IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v448y2023ics0096300323001133.html

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300323001133
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2023.127944?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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).
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wang, Junwei & Xiong, Weili & Ding, Feng & Zhou, Yihong & Yang, Erfu, 2025. "Parameter estimation method for separable fractional-order Hammerstein nonlinear systems based on the on-line measurements," Applied Mathematics and Computation, Elsevier, vol. 488(C).
    2. Zhang, Hui & Zhou, Shenglong & Li, Geoffrey Ye & Xiu, Naihua & Wang, Yiju, 2025. "A step function based recursion method for 0/1 deep neural networks," Applied Mathematics and Computation, Elsevier, vol. 488(C).
    3. Mao, Jianfeng & Li, Zheng & Yu, Zhiwu & Hu, Lianjun & Khan, Mansoor & Wu, Jun, 2025. "A novel hybrid approach combining PDEM and bayesian optimization deep learning for stochastic vibration analysis in train-track-bridge coupled system," Reliability Engineering and System Safety, Elsevier, vol. 257(PA).
    4. Edson Fernandez & Victor Huilcapi & Isabela Birs & Ricardo Cajo, 2025. "The Role of Fractional Calculus in Modern Optimization: A Survey of Algorithms, Applications, and Open Challenges," Mathematics, MDPI, vol. 13(19), pages 1-34, October.
    5. Harjule, Priyanka & Sharma, Rinki & Kumar, Rajesh, 2025. "Fractional-order gradient approach for optimizing neural networks: A theoretical and empirical analysis," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    6. Elnady, Sroor M. & El-Beltagy, Mohamed & Radwan, Ahmed G. & Fouda, Mohammed E., 2025. "A comprehensive survey of fractional gradient descent methods and their convergence analysis," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Elnady, Sroor M. & El-Beltagy, Mohamed & Radwan, Ahmed G. & Fouda, Mohammed E., 2025. "A comprehensive survey of fractional gradient descent methods and their convergence analysis," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    2. Changqing Teng & Guanglian Li, 2025. "Efficient Simulation and Calibration of the Rough Bergomi Model via Wasserstein Distance," Papers 2512.00448, arXiv.org, revised Apr 2026.
    3. Patrick Büchel & Michael Kratochwil & Maximilian Nagl & Daniel Rösch, 2022. "Deep calibration of financial models: turning theory into practice," Review of Derivatives Research, Springer, vol. 25(2), pages 109-136, July.
    4. Eduardo Abi Jaber & Shaun & Li, 2024. "Volatility models in practice: Rough, Path-dependent or Markovian?," Papers 2401.03345, arXiv.org, revised Apr 2025.
    5. Alessio Brini & David A. Hsieh & Patrick Kuiper & Sean Moushegian & David Ye, 2025. "Empirical Models of the Time Evolution of SPX Option Prices," Papers 2506.17511, arXiv.org.
    6. Hyun-Gyoon Kim & Hyeongmi Kim & Jeonggyu Huh, 2025. "Considering Appropriate Input Features of Neural Network to Calibrate Option Pricing Models," Computational Economics, Springer;Society for Computational Economics, vol. 66(1), pages 77-104, July.
    7. Naveed Ishtiaq Chaudhary & Muhammad Asif Zahoor Raja & Zeshan Aslam Khan & Khalid Mehmood Cheema & Ahmad H. Milyani, 2021. "Hierarchical Quasi-Fractional Gradient Descent Method for Parameter Estimation of Nonlinear ARX Systems Using Key Term Separation Principle," Mathematics, MDPI, vol. 9(24), pages 1-14, December.
    8. Jiří Witzany & Milan Fičura, 2023. "Machine Learning Applications to Valuation of Options on Non-liquid Markets," FFA Working Papers 5.001, Prague University of Economics and Business, revised 24 Jan 2023.
    9. Guo, Jingjun & Kang, Weiyi & Wang, Yubing, 2024. "Multi-perspective option price forecasting combining parametric and non-parametric pricing models with a new dynamic ensemble framework," Technological Forecasting and Social Change, Elsevier, vol. 204(C).
    10. Lijuan Wang & Yijia Hu & Yan Zhou, 2024. "Cross-border Commodity Pricing Strategy Optimization via Mixed Neural Network for Time Series Analysis," Papers 2408.12115, arXiv.org.
    11. Chaudhary, Naveed Ishtiaq & Raja, Muhammad Asif Zahoor & Khan, Zeshan Aslam & Mehmood, Ammara & Shah, Syed Muslim, 2022. "Design of fractional hierarchical gradient descent algorithm for parameter estimation of nonlinear control autoregressive systems," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    12. Villarino, Joel P. & Leitao, Alvaro, 2026. "On deep learning for computing the dynamic initial margin and margin value adjustment," Applied Mathematics and Computation, Elsevier, vol. 510(C).
    13. Jian Lv & Chenxu Wang & Wenyong Yuan & Zhenyi Zhang, 2025. "The Study on Option Pricing Based on Wiener–Itô Chaos Expansion and Generative Adversarial Networks," Computational Economics, Springer;Society for Computational Economics, vol. 66(4), pages 2675-2713, October.
    14. Fabio Baschetti & Giacomo Bormetti & Pietro Rossi, 2025. "Joint deep calibration of the 4-factor PDV model," Papers 2507.09412, arXiv.org.
    15. Aleksandar Arandjelovi'c & Julia Eisenberg, 2024. "Optimal risk mitigation by deep reinsurance," Papers 2408.06168, arXiv.org, revised Nov 2025.
    16. Qinwen Zhu & Gregoire Loeper & Wen Chen & Nicolas Langrené, 2021. "Markovian approximation of the rough Bergomi model for Monte Carlo option pricing," Post-Print hal-02910724, HAL.
    17. Bienvenue Feugang Nteumagné & Hermann Azemtsa Donfack & Celestin Wafo Soh, 2025. "Variational Autoencoders for Completing the Volatility Surfaces," JRFM, MDPI, vol. 18(5), pages 1-22, April.
    18. Daniele Angelini & Fabrizio Di Sciorio, 2025. "Integrating the implied regularity into implied volatility models: A study on free arbitrage model," Papers 2502.07518, arXiv.org.
    19. Federico M. Bandi & Nicola Fusari & Guido Gazzani & Roberto Ren`o, 2026. "Ultra-short-term volatility surfaces," Papers 2603.29430, arXiv.org.
    20. Eduardo Abi Jaber & Camille Illand & Shaun Xiaoyuan Li, 2024. "Joint SPX-VIX calibration with Gaussian polynomial volatility models: deep pricing with quantization hints," Post-Print hal-03902513, HAL.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:448:y:2023:i:c:s0096300323001133. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.