Neural network approximation of continuous functions in high dimensions with applications to inverse problems

DOI10.1016/j.cam.2023.115557zbMath1527.41002arXiv2208.13305OpenAlexW4386865483MaRDI QIDQ6056231

Mark A. Iwen, Santhosh Karnik, Rongrong Wang

Publication date: 30 October 2023

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.13305

zbMATH Keywords

neural networkinverse problemsapproximation theorydeep learningJohnson-Lindenstrauss embedding

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Approximation by other special function classes (41A30)

Cites Work

• Unnamed Item
• New bounds for circulant Johnson-Lindenstrauss embeddings
• Random projections of smooth manifolds
• Universal approximations of invariant maps by neural networks
• Universality of deep convolutional neural networks
• Blind Deconvolution Using Convex Programming
• On variants of the Johnson–Lindenstrauss lemma
• Deep Convolutional Neural Network for Inverse Problems in Imaging
• High-Dimensional Probability
• Equivalence of approximation by convolutional neural networks and fully-connected networks
• Tight Oracle Inequalities for Low-Rank Matrix Recovery From a Minimal Number of Noisy Random Measurements
• On the extension of Lipschitz, Lipschitz-Hölder continuous, and monotone functions
• Perturbation bounds in connection with singular value decomposition
• Nonparametric regression on low-dimensional manifolds using deep ReLU networks: function approximation and statistical recovery

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