Approximation results for Gradient Descent trained Shallow Neural Networks in $1d$

17 September 2022

Papers citing "Approximation results for Gradient Descent trained Shallow Neural Networks in $1d$"

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Title
A brief review of the Deep BSDE method for solving high-dimensional partial differential equations Jiequn Han Arnulf Jentzen Weinan E AI4CE 63 0 0 07 May 2025
Neural Tangent Kernel Analysis of Deep Narrow Neural Networks Jongmin Lee Jooyeon Choi Ernest K. Ryu Albert No 23 10 0 07 Feb 2022
Tight Convergence Rate Bounds for Optimization Under Power Law Spectral Conditions Maksim Velikanov Dmitry Yarotsky 62 8 0 02 Feb 2022
Neural Tangent Kernel Beyond the Infinite-Width Limit: Effects of Depth and Initialization Mariia Seleznova Gitta Kutyniok 217 20 0 01 Feb 2022
Subquadratic Overparameterization for Shallow Neural Networks Chaehwan Song Ali Ramezani-Kebrya Thomas Pethick Armin Eftekhari Volkan Cevher 73 31 0 02 Nov 2021
Optimal Convergence Rates for the Orthogonal Greedy Algorithm Jonathan W. Siegel Jinchao Xu 100 18 0 28 Jun 2021
The Modern Mathematics of Deep Learning Julius Berner Philipp Grohs Gitta Kutyniok P. Petersen 43 116 0 09 May 2021
Universal scaling laws in the gradient descent training of neural networks Maksim Velikanov Dmitry Yarotsky 78 9 0 02 May 2021
Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces Philipp Grohs F. Voigtlaender 64 36 0 06 Apr 2021
Deep learning versus kernel learning: an empirical study of loss landscape geometry and the time evolution of the Neural Tangent Kernel Stanislav Fort Gintare Karolina Dziugaite Mansheej Paul Sepideh Kharaghani Daniel M. Roy Surya Ganguli 105 193 0 28 Oct 2020
Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities C. Marcati J. Opschoor P. Petersen Christoph Schwab 61 30 0 23 Oct 2020
Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't E. Weinan Chao Ma Stephan Wojtowytsch Lei Wu AI4CE 99 134 0 22 Sep 2020
Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS Lin Chen Sheng Xu 148 94 0 22 Sep 2020
Complexity Measures for Neural Networks with General Activation Functions Using Path-based Norms Zhong Li Chao Ma Lei Wu 53 24 0 14 Sep 2020
Finite Versus Infinite Neural Networks: an Empirical Study Jaehoon Lee S. Schoenholz Jeffrey Pennington Ben Adlam Lechao Xiao Roman Novak Jascha Narain Sohl-Dickstein 77 214 0 31 Jul 2020
On the Similarity between the Laplace and Neural Tangent Kernels Amnon Geifman A. Yadav Yoni Kasten Meirav Galun David Jacobs Ronen Basri 125 95 0 03 Jul 2020
Sharp Representation Theorems for ReLU Networks with Precise Dependence on Depth Guy Bresler Dheeraj M. Nagaraj 43 21 0 07 Jun 2020
Global Convergence of Deep Networks with One Wide Layer Followed by Pyramidal Topology Quynh N. Nguyen Marco Mondelli ODL AI4CE 55 70 0 18 Feb 2020
The gap between theory and practice in function approximation with deep neural networks Ben Adcock N. Dexter 57 94 0 16 Jan 2020
Deep Network Approximation for Smooth Functions Jianfeng Lu Zuowei Shen Haizhao Yang Shijun Zhang 116 248 0 09 Jan 2020
PyTorch: An Imperative Style, High-Performance Deep Learning Library Adam Paszke Sam Gross Francisco Massa Adam Lerer James Bradbury ... Sasank Chilamkurthy Benoit Steiner Lu Fang Junjie Bai Soumith Chintala ODL 547 42,639 0 03 Dec 2019
How Much Over-parameterization Is Sufficient to Learn Deep ReLU Networks? Zixiang Chen Yuan Cao Difan Zou Quanquan Gu 75 123 0 27 Nov 2019
Neural tangent kernels, transportation mappings, and universal approximation Ziwei Ji Matus Telgarsky Ruicheng Xian 59 39 0 15 Oct 2019
Beyond Linearization: On Quadratic and Higher-Order Approximation of Wide Neural Networks Yu Bai Jason D. Lee 52 116 0 03 Oct 2019
