Evaluation of the feedforward neural network covariance matrix error

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