IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v448y2023ics0096300323001133.html
   My bibliography  Save this article

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 search 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)

    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. 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.
    2. Eduardo Abi Jaber & Shaun & Li, 2024. "Volatility models in practice: Rough, Path-dependent or Markovian?," Papers 2401.03345, arXiv.org.
    3. 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.
    4. 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.
    5. 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.
    6. 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).
    7. Aleksandar Arandjelovi'c & Julia Eisenberg, 2024. "Reinsurance with neural networks," Papers 2408.06168, arXiv.org.
    8. 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.
    9. Chaudhary, Naveed Ishtiaq & Khan, Zeshan Aslam & Kiani, Adiqa Kausar & Raja, Muhammad Asif Zahoor & Chaudhary, Iqra Ishtiaq & Pinto, Carla M.A., 2022. "Design of auxiliary model based normalized fractional gradient algorithm for nonlinear output-error systems," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    10. Wang, Ziyun & Wang, Xianzhe & Wang, Yan, 2024. "Orthotope-search-expansion-based extended zonotopic Kalman filter design for a discrete-time linear parameter-varying system with a dual-noise term," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    11. Francisco G'omez Casanova & 'Alvaro Leitao & Fernando de Lope Contreras & Carlos V'azquez, 2024. "Deep Joint Learning valuation of Bermudan Swaptions," Papers 2404.11257, arXiv.org.
    12. Mark Kiermayer & Christian Wei{ss}, 2022. "Neural calibration of hidden inhomogeneous Markov chains -- Information decompression in life insurance," Papers 2201.02397, arXiv.org.
    13. Antonis Papapantoleon & Jasper Rou, 2024. "A time-stepping deep gradient flow method for option pricing in (rough) diffusion models," Papers 2403.00746, arXiv.org.
    14. Dangxing Chen & Yuan Gao, 2024. "Attribution Methods in Asset Pricing: Do They Account for Risk?," Papers 2407.08953, arXiv.org.
    15. Laurens Van Mieghem & Antonis Papapantoleon & Jonas Papazoglou-Hennig, 2023. "Machine learning for option pricing: an empirical investigation of network architectures," Papers 2307.07657, arXiv.org.
    16. Guido Gazzani & Julien Guyon, 2024. "Pricing and calibration in the 4-factor path-dependent volatility model," Papers 2406.02319, arXiv.org.
    17. Eduardo Abi Jaber & Camille Illand & Shaun & Li, 2022. "Joint SPX-VIX calibration with Gaussian polynomial volatility models: deep pricing with quantization hints," Papers 2212.08297, arXiv.org.
    18. Jan Matas & Jan Pospíšil, 2023. "Robustness and sensitivity analyses of rough Volterra stochastic volatility models," Annals of Finance, Springer, vol. 19(4), pages 523-543, December.
    19. Mathieu Rosenbaum & Jianfei Zhang, 2021. "Deep calibration of the quadratic rough Heston model," Papers 2107.01611, arXiv.org, revised May 2022.
    20. Zijian Liu & Yaning Wang & Yang Luo & Chunbo Luo, 2022. "A Regularized Graph Neural Network Based on Approximate Fractional Order Gradients," Mathematics, MDPI, vol. 10(8), pages 1-20, April.

    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.