Deep Neural Network Approximation Theory
From MaRDI portal
Publication:5001568
DOI10.1109/TIT.2021.3062161zbMath1473.68178arXiv1901.02220OpenAlexW3133816032MaRDI QIDQ5001568
Dennis Elbrächter, Dmytro Perekrestenko, Helmut Bölcskei, Philipp Grohs
Publication date: 22 July 2021
Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1901.02220
Related Items (41)
Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black--Scholes Partial Differential Equations ⋮ Neural network approximation ⋮ Metric entropy limits on recurrent neural network learning of linear dynamical systems ⋮ On sharpness of an error bound for deep ReLU network approximation ⋮ Scientific machine learning through physics-informed neural networks: where we are and what's next ⋮ Variational physics informed neural networks: the role of quadratures and test functions ⋮ Approximations with deep neural networks in Sobolev time-space ⋮ Full error analysis for the training of deep neural networks ⋮ Deep ReLU neural network approximation in Bochner spaces and applications to parametric PDEs ⋮ Convergence of deep convolutional neural networks ⋮ Relaxation approach for learning neural network regularizers for a class of identification problems ⋮ Physics-informed neural networks for approximating dynamic (hyperbolic) PDEs of second order in time: error analysis and algorithms ⋮ Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations ⋮ Deep Learning in High Dimension: Neural Network Expression Rates for Analytic Functions in \(\pmb{L^2(\mathbb{R}^d,\gamma_d)}\) ⋮ Drift estimation for a multi-dimensional diffusion process using deep neural networks ⋮ Invariant spectral foliations with applications to model order reduction and synthesis ⋮ Phase transitions in rate distortion theory and deep learning ⋮ A multivariate Riesz basis of ReLU neural networks ⋮ Collocation approximation by deep neural ReLU networks for parametric and stochastic PDEs with lognormal inputs ⋮ Hierarchical regularization networks for sparsification based learning on noisy datasets ⋮ Neural network approximation and estimation of classifiers with classification boundary in a Barron class ⋮ Data-driven reduced order models using invariant foliations, manifolds and autoencoders ⋮ Solving Kolmogorov PDEs without the curse of dimensionality via deep learning and asymptotic expansion with Malliavin calculus ⋮ Deep learning for inverse problems with unknown operator ⋮ Computation and learning in high dimensions. Abstracts from the workshop held August 1--7, 2021 (hybrid meeting) ⋮ Sobolev-type embeddings for neural network approximation spaces ⋮ Approximation in shift-invariant spaces with deep ReLU neural networks ⋮ Integral representations of shallow neural network with Rectified Power Unit activation function ⋮ Gabor neural networks with proven approximation properties ⋮ Solving the Kolmogorov PDE by means of deep learning ⋮ On the rate of convergence of fully connected deep neural network regression estimates ⋮ High-dimensional distribution generation through deep neural networks ⋮ Solving PDEs by variational physics-informed neural networks: an a posteriori error analysis ⋮ Design of the monodomain model by artificial neural networks ⋮ A phase transition for finding needles in nonlinear haystacks with LASSO artificial neural networks ⋮ A measure theoretical approach to the mean-field maximum principle for training NeurODEs ⋮ Explicitly antisymmetrized neural network layers for variational Monte Carlo simulation ⋮ Optimal Approximation with Sparsely Connected Deep Neural Networks ⋮ DNN expression rate analysis of high-dimensional PDEs: application to option pricing ⋮ A theoretical analysis of deep neural networks and parametric PDEs ⋮ Robust and resource-efficient identification of two hidden layer neural networks
This page was built for publication: Deep Neural Network Approximation Theory