Monotonicity and convergence of asynchronous update gradient method for ridge polynomial neural network

The ridge polynomial neural network is a special type of higher-order neural networks. It not only provides a more efficient and regular architecture compared to ordinary higher-order feedforward networks, but also maintains the fast learning property and powerful nonlinear mapping capability while avoiding the combinatorial increase in the number of required weights. In this paper, a monotonicity theorem and two convergence theorems of the asynchronous gradient method for training the ridge polynomial neural network are proved. They are important to choosing appropriate learning rate and initial weights to perform effective training. To illustrate the theoretical finding, numerical experiments are carried out for 4-dimensional parity problem and function approximation problem. It is shown that the experimental results are in agreement with the proposed theorems.