The Barron Space and the Flow-Induced Function Spaces for Neural Network Models

• Published in: Constructive approximation Vol. 55; no. 1; pp. 369 - 406
• Main Authors: E, Weinan, Ma, Chao, Wu, Lei
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2022; Springer Nature B.V
• Subjects: Analysis; Approximation; Artificial neural networks; Function space; Machine learning; Mathematical analysis; Mathematics; Mathematics and Statistics; Neural networks; Norms; Numerical Analysis; Theorems; Upper bounds; Approximation; Function space; 68T05; Rademacher complexity; 46B99; Neural network; 65D15

One of the key issues in the analysis of machine learning models is to identify the appropriate function space and norm for the model. This is the set of functions endowed with a quantity which can control the approximation and estimation errors by a particular machine learning model. In this paper,...