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

Khidir Shaib Mohamed1, Raed Muhammad Albadrani2, Ekram Adam3

  • 1Department of Mathematics, College of Sciences, Qassim University, Buraydah, Saudi Arabia. k.idris@qu.edu.sa.

Scientific Reports
|July 8, 2025
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Summary

This study introduces a smoothing L2/3 regularization method for Pi-Sigma neural networks (PSNNs) to improve model sparsity and learning speed. The new method overcomes oscillation issues and demonstrates superior performance in simulations.

Keywords:
Batch gradient methodNumerical resultsPi-sigma neural networkSmoothing L 2/3 regularization

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Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Neural Networks

Background:

  • Pi-Sigma neural networks (PSNNs) generalize feedforward networks for function approximation.
  • L2/3 regularization promotes sparse modeling but can cause oscillations due to non-smoothness.

Purpose of the Study:

  • To develop a smoothing L2/3 regularization method for PSNNs.
  • To enhance model sparsity and accelerate learning in PSNNs.
  • To address oscillation issues associated with traditional L2/3 regularization.

Main Methods:

  • A novel smoothing L2/3 regularizer was proposed for PSNNs.
  • Analysis of weak and strong convergence properties for PSNNs with the new regularizer.
  • Linking learning rate and penalty parameters to ensure convergence.

Main Results:

  • The smoothing L2/3 regularizer effectively eliminates oscillation phenomena.
  • Demonstrated significant performance improvements compared to the original L2/3 regularization.
  • Simulation results support the theoretical convergence findings.

Conclusions:

  • The proposed smoothing L2/3 regularization is effective for PSNNs.
  • This method enhances sparsity, speeds up learning, and ensures convergence.
  • The approach offers a more robust alternative to traditional L2/3 regularization for PSNNs.