Neural Network Approximation: Three Hidden Layers Are Enough

25 October 2020

Papers citing "Neural Network Approximation: Three Hidden Layers Are Enough"

50 / 51 papers shown

Title
Transformers Can Overcome the Curse of Dimensionality: A Theoretical Study from an Approximation Perspective Yuling Jiao Yanming Lai Yang Wang Bokai Yan 39 0 0 18 Apr 2025
Unveiling the Potential of Superexpressive Networks in Implicit Neural Representations Uvini Balasuriya Mudiyanselage Woojin Cho Minju Jo Noseong Park Kookjin Lee 47 0 0 27 Mar 2025
From Equations to Insights: Unraveling Symbolic Structures in PDEs with LLMs Rohan Bhatnagar Ling Liang Krish Patel Haizhao Yang 36 0 0 13 Mar 2025
Curse of Dimensionality in Neural Network Optimization Sanghoon Na Haizhao Yang 56 0 0 07 Feb 2025
Solving High-Dimensional Partial Integral Differential Equations: The Finite Expression Method Gareth Hardwick Senwei Liang Haizhao Yang 31 1 0 01 Oct 2024
Don't Fear Peculiar Activation Functions: EUAF and Beyond Qianchao Wang Shijun Zhang Dong Zeng Zhaoheng Xie Hengtao Guo Feng-Lei Fan Tieyong Zeng 39 3 0 12 Jul 2024
Mixture of Experts Soften the Curse of Dimensionality in Operator Learning Anastasis Kratsios Takashi Furuya Jose Antonio Lara Benitez Matti Lassas Maarten V. de Hoop 50 13 0 13 Apr 2024
Operator Learning: Algorithms and Analysis Nikola B. Kovachki S. Lanthaler Andrew M. Stuart 46 22 0 24 Feb 2024
Deep Neural Networks and Finite Elements of Any Order on Arbitrary Dimensions Juncai He Jinchao Xu 27 7 0 21 Dec 2023
Approximating Langevin Monte Carlo with ResNet-like Neural Network architectures Charles Miranda Janina Enrica Schutte David Sommer Martin Eigel 32 3 0 06 Nov 2023
On the Kolmogorov neural networks Aysu Ismayilova V. Ismailov 31 17 0 31 Oct 2023
Deep ReLU networks and high-order finite element methods II: Chebyshev emulation J. Opschoor Christoph Schwab 34 2 0 11 Oct 2023
Solving Two-Player General-Sum Games Between Swarms Mukesh Ghimire Lei Zhang Wenlong Zhang Yi Ren Zhenni Xu 26 1 0 02 Oct 2023
Noncompact uniform universal approximation T. V. Nuland 22 5 0 07 Aug 2023
Deep Operator Network Approximation Rates for Lipschitz Operators Ch. Schwab A. Stein Jakob Zech 33 9 0 19 Jul 2023
Why Shallow Networks Struggle with Approximating and Learning High Frequency: A Numerical Study Shijun Zhang Hongkai Zhao Yimin Zhong Haomin Zhou 21 7 0 29 Jun 2023
On the Generalization and Approximation Capacities of Neural Controlled Differential Equations Linus Bleistein Agathe Guilloux 40 1 0 26 May 2023
Interpretability of Machine Learning: Recent Advances and Future Prospects Lei Gao L. Guan AAML 43 31 0 30 Apr 2023
Universal Approximation Property of Hamiltonian Deep Neural Networks M. Zakwan M. d’Angelo Giancarlo Ferrari-Trecate 33 5 0 21 Mar 2023
On Enhancing Expressive Power via Compositions of Single Fixed-Size ReLU Network Shijun Zhang Jianfeng Lu Hongkai Zhao CoGe 30 4 0 29 Jan 2023
Inference on Time Series Nonparametric Conditional Moment Restrictions Using General Sieves Xiaohong Chen Yuan Liao Weichen Wang 17 0 0 31 Dec 2022
Deep Neural Network Approximation of Invariant Functions through Dynamical Systems Qianxiao Li T. Lin Zuowei Shen 21 6 0 18 Aug 2022
Expressive power of binary and ternary neural networks A. Beknazaryan MQ 13 0 0 27 Jun 2022
Concentration inequalities and optimal number of layers for stochastic deep neural networks Michele Caprio Sayan Mukherjee BDL 19 1 0 22 Jun 2022
