Homogeneous ridge polynomial neural network training by PS module asynchronous gradient method

To address the issue that the passive increase in network order resulting from the rise of the Pi-Sigma (PS) modules for the ridge polynomial neural network (RPNN) adversely affects network performance, we propose a homogeneous ridge polynomial neural network (HRPNN) with a symmetrical structure. Furthermore, based on its characteristic of a two-layer weight structure, an asynchronous gradient method with the PS module as the gradient update unit is presented to enhance the network performance. The convergence theorem of this method is strictly proven, theoretically confirming the feasibility. The experimental results of the UCI datasets also verify the effectiveness and practicability of the proposed network structure and the training method. The Homogeneous ridge polynomial neural network significantly outperforms the ridge polynomial neural network in classification tasks, especially on the Wbc dataset, where classification accuracy is approximately 36.30% higher, demonstrating higher accuracy and stability. In function fitting tasks, the mean squared error of HRPNN using the PS module asynchronous gradient (PSMAG) method was reduced by 31.38% and 41.10% compared to the other two algorithms, respectively. These comparison results show that our network with the novel training method has excellent classification and approximation capabilities.