Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review

2 November 2016

Papers citing "Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review"

50 / 95 papers shown

Title
Emergence of Structure in Ensembles of Random Neural Networks Luca Muscarnera Luigi Loreti Giovanni Todeschini Alessio Fumagalli Francesco Regazzoni 31 0 0 15 May 2025
Is the end of Insight in Sight ? J. Tucny M. Durve S. Succi 69 0 0 07 May 2025
Information Filtering Networks: Theoretical Foundations, Generative Methodologies, and Real-World Applications Tomaso Aste GNN 39 0 0 02 May 2025
Approximation properties of neural ODEs Arturo De Marinis Davide Murari E. Celledoni Nicola Guglielmi B. Owren Francesco Tudisco 52 1 0 19 Mar 2025
Variational Bayesian Adaptive Learning of Deep Latent Variables for Acoustic Knowledge Transfer Hu Hu Sabato Marco Siniscalchi Chao-Han Huck Yang Chin-Hui Lee 85 0 0 28 Jan 2025
An Analysis Framework for Understanding Deep Neural Networks Based on Network Dynamics Yuchen Lin Yong Zhang Sihan Feng Hong Zhao 41 0 0 05 Jan 2025
Probing the Latent Hierarchical Structure of Data via Diffusion Models Antonio Sclocchi Alessandro Favero Noam Itzhak Levi M. Wyart DiffM 35 3 0 17 Oct 2024
Highly Adaptive Ridge Alejandro Schuler Alexander Hagemeister Mark van der Laan 28 0 0 03 Oct 2024
U-Nets as Belief Propagation: Efficient Classification, Denoising, and Diffusion in Generative Hierarchical Models Song Mei 3DV AI4CE DiffM 45 11 0 29 Apr 2024
Macroscopic auxiliary asymptotic preserving neural networks for the linear radiative transfer equations Hongyan Li Song Jiang Wenjun Sun Liwei Xu Guanyu Zhou 35 2 0 04 Mar 2024
Mathematical Algorithm Design for Deep Learning under Societal and Judicial Constraints: The Algorithmic Transparency Requirement Holger Boche Adalbert Fono Gitta Kutyniok FaML 31 4 0 18 Jan 2024
Expressivity and Approximation Properties of Deep Neural Networks with ReLU $^k$ Activation Juncai He Tong Mao Jinchao Xu 43 3 0 27 Dec 2023
Identifying Interpretable Visual Features in Artificial and Biological Neural Systems David A. Klindt Sophia Sanborn Francisco Acosta Frédéric Poitevin Nina Miolane MILM FAtt 44 7 0 17 Oct 2023
Time integration schemes based on neural networks for solving partial differential equations on coarse grids Xinxin Yan Zhideng Zhou Xiaohan Cheng Xiaolei Yang AI4TS AI4CE 23 0 0 16 Oct 2023
Multi-Grade Deep Learning for Partial Differential Equations with Applications to the Burgers Equation Yuesheng Xu Taishan Zeng AI4CE 32 4 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
Deep Stochastic Mechanics Elena Orlova Aleksei Ustimenko Ruoxi Jiang Peter Y. Lu Rebecca Willett DiffM 49 0 0 31 May 2023
Theoretical Analysis of Inductive Biases in Deep Convolutional Networks Zihao Wang Lei Wu 25 20 0 15 May 2023
Deep neural network approximation of composite functions without the curse of dimensionality Adrian Riekert 26 0 0 12 Apr 2023
Locality-constrained autoregressive cum conditional normalizing flow for lattice field theory simulations R. DineshP. AI4CE 22 0 0 04 Apr 2023
Beyond Multilayer Perceptrons: Investigating Complex Topologies in Neural Networks T. Boccato Matteo Ferrante A. Duggento N. Toschi 30 2 0 31 Mar 2023
Topological Feature Selection Antonio Briola T. Aste 31 3 0 19 Feb 2023
Optimal Approximation Complexity of High-Dimensional Functions with Neural Networks Vincent P. H. Goverse Jad Hamdan Jared Tanner 26 0 0 30 Jan 2023
Precision Machine Learning Eric J. Michaud Ziming Liu Max Tegmark 24 34 0 24 Oct 2022
