Optimal approximation of piecewise smooth functions using deep ReLU neural networks

15 September 2017

Papers citing "Optimal approximation of piecewise smooth functions using deep ReLU neural networks"

50 / 70 papers shown

Title
Super-fast rates of convergence for Neural Networks Classifiers under the Hard Margin Condition Nathanael Tepakbong Ding-Xuan Zhou Xiang Zhou 39 0 0 13 May 2025
Universal Approximation Theorem of Deep Q-Networks Qian Qi 37 1 0 04 May 2025
Extended Fiducial Inference for Individual Treatment Effects via Deep Neural Networks Sehwan Kim F. Liang FedML 57 0 0 04 May 2025
An extension of linear self-attention for in-context learning Katsuyuki Hagiwara 41 0 0 31 Mar 2025
Learning with Noisy Labels: the Exploration of Error Bounds in Classification Haixia Liu Boxiao Li Can Yang Yang Wang 41 0 0 28 Jan 2025
Higher Order Approximation Rates for ReLU CNNs in Korobov Spaces Yuwen Li Guozhi Zhang 46 1 0 20 Jan 2025
High-dimensional classification problems with Barron regular boundaries under margin conditions Jonathan García Philipp Petersen 74 1 0 10 Dec 2024
On the optimal approximation of Sobolev and Besov functions using deep ReLU neural networks Yunfei Yang 62 2 0 02 Sep 2024
Model Free Prediction with Uncertainty Assessment Yuling Jiao Lican Kang Jin Liu Heng Peng Heng Zuo DiffM 34 0 0 21 May 2024
Approximation Error and Complexity Bounds for ReLU Networks on Low-Regular Function Spaces Owen Davis Gianluca Geraci Mohammad Motamed 46 2 0 10 May 2024
Universal Consistency of Wide and Deep ReLU Neural Networks and Minimax Optimal Convergence Rates for Kolmogorov-Donoho Optimal Function Classes Hyunouk Ko Xiaoming Huo 39 1 0 08 Jan 2024
Understanding Vector-Valued Neural Networks and Their Relationship with Real and Hypercomplex-Valued Neural Networks Marcos Eduardo Valle 19 3 0 14 Sep 2023
Fundamental Limits of Deep Learning-Based Binary Classifiers Trained with Hinge Loss T. Getu Georges Kaddoum M. Bennis 40 1 0 13 Sep 2023
Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution Elen Vardanyan Sona Hunanyan T. Galstyan A. Minasyan A. Dalalyan 37 2 0 31 Jul 2023
Rates of Approximation by ReLU Shallow Neural Networks Tong Mao Ding-Xuan Zhou 29 19 0 24 Jul 2023
Deep neural network approximation of composite functions without the curse of dimensionality Adrian Riekert 24 0 0 12 Apr 2023
Approximation of Nonlinear Functionals Using Deep ReLU Networks Linhao Song Jun Fan Dirong Chen Ding-Xuan Zhou 15 14 0 10 Apr 2023
Limitations on approximation by deep and shallow neural networks G. Petrova P. Wojtaszczyk 19 7 0 30 Nov 2022
NEON: Enabling Efficient Support for Nonlinear Operations in Resistive RAM-based Neural Network Accelerators Aditya Manglik Minesh Patel Haiyu Mao Behzad Salami Jisung Park Lois Orosa O. Mutlu 17 1 0 10 Nov 2022
Deep neural network expressivity for optimal stopping problems Lukas Gonon 24 6 0 19 Oct 2022
Limitations of neural network training due to numerical instability of backpropagation Clemens Karner V. Kazeev P. Petersen 32 3 0 03 Oct 2022
Approximation results for Gradient Descent trained Shallow Neural Networks in $1d$ R. Gentile G. Welper ODL 52 6 0 17 Sep 2022
Extending the Universal Approximation Theorem for a Broad Class of Hypercomplex-Valued Neural Networks Wington L. Vital Guilherme Vieira Marcos Eduardo Valle 15 5 0 06 Sep 2022
Optimal Convergence Rates of Deep Neural Networks in a Classification Setting Josephine T. Meyer 24 2 0 25 Jul 2022
Approximating Discontinuous Nash Equilibrial Values of Two-Player General-Sum Differential Games Lei Zhang Mukesh Ghimire Wenlong Zhang Zhenni Xu Yi Ren 24 7 0 05 Jul 2022
