Computing the Approximation Error for Neural Networks with Weights Varying on Fixed Directions. (10th September 2019)

• Record Type: Journal Article
• Authors: Ismailov, Vugar E.
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 12(2019)
• Page Start: 1395
• Page End: 1409
• Publication Date: 2019-09-10
• Subjects: Approximation error -- Borel measure -- extremal element -- Jordan decomposition -- neural network -- path -- weight; 41A30 -- 41A63 -- 92B20 -- 46E27 -- 46N60; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1605523
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: We obtain a sharp lower bound estimate for the approximation error of a continuous function by single hidden layer neural networks with a continuous activation function and weights varying on two fixed directions. We show that for a certain class of activation functions this lower bound estimate turns into equality. The obtained result provides us with a method for direct computation of the approximation error. As an application, we give a formula, which can be used to compute instantly the approximation error for a class of functions having second order partial derivatives.