$r-$ Adaptive Deep Learning Method for Solving Partial Differential Equations Ángel J. Omella David Pardo AI4CE 31 4 0 19 Oct 2022
Approximation results for Gradient Descent trained Shallow Neural Networks in $1d$ R. Gentile G. Welper ODL 56 6 0 17 Sep 2022
On the Number of Regions of Piecewise Linear Neural Networks Alexis Goujon Arian Etemadi M. Unser 44 13 0 17 Jun 2022
Convergence of Deep Neural Networks with General Activation Functions and Pooling Wentao Huang Yuesheng Xu Haizhang Zhang MLT AI4CE 23 0 0 13 May 2022
ExSpliNet: An interpretable and expressive spline-based neural network Daniele Fakhoury Emanuele Fakhoury H. Speleers 11 34 0 03 May 2022
RAR-PINN algorithm for the data-driven vector-soliton solutions and parameter discovery of coupled nonlinear equations Shulan Qin Min Li Tao Xu Shaotong Dong 25 9 0 29 Apr 2022
On the Spectral Bias of Convolutional Neural Tangent and Gaussian Process Kernels Amnon Geifman Meirav Galun David Jacobs Ronen Basri 30 13 0 17 Mar 2022
Data-Driven Computational Methods for the Domain of Attraction and Zubov's Equation W. Kang Kai Sun Liang Xu 20 13 0 29 Dec 2021
Optimization-Based Separations for Neural Networks Itay Safran Jason D. Lee 185 14 0 04 Dec 2021
Variational encoder geostatistical analysis (VEGAS) with an application to large scale riverine bathymetry M. Forghani Yizhou Qian Jonghyun Lee Matthew W. Farthing T. Hesser P. Kitanidis Eric F. Darve 24 8 0 23 Nov 2021
Multi-Objective Loss Balancing for Physics-Informed Deep Learning Rafael Bischof M. Kraus PINN AI4CE 35 92 0 19 Oct 2021
Convergence of Deep Convolutional Neural Networks Yuesheng Xu Haizhang Zhang MLT 40 44 0 28 Sep 2021
BioLCNet: Reward-modulated Locally Connected Spiking Neural Networks Hafez Ghaemi Erfan Mirzaei Mahbod Nouri Saeed Reza Kheradpisheh 19 2 0 12 Sep 2021
Adaptive Group Lasso Neural Network Models for Functions of Few Variables and Time-Dependent Data L. Ho Nicholas Richardson Giang Tran 20 3 0 24 Aug 2021
Identifying Illicit Drug Dealers on Instagram with Large-scale Multimodal Data Fusion Chuanbo Hu Minglei Yin Bin Liu Xin Li Yanfang Ye 30 9 0 18 Aug 2021
Convergence of Deep ReLU Networks Yuesheng Xu Haizhang Zhang 37 27 0 27 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
Locality defeats the curse of dimensionality in convolutional teacher-student scenarios Alessandro Favero Francesco Cagnetta M. Wyart 30 31 0 16 Jun 2021
ReLU Deep Neural Networks from the Hierarchical Basis Perspective Juncai He Lin Li Jinchao Xu AI4CE 28 30 0 10 May 2021
On the approximation of functions by tanh neural networks Tim De Ryck S. Lanthaler Siddhartha Mishra 26 138 0 18 Apr 2021
Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets Sizhuang He Hanwen Wang P. Perdikaris AI4CE 40 671 0 19 Mar 2021
Depth separation beyond radial functions Luca Venturi Samy Jelassi Tristan Ozuch Joan Bruna 19 15 0 02 Feb 2021
Reproducing Activation Function for Deep Learning Senwei Liang Liyao Lyu Chunmei Wang Haizhao Yang 36 21 0 13 Jan 2021
Application of deep learning to large scale riverine flow velocity estimation M. Forghani Yizhou Qian Jonghyun Lee Matthew W. Farthing T. Hesser P. Kitanidis Eric F. Darve 14 21 0 04 Dec 2020
On the application of Physically-Guided Neural Networks with Internal Variables to Continuum Problems J. Ayensa-Jiménez M. H. Doweidar J. A. Sanz-Herrera Manuel Doblaré 24 1 0 23 Nov 2020
Neural Network Approximation: Three Hidden Layers Are Enough Zuowei Shen Haizhao Yang Shijun Zhang 30 115 0 25 Oct 2020