A Novel Method for Ridge Polynomial Neural Network-based Caputo Fractional-order Gradient Descent Algorithm

Ridge Polynomial neural network have been widely acknowledged for strong nonlinear mapping capability. Nevertheless, conventional training based on integer-order gradient methods often suffers from low efficiency and limited precision, which can undermine model performance. Therefore, this paper presents a novel approach for training Ridge Polynomial neural network using fractional-order gradient descent based on the Caputo fractional-order derivative. The method introduces fractional-order gradient to optimization process, enhancing model’s performance and generalization ability. Numerical simulations validate the proposed method, showing improved performance in comparison with traditional integer-order gradient descent, particularly in terms of accuracy and generalization. This work demonstrates the potential of fractional-order optimization method for Ridge Polynomial neural network training, offering significant improvements over classical method.