Deep Network Approximation: Achieving Arbitrary Accuracy with Fixed Number of Neurons

6 July 2021

Papers citing "Deep Network Approximation: Achieving Arbitrary Accuracy with Fixed Number of Neurons"

27 / 27 papers shown

Title
Kolmogorov-Arnold Networks: Approximation and Learning Guarantees for Functions and their Derivatives Anastasis Kratsios Takashi Furuya 27 0 0 21 Apr 2025
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
Approximation Bounds for Transformer Networks with Application to Regression Yuling Jiao Yanming Lai Defeng Sun Yang Wang Bokai Yan 29 0 0 16 Apr 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
Fourier Multi-Component and Multi-Layer Neural Networks: Unlocking High-Frequency Potential Shijun Zhang Hongkai Zhao Yimin Zhong Haomin Zhou 57 0 0 26 Feb 2025
Neural Operators Can Play Dynamic Stackelberg Games Guillermo Alvarez Ibrahim Ekren Anastasis Kratsios Xuwei Yang 35 0 0 14 Nov 2024
Solving High-Dimensional Partial Integral Differential Equations: The Finite Expression Method Gareth Hardwick Senwei Liang Haizhao Yang 31 1 0 01 Oct 2024
Hyper-Compression: Model Compression via Hyperfunction Fenglei Fan Juntong Fan Dayang Wang Jingbo Zhang Zelin Dong Shijun Zhang Ge Wang Tieyong Zeng 29 0 0 01 Sep 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
Structured and Balanced Multi-component and Multi-layer Neural Networks Shijun Zhang Hongkai Zhao Yimin Zhong Haomin Zhou 34 1 0 30 Jun 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
Approximation Rates and VC-Dimension Bounds for (P)ReLU MLP Mixture of Experts Anastasis Kratsios Haitz Sáez de Ocáriz Borde Takashi Furuya Marc T. Law MoE 41 1 0 05 Feb 2024
Deep ReLU networks and high-order finite element methods II: Chebyshev emulation J. Opschoor Christoph Schwab 34 2 0 11 Oct 2023
Noncompact uniform universal approximation T. V. Nuland 22 5 0 07 Aug 2023
Deep Network Approximation: Beyond ReLU to Diverse Activation Functions Shijun Zhang Jianfeng Lu Hongkai Zhao 24 17 0 13 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
Orthogonal Transforms in Neural Networks Amount to Effective Regularization Krzysztof Zajkac Wojciech Sopot Paweł Wachel 31 0 0 10 May 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
SignReLU neural network and its approximation ability Jianfei Li Han Feng Ding-Xuan Zhou 25 3 0 19 Oct 2022
Deep Neural Network Approximation of Invariant Functions through Dynamical Systems Qianxiao Li T. Lin Zuowei Shen 21 6 0 18 Aug 2022
Finite Expression Method for Solving High-Dimensional Partial Differential Equations Senwei Liang Haizhao Yang 31 18 0 21 Jun 2022
Neural Network Architecture Beyond Width and Depth Zuowei Shen Haizhao Yang Shijun Zhang 3DV MDE 33 13 0 19 May 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
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
Optimal Approximation Rate of ReLU Networks in terms of Width and Depth Zuowei Shen Haizhao Yang Shijun Zhang 101 115 0 28 Feb 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
Improving neural networks by preventing co-adaptation of feature detectors Geoffrey E. Hinton Nitish Srivastava A. Krizhevsky Ilya Sutskever Ruslan Salakhutdinov VLM 266 7,636 0 03 Jul 2012