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<p>A Pi-Sigma neural network (PSNN) is a kind of neural network architecture that blends the structure of conventional neural networks with the ideas of polynomial approximation. Training a PSNN requires modifying the weights and coefficients of the polynomial functions to reduce the error between the expected and actual outputs. It is a generalization of the conventional feedforward neural network and is especially helpful for function approximation applications. Eliminating superfluous connections from enormous networks is a well-liked and practical method of figuring out the right size for a neural network. We have acknowledged the benefit of <i>L</i><sub>2/3</sub> regularization for sparse modeling. However, an oscillation phenomenon could result from <i>L</i><sub>2/3</sub> regularization’s nonsmoothness. This study suggests a smoothing <i>L</i><sub>2/3</sub> regularization method for a PSNN in order to make the models more sparse and help them learn more quickly. The new smoothing <i>L</i><sub>2/3</sub> regularizer eliminates the oscillation. Additionally, it enables us to show the PSNN’s weak and strong convergence findings. In order to guarantee convergence, we also link the learning rate parameter and the penalty parameter. Results of the simulation are provided. We present the simulation results, which demonstrate that the smoothing <i>L</i><sub>2/3</sub> regularization performs significantly better than the original <i>L</i><sub>2/3</sub> regularization, thereby supporting the theoretical conclusions are offered as well.</p>

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Batch gradient based smoothing L2/3 regularization for training pi-sigma higher-order networks

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月8日

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  • Khidir Shaib Mohamed,
  • Raed Muhammad Albadrani,
  • Ekram Adam,
  • Yan Xiong

摘要

A Pi-Sigma neural network (PSNN) is a kind of neural network architecture that blends the structure of conventional neural networks with the ideas of polynomial approximation. Training a PSNN requires modifying the weights and coefficients of the polynomial functions to reduce the error between the expected and actual outputs. It is a generalization of the conventional feedforward neural network and is especially helpful for function approximation applications. Eliminating superfluous connections from enormous networks is a well-liked and practical method of figuring out the right size for a neural network. We have acknowledged the benefit of L2/3 regularization for sparse modeling. However, an oscillation phenomenon could result from L2/3 regularization’s nonsmoothness. This study suggests a smoothing L2/3 regularization method for a PSNN in order to make the models more sparse and help them learn more quickly. The new smoothing L2/3 regularizer eliminates the oscillation. Additionally, it enables us to show the PSNN’s weak and strong convergence findings. In order to guarantee convergence, we also link the learning rate parameter and the penalty parameter. Results of the simulation are provided. We present the simulation results, which demonstrate that the smoothing L2/3 regularization performs significantly better than the original L2/3 regularization, thereby supporting the theoretical conclusions are offered as well.