Sensitivity analysis of weights in multi-layer perceptron realizing continuous mappings

In Multi-Layer Perceptron (MLP) which realizes continuous mappings, the output errors is directly affected by the weight errors which may be caused by the limited precision of digital or analog hardware in implementations. So, it is important to study the sensitivity due to the perturbation of connection weights between neurons. In this paper, we derive a sensitivity function to the statistical weight perturbations in MLP with differentiable activation functions. This sensitivity function can be regarded as an ensemble average of deterministic sensitivity measures due to the perturbations of weights. Hence, this sensitivity function can be used as the criteria for selecting weights with the minimum sensitivity among possible sets of connection weights in MLP. For the verification of the validity of the proposed sensitivity function, computer simulations have been performed and through the simulations we find good agreement between the theoretical and simulation results.