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Related Experiment Video

Updated: Jan 8, 2026

Deep Neural Networks for Image-Based Dietary Assessment
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Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

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Convergence analysis and application for high-order neural networks based on gradient descent learning algorithm via

Khidir Shaib Mohamed1, Alawia Adam2, Yousif Shoaib Mohammed3

  • 1Department of Mathematics, College of Sciences, Qassim University, Buraydah 51452, Saudi Arabia. k.idris@qu.edu.sa.

Scientific Reports
|December 12, 2025
PubMed
Summary

This study introduces a novel gradient descent algorithm for pi-sigma networks (PSNs) using smoothed L1 regularization. The new method, GDS L1, enhances learning efficiency and generalization compared to existing techniques.

Keywords:
ConvergenceGradient descent algorithmNumerical resultsPi-sigma networkSmoothing [Formula: see text] regularization

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Last Updated: Jan 8, 2026

Deep Neural Networks for Image-Based Dietary Assessment
13:19

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Published on: March 13, 2021

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Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Neural Networks

Background:

  • Pi-sigma networks (PSNs) are high-order networks adept at rapid learning and nonlinear processing.
  • Direct application of L1 regularization in PSNs faces challenges like numerical oscillations and gradient computation issues at the origin.

Purpose of the Study:

  • To propose a novel algorithm for PSNs using batch gradient descent with L1 regularization.
  • To address the drawbacks of direct L1 regularization by introducing smoothing functions.

Main Methods:

  • Developed a gradient descent method based on smoothing L1 regularization (GDS L1).
  • Approximated L1 regularization using smoothing functions to overcome numerical and theoretical challenges.
  • Utilized batch gradient descent for network training.

Main Results:

  • GDS L1 algorithms demonstrated superior performance over four other regularization methods.
  • The proposed method showed improvements in generalization and pruning efficiency.
  • Numerical results were validated on the 4-dimensional parity problem and nonlinear Gabor function problem.

Conclusions:

  • Theoretical analysis and experimental results confirm the monotonicity and convergence (strong and weak) of PSNs trained with GDS L1.
  • The GDS L1 method offers a robust and efficient approach for PSN training.