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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 / 238 papers shown

Title
Superposed Parameterised Quantum Circuits Viktoria Patapovich Mo Kordzanganeh A. Melnikov 23 0 0 10 Jun 2025
Neural Tangent Kernel Analysis to Probe Convergence in Physics-informed Neural Solvers: PIKANs vs. PINNs Salah A Faroughi Farinaz Mostajeran 15 0 0 09 Jun 2025
Emergence of Structure in Ensembles of Random Neural Networks Luca Muscarnera Luigi Loreti Giovanni Todeschini Alessio Fumagalli Francesco Regazzoni 63 0 0 15 May 2025
Is the end of Insight in Sight ? J. Tucny M. Durve S. Succi 115 0 0 07 May 2025
Information Filtering Networks: Theoretical Foundations, Generative Methodologies, and Real-World Applications Tomaso Aste GNN 61 0 0 02 May 2025
Erzeugunsgrad, VC-Dimension and Neural Networks with rational activation function Luis Miguel Pardo Daniel Sebastián 45 0 0 15 Apr 2025
F-INR: Functional Tensor Decomposition for Implicit Neural Representations Sai Karthikeya Vemuri Tim Buchner Joachim Denzler AI4CE 87 2 0 27 Mar 2025
Approximation properties of neural ODEs Arturo De Marinis Davide Murari E. Celledoni Nicola Guglielmi B. Owren Francesco Tudisco 78 1 0 19 Mar 2025
Curse of Dimensionality in Neural Network Optimization Sanghoon Na Haizhao Yang 87 0 0 07 Feb 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 123 0 0 28 Jan 2025
Network Dynamics-Based Framework for Understanding Deep Neural Networks Yuchen Lin Yong Zhang Sihan Feng Hong Zhao 99 1 0 05 Jan 2025
Weighted Sobolev Approximation Rates for Neural Networks on Unbounded Domains Ahmed Abdeljawad Thomas Dittrich 55 0 0 06 Nov 2024
Probing the Latent Hierarchical Structure of Data via Diffusion Models Antonio Sclocchi Alessandro Favero Noam Itzhak Levi Matthieu Wyart DiffM 121 5 0 17 Oct 2024
Highly Adaptive Ridge Alejandro Schuler Alexander Hagemeister Mark van der Laan 236 0 0 03 Oct 2024
Nonuniform random feature models using derivative information Konstantin Pieper Zezhong Zhang Guannan Zhang 61 2 0 03 Oct 2024
Towards Narrowing the Generalization Gap in Deep Boolean Networks Youngsung Kim NAI AI4CE 69 0 0 06 Sep 2024
Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations Jin Song Ming Zhong George Karniadakis Zhenya Yan PINN 74 14 0 02 Sep 2024
Solving Oscillator Ordinary Differential Equations via Soft-constrained Physics-informed Neural Network with Small Data Kai-liang Lu Yu-meng Su Zhuo Bi Cheng Qiu Wen-jun Zhang PINN 63 0 0 19 Aug 2024
A Survey on Universal Approximation Theorems Midhun T. Augustine 131 6 0 17 Jul 2024
Contribution Evaluation of Heterogeneous Participants in Federated Learning via Prototypical Representations Qi Guo Minghao Yao Zhen Tian Saiyu Qi Yong Qi Yun Lin Jin Song Dong 58 1 0 02 Jul 2024
Newton Informed Neural Operator for Computing Multiple Solutions of Nonlinear Partials Differential Equations Wenrui Hao Xinliang Liu Yahong Yang 69 4 0 23 May 2024
U-Nets as Belief Propagation: Efficient Classification, Denoising, and Diffusion in Generative Hierarchical Models Song Mei 3DV AI4CE DiffM 81 13 0 29 Apr 2024
How Deep Networks Learn Sparse and Hierarchical Data: the Sparse Random Hierarchy Model Umberto M. Tomasini Matthieu Wyart BDL 106 7 0 16 Apr 2024
Learning smooth functions in high dimensions: from sparse polynomials to deep neural networks Ben Adcock Simone Brugiapaglia N. Dexter S. Moraga 61 4 0 04 Apr 2024
Macroscopic auxiliary asymptotic preserving neural networks for the linear radiative transfer equations Hongyan Li Song Jiang Wenjun Sun Liwei Xu Guanyu Zhou 59 2 0 04 Mar 2024
