Sensitivity Study Of Madalines

The sensitivity of neural networks' output to parameter perturbation is an important issue in the design and implementation of neural networks. What will be the effects of parameter perturbation on the output of neural networks? How can the degree of the response of neural networks due to parameter perturbation be measured? In this dissertation, the sensitivity of Madalines to input and weight perturbations is systematically and theoretically studied.Based on the structural characteristics of Madalines, a bottom-up approach is adopted. The sensitivity of a single neuron, i.e. an Adaline, is considered first. Then followed is the sensitivity of the entire Madaline networks.Sensitivity is defined as the mathematical expectation of output deviation due to input and weight perturbations. For a trained Madaline, whose architecture and weight are all given, the dissertation proposes a hypercube model and a probability model to compute its sensitivity. The hypercube model is successfully used to compute the sensitivity with high accuracy, while the probability model is successfully used to compute the sensitivity with low complexity. The probability model is also used to consider the sensitivity of untrained Madalines. The sensitivity analysis of Madalines without fixed weight is also conducted, which is hopeful to provide useful guidelines to aid the design of a Madaline.Finally, the direction of the future research is discussed.