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Applications of fractional gradient descent method with adaptive momentum in BP neural networks

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  • Han, Xiaohui
  • Dong, Jianping

Abstract

A novel fractional gradient descent method with adaptive momentum is presented in this paper to improve the convergence speed and stability for BP neural network training. The fractional Grünwald-Letnikov derivative is used for the fractional gradient. The coefficient of the momentum term is set as an adaptive variable, depending on the fractional gradient of the current step and the weight change of the previous step. We give a detailed convergence proof of the proposed method. Experiments on MNIST data sets and XOR problem demonstrate that the fractional gradient descent method with adaptive momentum term can effectively improve convergence speed, maintain stability of BP neural network training, help escape from local minimum points, and enlarge the selection range of the learning rate.

Suggested Citation

  • Han, Xiaohui & Dong, Jianping, 2023. "Applications of fractional gradient descent method with adaptive momentum in BP neural networks," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    • Handle: RePEc:eee:apmaco:v:448:y:2023:i:c:s0096300323001133
    DOI: 10.1016/j.amc.2023.127944
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    References listed on IDEAS

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    1. Liu, Jianjun & Zhai, Rui & Liu, Yuhan & Li, Wenliang & Wang, Bingzhe & Huang, Liyuan, 2021. "A quasi fractional order gradient descent method with adaptive stepsize and its application in system identification," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    2. Lingge Li & Andrew Holbrook & Babak Shahbaba & Pierre Baldi, 2019. "Neural network gradient Hamiltonian Monte Carlo," Computational Statistics, Springer, vol. 34(1), pages 281-299, March.
    3. Blanka Horvath & Aitor Muguruza & Mehdi Tomas, 2021. "Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 11-27, January.
    4. Chen, Yuquan & Gao, Qing & Wei, Yiheng & Wang, Yong, 2017. "Study on fractional order gradient methods," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 310-321.
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