the Universality of Neural Networks","created":"2021-12-30","cited_by_count":4,"area":null},{"id":"2209.01173","title":"Optimal bump functions for shallow ReLU networks: Weight decay, depth separation and the curse of dimensionality","created":"2022-09-02","cited_by_count":4,"area":null},{"id":"2210.10264","title":"SignReLU neural network and its approximation ability","created":"2022-10-19","cited_by_count":4,"area":null},{"id":"2308.03230","title":"Tractability of approximation by general shallow networks","created":"2023-08-07","cited_by_count":4,"area":null},{"id":"2311.04779","title":"Optimal Deep Neural Network Approximation for Korobov Functions with respect to Sobolev Norms","created":"2023-11-08","cited_by_count":4,"area":null},{"id":"2110.03673","title":"Tighter Sparse Approximation Bounds for ReLU Neural Networks","created":"2021-10-07","cited_by_count":3,"area":null},{"id":"2211.08900","title":"Convergence analysis of unsupervised Legendre-Galerkin neural networks for linear second-order elliptic PDEs","created":"2022-11-16","cited_by_count":3,"area":null},{"id":"2302.00834","title":"Sharp Lower Bounds on Interpolation by Deep ReLU Neural Networks at Irregularly Spaced Data","created":"2023-02-02","cited_by_count":3,"area":null},{"id":"2501.02791","title":"Orthogonal greedy algorithm for linear operator learning with shallow neural network","created":"2025-01-06","cited_by_count":3,"area":null},{"id":"2106.04795","title":"Nonasymptotic theory for two-layer neural networks: Beyond the bias-variance trade-off","created":"2021-06-09","cited_by_count":2,"area":null},{"id":"2203.13410","title":"Qualitative neural network approximation over R and C: Elementary proofs for analytic and polynomial activation","created":"2022-03-25","cited_by_count":2,"area":null},{"id":"2305.00723","title":"Predictions Based on Pixel Data: Insights from PDEs and Finite Differences","created":"2023-05-01","cited_by_count":2,"area":null},{"id":"2307.07679","title":"Sharp Convergence Rates for Matching Pursuit","created":"2023-07-15","cited_by_count":2,"area":null},{"id":"2309.04860","title":"Approximation Results for Gradient Descent trained Neural Networks","created":"2023-09-09","cited_by_count":2,"area":null},{"id":"2408.05540","title":"Convergence Analysis for Deep Sparse Coding via Convolutional Neural Networks","created":"2024-08-10","cited_by_count":2,"area":null},{"id":"2410.02132","title":"Nonuniform random feature models using derivative information","created":"2024-10-03","cited_by_count":2,"area":null},{"id":"2412.01619","title":"Representation and Regression Problems in Neural Networks: Relaxation, Generalization, and Numerics","created":"2024-12-02","cited_by_count":2,"area":null},{"id":"2504.04847","title":"Nonlocal techniques for the analysis of deep ReLU neural network approximations","created":"2025-04-07","cited_by_count":2,"area":null},{"id":"2506.00573","title":"Neural Estimation for Scaling Entropic Multimarginal Optimal Transport","created":"2025-05-31","cited_by_count":2,"area":null},{"id":"2511.02625","title":"Condition Numbers and Eigenvalue Spectra of Shallow Networks on Spheres","created":"2025-11-04","cited_by_count":2,"area":null},{"id":"2512.15992","title":"Time-Frequency Analysis for Neural Networks","created":"2025-12-17","cited_by_count":2,"area":null},{"id":"2301.11732","title":"Convolutional neural networks for valid and efficient causal inference","created":"2023-01-27","cited_by_count":1,"area":null},{"id":"2403.01900","title":"Universality of reservoir systems with recurrent neural networks","created":"2024-03-04","cited_by_count":1,"area":null},{"id":"2405.11696","title":"Approximation and Gradient Descent Training with Neural Networks","created":"2024-05-19","cited_by_count":1,"area":null},{"id":"2410.19300","title":"Golden Ratio-Based Sufficient Dimension Reduction","created":"2024-10-25","cited_by_count":1,"area":null},{"id":"2507.12766","title":"Layer Separation Deep Learning Model with Auxiliary Variables for Partial Differential Equations","created":"2025-07-17","cited_by_count":1,"area":null},{"id":"2510.04060","title":"Configuration-Dependent Lower Bounds for Approximation by Shallow ReLU$^k$ Networks on the Sphere","created":"2025-10-05","cited_by_count":1,"area":null},{"id":"2510.18388","title":"Approximation Rates of Shallow Neural Networks: Barron Spaces, Activation Functions and Optimality Analysis","created":"2025-10-21","cited_by_count":1,"area":null},{"id":"2602.20370","title":"Quantitative Approximation Rates for Group Equivariant Learning","created":"2026-02-23","cited_by_count":1,"area":null},{"id":"2603.03084","title":"On the Expressive Power of Transformers for Maxout Networks and Continuous Piecewise Linear Functions","created":"2026-03-03","cited_by_count":1,"area":null},{"id":"2608.01357","title":"Do Neural Networks Really Beat the Curse of Dimensionality? A Bit-Complexity View","created":"2026-08-02","cited_by_count":1,"area":null},{"id":"2509.22748","title":"Generalization Analysis for Classification on Korobov Space","created":"2025-09-26","cited_by_count":0,"area":null},{"id":"2605.22557","title":"Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations","created":"2026-05-21","cited_by_count":0,"area":null},{"id":"2606.00469","title":"Constructive interpolation and generalization rates for neural ODEs: a control perspective","created":"2026-05-30","cited_by_count":0,"area":null},{"id":"2608.06687","title":"Optimal Neural Network Approximation via Empirical Least Squares with Deterministic Samples","created":"2026-08-07","cited_by_count":0,"area":null},{"id":"2608.20812","title":"Resolution-Consistent Greedy Neural Approximation on Infinite-Dimensional Spaces","created":"2026-08-21","cited_by_count":0,"area":null},{"id":"2609.05263","title":"Shallow neural network approximation in mixed Sobolev spaces","created":"2026-09-04","cited_by_count":0,"area":null},{"id":"2609.33016","title":"Relative Generalization Invariance of LLM Pretraining","created":"2026-09-26","cited_by_count":0,"area":null},{"id":"2609.39020","title":"Minimax rates for learning spectral Barron functions by deep ReLU neural networks","created":"2026-09-30","cited_by_count":0,"area":null}],"next_cursor":null}