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Related Experiment Video

Updated: Apr 2, 2026

Deep Neural Networks for Image-Based Dietary Assessment
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Fractional-order gradient descent learning for Elman neural networks.

He Li1, Shanze Wang1, Yangquan Chen2

  • 1Shenyang Aerospace University, No.37 Daoyi South Avenue, Daoyi District, Shenyang, 110136, Liaoning Province, China.

Neural Networks : the Official Journal of the International Neural Network Society
|March 31, 2026
PubMed
Summary

This study introduces a fractional-order gradient descent (FO-Elman) algorithm to enhance Elman neural network training. FO-Elman improves convergence and avoids local minima by incorporating historical gradient information.

Keywords:
Elman neural networkFractional-order gradient descentGrünwald-Letnikov definitionRecurrent neural networkSystem identificationTime series prediction

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Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Deep Learning

Background:

  • Conventional integer-order gradient descent methods face limitations in training Elman neural networks, including susceptibility to local minima and slow convergence.
  • Elman neural networks are recurrent neural networks widely used in time-series prediction and system identification.

Purpose of the Study:

  • To propose a novel fractional-order gradient descent learning algorithm for Elman networks (FO-Elman) to overcome the limitations of conventional methods.
  • To theoretically establish the convergence of the proposed FO-Elman algorithm.
  • To demonstrate the effectiveness of FO-Elman through experimental validation.

Main Methods:

  • Derivation of fractional-order gradient expressions for each layer of the Elman network.
  • Establishment of a complete backpropagation framework for fractional-order gradients.
  • Incorporation of historical gradient information using the memory property of fractional calculus into the parameter update rule.

Main Results:

  • Theoretical proof of the convergence of the FO-Elman algorithm.
  • Experimental results on system identification and time-series prediction tasks show improved optimization performance compared to conventional methods.
  • Demonstration of FO-Elman's ability to mitigate local minima and accelerate convergence.

Conclusions:

  • The proposed FO-Elman algorithm offers a new theoretical and algorithmic tool for training Elman neural networks.
  • Fractional-order calculus provides a mechanism to enhance gradient descent optimization by leveraging historical information.
  • FO-Elman presents a promising approach for improving the performance of recurrent neural networks in various applications.