On the error and parameter convergence of back-propagation learning

The author presents a convergence result based on a modified backpropagation training rule, which is the same as the standard backpropagation algorithm except that a dead-zone around the origin of the error coordinates is incorporated in the training rule. It is shown that, if the network modeling error and the initial parameter errors are small enough, then the norm of the parameter error will converge to a constant, the increment of network parameters will converge to zero, and the output error between the network and the nonlinear function will converge into a small ball. Simulations are used to verify the theoretical results.