{"total":51,"rows":[{"id":"2105.14835","title":"Towards Lower Bounds on the Depth of ReLU Neural Networks","created":"2021-05-31","cited_by_count":56,"area":null},{"id":"2109.09710","title":"Understanding neural networks with reproducing kernel Banach spaces","created":"2021-09-20","cited_by_count":50,"area":null},{"id":"2101.05390","title":"Universal Approximation Theorems for Differentiable Geometric Deep Learning","created":"2021-01-13","cited_by_count":41,"area":null},{"id":"2212.03130","title":"Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems","created":"2022-12-06","cited_by_count":34,"area":null},{"id":"2307.06555","title":"Deep Network Approximation: Beyond ReLU to Diverse Activation Functions","created":"2023-07-13","cited_by_count":33,"area":null},{"id":"2104.02746","title":"Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces","created":"2021-04-06","cited_by_count":30,"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":"2201.13094","title":"Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer","created":"2022-01-31","cited_by_count":22,"area":null},{"id":"2205.09459","title":"Neural Network Architecture Beyond Width and Depth","created":"2022-05-19","cited_by_count":17,"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":"2111.07964","title":"Deep Network Approximation in Terms of Intrinsic Parameters","created":"2021-11-15","cited_by_count":12,"area":null},{"id":"2107.14742","title":"Connections between Numerical Algorithms for PDEs and Neural Networks","created":"2021-07-30","cited_by_count":10,"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":"2103.00542","title":"Deep Neural Networks with ReLU-Sine-Exponential Activations Break Curse of Dimensionality in Approximation on H\\\"older Class","created":"2021-02-28","cited_by_count":7,"area":null},{"id":"2108.04964","title":"A spectral-based analysis of the separation between two-layer neural networks and linear methods","created":"2021-08-10","cited_by_count":7,"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":"2204.11231","title":"Do ReLU Networks Have An Edge When Approximating Compactly-Supported Functions?","created":"2022-04-24","cited_by_count":6,"area":null},{"id":"2301.12353","title":"On Enhancing Expressive Power via Compositions of Single Fixed-Size ReLU Network","created":"2023-01-29","cited_by_count":6,"area":null},{"id":"2112.09181","title":"Approximation of functions with one-bit neural networks","created":"2021-12-16","cited_by_count":5,"area":null},{"id":"2105.07743","title":"Universal Regular Conditional Distributions","created":"2021-05-17","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":"2502.18959","title":"Fourier Multi-Component and Multi-Layer Neural Networks: Unlocking High-Frequency Potential","created":"2025-02-26","cited_by_count":4,"area":null},{"id":"2504.15110","title":"Approximation Rates in Besov Norms and Sample-Complexity of Kolmogorov-Arnold Networks with Residual Connections","created":"2025-04-21","cited_by_count":4,"area":null},{"id":"2511.01125","title":"One model to solve them all: 2BSDE families via neural operators","created":"2025-11-03","cited_by_count":4,"area":null},{"id":"2101.11932","title":"Approximation Theory of Tree Tensor Networks: Tensorized Multivariate Functions","created":"2021-01-28","cited_by_count":3,"area":null},{"id":"2108.13993","title":"Designing Rotationally Invariant Neural Networks from PDEs and Variational Methods","created":"2021-08-31","cited_by_count":3,"area":null},{"id":"2201.12795","title":"Training Thinner and Deeper Neural Networks: Jumpstart Regularization","created":"2022-01-30","cited_by_count":3,"area":null},{"id":"2305.16910","title":"Universal approximation with complex-valued deep narrow neural networks","created":"2023-05-26","cited_by_count":3,"area":null},{"id":"2407.00765","title":"Structured and Balanced Multi-Component and Multi-Layer Neural Networks","created":"2024-06-30","cited_by_count":3,"area":null},{"id":"2111.00215","title":"Approximation properties of Residual Neural Networks for Kolmogorov PDEs","created":"2021-10-30","cited_by_count":2,"area":null},{"id":"2112.11157","title":"Integral representations of shallow neural network with Rectified Power Unit activation function","created":"2021-12-20","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":"2301.01327","title":"Operator theory, kernels, and Feedforward Neural Networks","created":"2023-01-03","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":"2311.03242","title":"Approximating Langevin Monte Carlo with ResNet-like Neural Network architectures","created":"2023-11-06","cited_by_count":2,"area":null},{"id":"2401.07874","title":"Do stable neural networks exist for classification problems? -- A new view on stability in AI","created":"2024-01-15","cited_by_count":2,"area":null},{"id":"2411.11242","title":"Mirror Descent on Reproducing Kernel Banach Spaces","created":"2024-11-18","cited_by_count":2,"area":null},{"id":"2508.18408","title":"Low-Rank Tensor Decompositions for the Theory of Neural Networks","created":"2025-08-25","cited_by_count":2,"area":null},{"id":"2508.19672","title":"$\\mathcal{C}^1$-approximation with rational functions and rational neural networks","created":"2025-08-27","cited_by_count":2,"area":null},{"id":"2601.16884","title":"Multigrade Neural Network Approximation","created":"2026-01-23","cited_by_count":2,"area":null},{"id":"2110.15304","title":"Sobolev-type embeddings for neural network approximation spaces","created":"2021-10-28","cited_by_count":1,"area":null},{"id":"2312.13379","title":"Sampling Complexity of Deep Approximation Spaces","created":"2023-12-20","cited_by_count":1,"area":null},{"id":"2401.10310","title":"Mathematical Algorithm Design for Deep Learning under Societal and Judicial Constraints: The Algorithmic Transparency Requirement","created":"2024-01-18","cited_by_count":1,"area":null},{"id":"2402.00094","title":"Deep Neural Networks: A Formulation Via Non-Archimedean Analysis","created":"2024-01-31","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":"2407.11678","title":"Theoretical Insights into CycleGAN: Analyzing Approximation and Estimation Errors in Unpaired Data Generation","created":"2024-07-16","cited_by_count":1,"area":null},{"id":"2406.14936","title":"On the growth of the parameters of approximating ReLU neural networks","created":"2024-06-21","cited_by_count":0,"area":null},{"id":"2508.17167","title":"Error analysis for the deep Kolmogorov method","created":"2025-08-23","cited_by_count":0,"area":null},{"id":"2606.20417","title":"Neural network surrogates with uncertainty quantification for inverse problems in partial differential equations","created":"2026-06-18","cited_by_count":0,"area":null}],"next_cursor":null}