A general approximation lower bound in $L^p$ norm, with applications to feed-forward neural networks E. M. Achour Armand Foucault Sébastien Gerchinovitz Franccois Malgouyres 32 7 0 09 Jun 2022
Deep Neural Network Classifier for Multi-dimensional Functional Data Shuoyang Wang Guanqun Cao Zuofeng Shang 29 12 0 17 May 2022
On the inability of Gaussian process regression to optimally learn compositional functions M. Giordano Kolyan Ray Johannes Schmidt-Hieber 39 12 0 16 May 2022
Robust stabilization of polytopic systems via fast and reliable neural network-based approximations F. Fabiani Paul Goulart 17 5 0 27 Apr 2022
Qualitative neural network approximation over R and C: Elementary proofs for analytic and polynomial activation Josiah Park Stephan Wojtowytsch 26 1 0 25 Mar 2022
De Rham compatible Deep Neural Network FEM M. Longo J. Opschoor Nico Disch Christoph Schwab Jakob Zech 19 8 0 14 Jan 2022
Optimal learning of high-dimensional classification problems using deep neural networks P. Petersen F. Voigtlaender 33 10 0 23 Dec 2021
The Geometry of Adversarial Training in Binary Classification Leon Bungert Nicolas García Trillos Ryan W. Murray AAML 27 22 0 26 Nov 2021
$Deep Learning in High Dimension: Neural Network Approximation of Analytic Functions in $L^2(\mathbb{R}^d,γ_d)$$ Deep Learning in High Dimension: Neural Network Approximation of Analytic Functions in $L^2(\mathbb{R}^d,γ_d)$ Christoph Schwab Jakob Zech 14 3 0 13 Nov 2021
Deep Network Approximation: Achieving Arbitrary Accuracy with Fixed Number of Neurons Zuowei Shen Haizhao Yang Shijun Zhang 56 36 0 06 Jul 2021
Theory of Deep Convolutional Neural Networks III: Approximating Radial Functions Tong Mao Zhongjie Shi Ding-Xuan Zhou 16 33 0 02 Jul 2021
Layer Folding: Neural Network Depth Reduction using Activation Linearization Amir Ben Dror Niv Zehngut Avraham Raviv E. Artyomov Ran Vitek R. Jevnisek 29 20 0 17 Jun 2021
Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces Philipp Grohs F. Voigtlaender 13 34 0 06 Apr 2021
A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equations N. R. Franco Andrea Manzoni P. Zunino 26 45 0 10 Mar 2021
Optimal Approximation Rate of ReLU Networks in terms of Width and Depth Zuowei Shen Haizhao Yang Shijun Zhang 101 115 0 28 Feb 2021
Quantitative approximation results for complex-valued neural networks A. Caragea D. Lee J. Maly G. Pfander F. Voigtlaender 13 5 0 25 Feb 2021
Convergence of stochastic gradient descent schemes for Lojasiewicz-landscapes Steffen Dereich Sebastian Kassing 34 27 0 16 Feb 2021
Size and Depth Separation in Approximating Benign Functions with Neural Networks Gal Vardi Daniel Reichman T. Pitassi Ohad Shamir 26 7 0 30 Jan 2021
Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data Ben Adcock Simone Brugiapaglia N. Dexter S. Moraga 34 29 0 11 Dec 2020
The universal approximation theorem for complex-valued neural networks F. Voigtlaender 27 62 0 06 Dec 2020
Neural Network Approximation: Three Hidden Layers Are Enough Zuowei Shen Haizhao Yang Shijun Zhang 30 115 0 25 Oct 2020
Phase Transitions in Rate Distortion Theory and Deep Learning Philipp Grohs Andreas Klotz F. Voigtlaender 14 7 0 03 Aug 2020
Approximation of Smoothness Classes by Deep Rectifier Networks Mazen Ali A. Nouy 9 9 0 30 Jul 2020
Expressivity of Deep Neural Networks Ingo Gühring Mones Raslan Gitta Kutyniok 16 51 0 09 Jul 2020
Approximation in shift-invariant spaces with deep ReLU neural networks Yunfei Yang Zhen Li Yang Wang 34 14 0 25 May 2020