Provable approximation properties for deep neural networks

24 September 2015

Papers citing "Provable approximation properties for deep neural networks"

50 / 53 papers shown

Title
Transformers for Learning on Noisy and Task-Level Manifolds: Approximation and Generalization Insights Zhaiming Shen Alex Havrilla Rongjie Lai A. Cloninger Wenjing Liao 39 0 0 06 May 2025
Just How Flexible are Neural Networks in Practice? Ravid Shwartz-Ziv Micah Goldblum Arpit Bansal C. Bayan Bruss Yann LeCun Andrew Gordon Wilson 47 4 0 17 Jun 2024
Cross Entropy versus Label Smoothing: A Neural Collapse Perspective Li Guo Keith Ross Zifan Zhao George Andriopoulos Shuyang Ling Yufeng Xu Zixuan Dong UQCV NoLa 30 9 0 06 Feb 2024
Statistical learning by sparse deep neural networks Felix Abramovich BDL 26 1 0 15 Nov 2023
Rates of Approximation by ReLU Shallow Neural Networks Tong Mao Ding-Xuan Zhou 31 19 0 24 Jul 2023
Approximation of Nonlinear Functionals Using Deep ReLU Networks Linhao Song Jun Fan Dirong Chen Ding-Xuan Zhou 20 14 0 10 Apr 2023
Mathematical Challenges in Deep Learning V. Nia Guojun Zhang I. Kobyzev Michael R. Metel Xinlin Li ... S. Hemati M. Asgharian Linglong Kong Wulong Liu Boxing Chen AI4CE VLM 37 1 0 24 Mar 2023
Deep Nonparametric Estimation of Intrinsic Data Structures by Chart Autoencoders: Generalization Error and Robustness Hao Liu Alex Havrilla Rongjie Lai Wenjing Liao 39 6 0 17 Mar 2023
Local transfer learning from one data space to another H. Mhaskar Ryan O'Dowd 21 0 0 01 Feb 2023
On the Geometry of Reinforcement Learning in Continuous State and Action Spaces Saket Tiwari Omer Gottesman George Konidaris 26 0 0 29 Dec 2022
Effects of Data Geometry in Early Deep Learning Saket Tiwari George Konidaris 82 7 0 29 Dec 2022
Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems Derick Nganyu Tanyu Jianfeng Ning Tom Freudenberg Nick Heilenkötter A. Rademacher U. Iben Peter Maass AI4CE 23 34 0 06 Dec 2022
Deep neural network expressivity for optimal stopping problems Lukas Gonon 27 6 0 19 Oct 2022
Are All Losses Created Equal: A Neural Collapse Perspective Jinxin Zhou Chong You Xiao Li Kangning Liu Sheng Liu Qing Qu Zhihui Zhu 41 60 0 04 Oct 2022
Limitations of neural network training due to numerical instability of backpropagation Clemens Karner V. Kazeev P. Petersen 40 3 0 03 Oct 2022
Neural Collapse with Normalized Features: A Geometric Analysis over the Riemannian Manifold Can Yaras Peng Wang Zhihui Zhu Laura Balzano Qing Qu 25 42 0 19 Sep 2022
Approximation results for Gradient Descent trained Shallow Neural Networks in $1d$ R. Gentile G. Welper ODL 56 6 0 17 Sep 2022
Universal Solutions of Feedforward ReLU Networks for Interpolations Changcun Huang 23 2 0 16 Aug 2022
Why Robust Generalization in Deep Learning is Difficult: Perspective of Expressive Power Binghui Li Jikai Jin Han Zhong J. Hopcroft Liwei Wang OOD 84 27 0 27 May 2022
Low Dimensional Invariant Embeddings for Universal Geometric Learning Nadav Dym S. Gortler 34 39 0 05 May 2022
On the Optimization Landscape of Neural Collapse under MSE Loss: Global Optimality with Unconstrained Features Jinxin Zhou Xiao Li Tian Ding Chong You Qing Qu Zhihui Zhu 35 101 0 02 Mar 2022
Side Effects of Learning from Low-dimensional Data Embedded in a Euclidean Space Juncai He R. Tsai Rachel A. Ward 38 8 0 01 Mar 2022
Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer Beatrice Acciaio Anastasis Kratsios G. Pammer OOD 54 20 0 31 Jan 2022
