Learning neural networks with respect to tolerances to weight errors

The problem of neural network learning to get the most convenient configuration, i.e., the vector of synaptic weights and thresholds of formal neurons creating the network, is treated. The possible errors in keeping precise the designed configuration during the realization as well as fluctuations of the configuration during the net exploitation are taken into account using the theory of tolerances. A cumulative loss function that expresses the loss evoked by imprecise learning is introduced, allowing the mathematical formalism used in the theory of tolerances and sensitivity to be applied. Learning is expressed as the problem of maximization of the volume of the area in the configuration space where the neural network exhibits small values of the cumulative loss function. The general task of synthesizing the parameters and their tolerances is shown to be a nonconvex problem of stochastic optimization with stochastic constraints, and a stochastic approximation algorithm for solving this problem is given. Results of teaching a three-layer feedforward network are given.