Finite Expression Method for Solving High-Dimensional Partial Differential Equations Senwei Liang Haizhao Yang 31 18 0 21 Jun 2022
Simultaneous approximation of a smooth function and its derivatives by deep neural networks with piecewise-polynomial activations Denis Belomestny A. Naumov Nikita Puchkin S. Samsonov 11 20 0 20 Jun 2022
Data-Efficient Modeling for Precise Power Consumption Estimation of Quadrotor Operations Using Ensemble Learning Wei Dai Mingcheng Zhang K. H. Low 17 2 0 23 May 2022
Neural Network Architecture Beyond Width and Depth Zuowei Shen Haizhao Yang Shijun Zhang 3DV MDE 33 13 0 19 May 2022
A scalable deep learning approach for solving high-dimensional dynamic optimal transport Wei Wan Yuejin Zhang Chenglong Bao Bin Dong Zuoqiang Shi 19 5 0 16 May 2022
KASAM: Spline Additive Models for Function Approximation H. V. Deventer P. V. Rensburg Anna Sergeevna Bosman KELM CLL 14 3 0 12 May 2022
A Note on Machine Learning Approach for Computational Imaging Bin Dong 26 0 0 24 Feb 2022
Stochastic Causal Programming for Bounding Treatment Effects Kirtan Padh Jakob Zeitler David S. Watson Matt J. Kusner Ricardo M. A. Silva Niki Kilbertus CML 28 26 0 22 Feb 2022
Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer Beatrice Acciaio Anastasis Kratsios G. Pammer OOD 49 20 0 31 Jan 2022
Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces Hao Liu Haizhao Yang Minshuo Chen T. Zhao Wenjing Liao 32 36 0 01 Jan 2022
Deep Network Approximation in Terms of Intrinsic Parameters Zuowei Shen Haizhao Yang Shijun Zhang 18 9 0 15 Nov 2021
Efficient Estimation in NPIV Models: A Comparison of Various Neural Networks-Based Estimators Jiafeng Chen Xiaohong Chen E. Tamer 17 10 0 13 Oct 2021
Universal Approximation Under Constraints is Possible with Transformers Anastasis Kratsios Behnoosh Zamanlooy Tianlin Liu Ivan Dokmanić 53 26 0 07 Oct 2021
Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximation Nathan Gaby Fumin Zhang X. Ye PINN 37 39 0 27 Sep 2021
Arbitrary-Depth Universal Approximation Theorems for Operator Neural Networks Annan Yu Chloe Becquey Diana Halikias Matthew Esmaili Mallory Alex Townsend 59 8 0 23 Sep 2021
Deep Network Approximation: Achieving Arbitrary Accuracy with Fixed Number of Neurons Zuowei Shen Haizhao Yang Shijun Zhang 53 36 0 06 Jul 2021
Approximation capabilities of measure-preserving neural networks Aiqing Zhu Pengzhan Jin Yifa Tang 18 8 0 21 Jun 2021
Solving PDEs on Unknown Manifolds with Machine Learning Senwei Liang Shixiao W. Jiang J. Harlim Haizhao Yang AI4CE 39 16 0 12 Jun 2021
The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation Q. Du Yiqi Gu Haizhao Yang Chao Zhou 26 20 0 21 Mar 2021
Deep Neural Networks with ReLU-Sine-Exponential Activations Break Curse of Dimensionality in Approximation on Hölder Class Yuling Jiao Yanming Lai Xiliang Lu Fengru Wang J. Yang Yuanyuan Yang 13 3 0 28 Feb 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
Elementary superexpressive activations Dmitry Yarotsky 16 35 0 22 Feb 2021
Reproducing Activation Function for Deep Learning Senwei Liang Liyao Lyu Chunmei Wang Haizhao Yang 36 21 0 13 Jan 2021
Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning Fan Chen J. Huang Chunmei Wang Haizhao Yang 25 30 0 15 Dec 2020
A three layer neural network can represent any multivariate function V. Ismailov 15 15 0 05 Dec 2020
The Kolmogorov-Arnold representation theorem revisited Johannes Schmidt-Hieber 30 125 0 31 Jul 2020