Improved Overparametrization Bounds for Global Convergence of Stochastic Gradient Descent for Shallow Neural Networks Bartlomiej Polaczyk J. Cyranka ODL 35 3 0 28 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
Approximation of functions with one-bit neural networks C. S. Güntürk Weilin Li 19 8 0 16 Dec 2021
Theory of Deep Convolutional Neural Networks III: Approximating Radial Functions Tong Mao Zhongjie Shi Ding-Xuan Zhou 16 33 0 02 Jul 2021
A Geometric Analysis of Neural Collapse with Unconstrained Features Zhihui Zhu Tianyu Ding Jinxin Zhou Xiao Li Chong You Jeremias Sulam Qing Qu 40 196 0 06 May 2021
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
Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation Arnulf Jentzen Timo Welti 22 15 0 03 Mar 2020
Robust and Resource Efficient Identification of Two Hidden Layer Neural Networks M. Fornasier T. Klock Michael Rauchensteiner 24 18 0 30 Jun 2019
The phase diagram of approximation rates for deep neural networks Dmitry Yarotsky Anton Zhevnerchuk 30 121 0 22 Jun 2019
Fast Calculation of Probabilistic Power Flow: A Model-based Deep Learning Approach Yan Yang Zhifang Yang Juan Yu Baosen Zhang 20 95 0 14 Jun 2019
Deep Network Approximation Characterized by Number of Neurons Zuowei Shen Haizhao Yang Shijun Zhang 23 182 0 13 Jun 2019
How degenerate is the parametrization of neural networks with the ReLU activation function? Julius Berner Dennis Elbrächter Philipp Grohs ODL 33 28 0 23 May 2019
Nonlinear Approximation and (Deep) ReLU Networks Ingrid Daubechies Ronald A. DeVore S. Foucart Boris Hanin G. Petrova 22 138 0 05 May 2019
Deep Neural Networks for Rotation-Invariance Approximation and Learning C. Chui Shao-Bo Lin Ding-Xuan Zhou 32 34 0 03 Apr 2019
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs Gitta Kutyniok P. Petersen Mones Raslan R. Schneider 26 197 0 31 Mar 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 28 199 0 21 Feb 2019
The Oracle of DLphi Dominik Alfke W. Baines J. Blechschmidt Mauricio J. del Razo Sarmina Amnon Drory ... L. Thesing Philipp Trunschke Johannes von Lindheim David Weber Melanie Weber 39 0 0 17 Jan 2019
Deep Neural Network Approximation Theory Dennis Elbrächter Dmytro Perekrestenko Philipp Grohs Helmut Bölcskei 19 207 0 08 Jan 2019
PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network Zichao Long Yiping Lu Bin Dong AI4CE 31 543 0 30 Nov 2018
Enhanced Expressive Power and Fast Training of Neural Networks by Random Projections Jian-Feng Cai Dong Li Jiaze Sun Ke Wang 30 5 0 22 Nov 2018
A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients Arnulf Jentzen Diyora Salimova Timo Welti AI4CE 24 116 0 19 Sep 2018
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations Philipp Grohs F. Hornung Arnulf Jentzen Philippe von Wurstemberger 16 167 0 07 Sep 2018
Geometry of Deep Learning for Magnetic Resonance Fingerprinting Mohammad Golbabaee Dongdong Chen Pedro A. Gómez Marion I. Menzel Mike E. Davies 29 42 0 05 Sep 2018
Automatic Processing and Solar Cell Detection in Photovoltaic Electroluminescence Images E. Sovetkin A. Steland 12 25 0 26 Jul 2018
On the Universal Approximability and Complexity Bounds of Quantized ReLU Neural Networks Yukun Ding Jinglan Liu Jinjun Xiong Yiyu Shi MQ 37 21 0 10 Feb 2018
Optimal Approximation with Sparsely Connected Deep Neural Networks Helmut Bölcskei Philipp Grohs Gitta Kutyniok P. Petersen 41 255 0 04 May 2017