Quantitative Approximation Results for Complex-Valued Neural Networks

DOI10.1137/21M1429540MaRDI QIDQ5073921

Felix Voigtlaender, Andrei Caragea, Götz E. Pfander, Dae Gwan Lee, Johannes Maly

Publication date: 4 May 2022

Published in: SIAM Journal on Mathematics of Data Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.13092

zbMATH Keywords

function approximationcomplex-valued neural networksmodReLu activation function

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Rate of convergence, degree of approximation (41A25) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Uses Software

• ImageNet
• AlexNet

Cites Work

• Unnamed Item
• Neural networks in multidimensional domains. Fundamentals and new trends in modelling and control
• Multilayer feedforward networks are universal approximators
• Optimal approximation of piecewise smooth functions using deep ReLU neural networks
• Error bounds for approximations with deep ReLU networks
• Entropies of several sets of real valued functions
• High-Dimensional Probability
• Complex-Valued Neural Networks
• Optimal Approximation with Sparsely Connected Deep Neural Networks
• 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
• Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions
• Deep Network Approximation for Smooth Functions
• Approximation by superpositions of a sigmoidal function

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