Evaluation of the feedforward neural network covariance matrix error

Abstract

This paper presents a theoretical approach for the evaluation of a feedforward neural network covariance output error matrix. It is shown how the input signals errors and the different weights errors are linked together and spread over the neural network to form the output covariance matrix error which could may be used to determine an error bound. The formulas of the output covariance matrix error is derived arising the sensitivity of the additive weight perturbations or input perturbations. The analytical formulas is validated via simulation of a function approximation example showing that the theoretical result is in agreement with simulation result.