A Phase Transition in Diffusion Models Reveals the Hierarchical Nature of Data Antonio Sclocchi Alessandro Favero Matthieu Wyart DiffM 115 37 0 26 Feb 2024
Approximation of relation functions and attention mechanisms Awni Altabaa John Lafferty 75 7 0 13 Feb 2024
Depth Separations in Neural Networks: Separating the Dimension from the Accuracy Itay Safran Daniel Reichman Paul Valiant 107 0 0 11 Feb 2024
Mathematical Algorithm Design for Deep Learning under Societal and Judicial Constraints: The Algorithmic Transparency Requirement Holger Boche Adalbert Fono Gitta Kutyniok FaML 103 4 0 18 Jan 2024
Modelling Species Distributions with Deep Learning to Predict Plant Extinction Risk and Assess Climate Change Impacts Joaquim Estopinan P. Bonnet Maximilien Servajean Franccois Munoz Alexis Joly 26 3 0 10 Jan 2024
Expressivity and Approximation Properties of Deep Neural Networks with ReLU $^k$ Activation Juncai He Tong Mao Jinchao Xu 77 4 0 27 Dec 2023
Optimal Deep Neural Network Approximation for Korobov Functions with respect to Sobolev Norms Yahong Yang Yulong Lu 66 3 0 08 Nov 2023
Identifying Interpretable Visual Features in Artificial and Biological Neural Systems David A. Klindt Sophia Sanborn Francisco Acosta Frédéric Poitevin Nina Miolane MILM FAtt 105 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 56 0 0 16 Oct 2023
Multi-Grade Deep Learning for Partial Differential Equations with Applications to the Burgers Equation Yuesheng Xu Taishan Zeng AI4CE 52 4 0 14 Sep 2023
Fundamental Limits of Deep Learning-Based Binary Classifiers Trained with Hinge Loss T. Getu Georges Kaddoum M. Bennis 89 1 0 13 Sep 2023
Neural Network Layer Matrix Decomposition reveals Latent Manifold Encoding and Memory Capacity Ng Shyh‐Chang A-Li Luo Bo Qiu 17 0 0 12 Sep 2023
Approximation Results for Gradient Descent trained Neural Networks G. Welper 68 1 0 09 Sep 2023
Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks T. Şahin M. Danwitz A. Popp PINN 75 25 0 24 Aug 2023
How Deep Neural Networks Learn Compositional Data: The Random Hierarchy Model Francesco Cagnetta Leonardo Petrini Umberto M. Tomasini Alessandro Favero Matthieu Wyart BDL 118 27 0 05 Jul 2023
Uniform Convergence of Deep Neural Networks with Lipschitz Continuous Activation Functions and Variable Widths Yuesheng Xu Haizhang Zhang 132 3 0 02 Jun 2023
Deep Stochastic Mechanics Elena Orlova Aleksei Ustimenko Ruoxi Jiang Peter Y. Lu Rebecca Willett DiffM 85 0 0 31 May 2023
Theoretical Analysis of Inductive Biases in Deep Convolutional Networks Zihao Wang Lei Wu 82 22 0 15 May 2023
Successive Affine Learning for Deep Neural Networks Yuesheng Xu 54 2 0 13 May 2023
Foundations of Spatial Perception for Robotics: Hierarchical Representations and Real-time Systems Nathan Hughes Yun Chang Siyi Hu Rajat Talak Rumaisa Abdulhai Jared Strader Luca Carlone 65 54 0 11 May 2023
A Neural Network Transformer Model for Composite Microstructure Homogenization Emil Pitz K. Pochiraju AI4CE 60 10 0 16 Apr 2023
Deep neural network approximation of composite functions without the curse of dimensionality Adrian Riekert 53 0 0 12 Apr 2023
Locality-constrained autoregressive cum conditional normalizing flow for lattice field theory simulations R. DineshP. AI4CE 57 0 0 04 Apr 2023
Depth Separation with Multilayer Mean-Field Networks Y. Ren Mo Zhou Rong Ge OOD 79 3 0 03 Apr 2023
Beyond Multilayer Perceptrons: Investigating Complex Topologies in Neural Networks T. Boccato Matteo Ferrante A. Duggento N. Toschi 58 3 0 31 Mar 2023