Polylogarithmic width suffices for gradient descent to achieve arbitrarily small test error with shallow ReLU networks Ziwei Ji Matus Telgarsky 72 178 0 26 Sep 2019
Finite Depth and Width Corrections to the Neural Tangent Kernel Boris Hanin Mihai Nica MDE 74 152 0 13 Sep 2019
Gradient Descent Finds Global Minima for Generalizable Deep Neural Networks of Practical Sizes Kenji Kawaguchi Jiaoyang Huang ODL 51 57 0 05 Aug 2019
The phase diagram of approximation rates for deep neural networks Dmitry Yarotsky Anton Zhevnerchuk 65 122 0 22 Jun 2019
An Improved Analysis of Training Over-parameterized Deep Neural Networks Difan Zou Quanquan Gu 63 235 0 11 Jun 2019
Quadratic Suffices for Over-parametrization via Matrix Chernoff Bound Zhao Song Xin Yang 66 91 0 09 Jun 2019
On the Inductive Bias of Neural Tangent Kernels A. Bietti Julien Mairal 91 260 0 29 May 2019
On Learning Over-parameterized Neural Networks: A Functional Approximation Perspective Lili Su Pengkun Yang MLT 68 54 0 26 May 2019
Approximation spaces of deep neural networks Rémi Gribonval Gitta Kutyniok M. Nielsen Felix Voigtländer 89 125 0 03 May 2019
On Exact Computation with an Infinitely Wide Neural Net Sanjeev Arora S. Du Wei Hu Zhiyuan Li Ruslan Salakhutdinov Ruosong Wang 238 928 0 26 Apr 2019
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs Gitta Kutyniok P. Petersen Mones Raslan R. Schneider 87 198 0 31 Mar 2019
Nonlinear Approximation via Compositions Zuowei Shen Haizhao Yang Shijun Zhang 70 91 0 26 Feb 2019
$Error bounds for approximations with deep ReLU neural networks in $W^{s,p}$ norms$ Error bounds for approximations with deep ReLU neural networks in $W^{s,p}$ norms Ingo Gühring Gitta Kutyniok P. Petersen 89 200 0 21 Feb 2019
Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent Jaehoon Lee Lechao Xiao S. Schoenholz Yasaman Bahri Roman Novak Jascha Narain Sohl-Dickstein Jeffrey Pennington 213 1,108 0 18 Feb 2019
Towards moderate overparameterization: global convergence guarantees for training shallow neural networks Samet Oymak Mahdi Soltanolkotabi 52 322 0 12 Feb 2019
Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks Sanjeev Arora S. Du Wei Hu Zhiyuan Li Ruosong Wang MLT 208 974 0 24 Jan 2019
Deep Neural Network Approximation Theory Dennis Elbrächter Dmytro Perekrestenko Philipp Grohs Helmut Bölcskei 68 210 0 08 Jan 2019
Scaling description of generalization with number of parameters in deep learning Mario Geiger Arthur Jacot S. Spigler Franck Gabriel Levent Sagun Stéphane dÁscoli Giulio Biroli Clément Hongler Matthieu Wyart 96 196 0 06 Jan 2019
On Lazy Training in Differentiable Programming Lénaïc Chizat Edouard Oyallon Francis R. Bach 111 840 0 19 Dec 2018
A Convergence Theory for Deep Learning via Over-Parameterization Zeyuan Allen-Zhu Yuanzhi Li Zhao Song AI4CE ODL 266 1,469 0 09 Nov 2018
Gradient Descent Finds Global Minima of Deep Neural Networks S. Du Jason D. Lee Haochuan Li Liwei Wang Masayoshi Tomizuka ODL 229 1,136 0 09 Nov 2018
Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality Taiji Suzuki 182 246 0 18 Oct 2018
Gradient Descent Provably Optimizes Over-parameterized Neural Networks S. Du Xiyu Zhai Barnabás Póczós Aarti Singh MLT ODL 233 1,276 0 04 Oct 2018
Learning Overparameterized Neural Networks via Stochastic Gradient Descent on Structured Data Yuanzhi Li Yingyu Liang MLT 219 653 0 03 Aug 2018
Neural Tangent Kernel: Convergence and Generalization in Neural Networks Arthur Jacot Franck Gabriel Clément Hongler 273 3,223 0 20 Jun 2018
Optimal approximation of continuous functions by very deep ReLU networks Dmitry Yarotsky 196 294 0 10 Feb 2018

Approximation results for Gradient Descent trained Shallow Neural Networks in 1d1d1d

Papers citing "Approximation results for Gradient Descent trained Shallow Neural Networks in $1d$"

Approximation results for Gradient Descent trained Shallow Neural Networks in $1d$