Approximating smooth functions by deep neural networks with sigmoid activation function

DOI10.1016/j.jmva.2020.104696zbMath1456.41005arXiv2010.04596OpenAlexW3102087799MaRDI QIDQ2222228

Sophie Langer

Publication date: 26 January 2021

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.04596

zbMATH Keywords

neural networksuniform approximationdeep learningfull connectivity

Mathematics Subject Classification ID

Neural nets applied to problems in time-dependent statistical mechanics (82C32) Rate of convergence, degree of approximation (41A25)

Related Items (4)

A note on the applications of one primary function in deep neural networks ⋮ Estimation of a regression function on a manifold by fully connected deep neural networks ⋮ Neural Networks for Clustered and Longitudinal Data Using Mixed Effects Models ⋮ Approximation error for neural network operators by an averaged modulus of smoothness

Cites Work

• Optimal global rates of convergence for noiseless regression estimation problems with adaptively chosen design
• Multilayer feedforward networks are universal approximators
• Approximation of functions and their derivatives: A neural network implementation with applications
• Nonparametric regression using deep neural networks with ReLU activation function
• On deep learning as a remedy for the curse of dimensionality in nonparametric regression
• Universal Approximation Depth and Errors of Narrow Belief Networks with Discrete Units
• Approximation by superpositions of a sigmoidal function

This page was built for publication: Approximating smooth functions by deep neural networks with sigmoid activation function