Sensitivity analysis of multilayer perceptron to input perturbation

An important issue in the design and implementation of neural networks is the sensitivity of neural network output to parameter perturbations. Past research in this area has focused on network sensitivity analysis after training. Very few research projects have considered sensitivity analysis as a design issue prior to network implementation. The authors discuss the sensitivity of the most popular and general feedforward networks (multilayer perceptron (MLP)) to its input perturbation. The sensitivity is defined as the mathematical expectation of output errors of the MLP arising from input error with respect to all input and weight values in a given continuous interval. The sensitivity for a single neuron is discussed first, and an analytical expression that is a function of the input error is approximately derived. Then an algorithm is given to compute the sensitivity for an entire MLP network. The theoretical results of the derived formula were shown to agree with experimental results. By analyzing the derived analytical expression and implementing the given algorithm on a number of representative MLP networks, some significant observations on the behavior of sensitivity are discovered, which could be useful for network design consideration