Parallel distributed processing: explorations in the microstructure of cognition, vol. 2: psychological and biological models
A Sigma-Pi-Sigma Neural Network (SPSNN)
Neural Processing Letters
Convergence of an online gradient method for feedforward neural networks with stochastic inputs
Journal of Computational and Applied Mathematics - Special issue on proceedings of the international symposium on computational mathematics and applications
Expert Systems with Applications: An International Journal
Deterministic convergence of an online gradient method for BP neural networks
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
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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.