IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i23p3704-d1530019.html
   My bibliography  Save this article

Approximation of Time-Frequency Shift Equivariant Maps by Neural Networks

Author

Listed:
  • Dae Gwan Lee

    (Department of Mathematics and Big Data Science, Kumoh National Institute of Technology, Gumi 39177, Gyeongsangbuk-do, Republic of Korea)

Abstract

Based on finite-dimensional time-frequency analysis, we study the properties of time-frequency shift equivariant maps that are generally nonlinear. We first establish a one-to-one correspondence between Λ -equivariant maps and certain phase-homogeneous functions and also provide a reconstruction formula that expresses Λ -equivariant maps in terms of these phase-homogeneous functions, leading to a deeper understanding of the class of Λ -equivariant maps. Next, we consider the approximation of Λ -equivariant maps by neural networks. In the case where Λ is a cyclic subgroup of order N in Z N × Z N , we prove that every Λ -equivariant map can be approximated by a shallow neural network whose affine linear maps are simply linear combinations of time-frequency shifts by Λ . This aligns well with the proven suitability of convolutional neural networks (CNNs) in tasks requiring translation equivariance, particularly in image and signal processing applications.

Suggested Citation

  • Dae Gwan Lee, 2024. "Approximation of Time-Frequency Shift Equivariant Maps by Neural Networks," Mathematics, MDPI, vol. 12(23), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3704-:d:1530019
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/23/3704/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/23/3704/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. David Silver & Aja Huang & Chris J. Maddison & Arthur Guez & Laurent Sifre & George van den Driessche & Julian Schrittwieser & Ioannis Antonoglou & Veda Panneershelvam & Marc Lanctot & Sander Dieleman, 2016. "Mastering the game of Go with deep neural networks and tree search," Nature, Nature, vol. 529(7587), pages 484-489, January.
    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. Tian Zhu & Merry H. Ma, 2022. "Deriving the Optimal Strategy for the Two Dice Pig Game via Reinforcement Learning," Stats, MDPI, vol. 5(3), pages 1-14, August.
    2. Xiaoyue Li & John M. Mulvey, 2023. "Optimal Portfolio Execution in a Regime-switching Market with Non-linear Impact Costs: Combining Dynamic Program and Neural Network," Papers 2306.08809, arXiv.org.
    3. Pedro Afonso Fernandes, 2024. "Forecasting with Neuro-Dynamic Programming," Papers 2404.03737, arXiv.org.
    4. Nathan Companez & Aldeida Aleti, 2016. "Can Monte-Carlo Tree Search learn to sacrifice?," Journal of Heuristics, Springer, vol. 22(6), pages 783-813, December.
    5. Yuchen Zhang & Wei Yang, 2022. "Breakthrough invention and problem complexity: Evidence from a quasi‐experiment," Strategic Management Journal, Wiley Blackwell, vol. 43(12), pages 2510-2544, December.
    6. Yassine Chemingui & Adel Gastli & Omar Ellabban, 2020. "Reinforcement Learning-Based School Energy Management System," Energies, MDPI, vol. 13(23), pages 1-21, December.
    7. Zhewei Zhang & Youngjin Yoo & Kalle Lyytinen & Aron Lindberg, 2021. "The Unknowability of Autonomous Tools and the Liminal Experience of Their Use," Information Systems Research, INFORMS, vol. 32(4), pages 1192-1213, December.
    8. Yuhong Wang & Lei Chen & Hong Zhou & Xu Zhou & Zongsheng Zheng & Qi Zeng & Li Jiang & Liang Lu, 2021. "Flexible Transmission Network Expansion Planning Based on DQN Algorithm," Energies, MDPI, vol. 14(7), pages 1-21, April.
    9. JinHyo Joseph Yun & EuiSeob Jeong & Xiaofei Zhao & Sung Deuk Hahm & KyungHun Kim, 2019. "Collective Intelligence: An Emerging World in Open Innovation," Sustainability, MDPI, vol. 11(16), pages 1-15, August.
    10. Thomas P. Novak & Donna L. Hoffman, 2019. "Relationship journeys in the internet of things: a new framework for understanding interactions between consumers and smart objects," Journal of the Academy of Marketing Science, Springer, vol. 47(2), pages 216-237, March.
    11. Huang, Ruchen & He, Hongwen & Gao, Miaojue, 2023. "Training-efficient and cost-optimal energy management for fuel cell hybrid electric bus based on a novel distributed deep reinforcement learning framework," Applied Energy, Elsevier, vol. 346(C).
    12. Gokhale, Gargya & Claessens, Bert & Develder, Chris, 2022. "Physics informed neural networks for control oriented thermal modeling of buildings," Applied Energy, Elsevier, vol. 314(C).
    13. Li Xia, 2020. "Risk‐Sensitive Markov Decision Processes with Combined Metrics of Mean and Variance," Production and Operations Management, Production and Operations Management Society, vol. 29(12), pages 2808-2827, December.
    14. Sabrina Evans & Paolo Turrini, 2023. "Improving Strategic Decisions in Sequential Games by Exploiting Positional Similarity," Games, MDPI, vol. 14(3), pages 1-13, April.
    15. Neha Soni & Enakshi Khular Sharma & Narotam Singh & Amita Kapoor, 2019. "Impact of Artificial Intelligence on Businesses: from Research, Innovation, Market Deployment to Future Shifts in Business Models," Papers 1905.02092, arXiv.org.
    16. Wei-Chang Yeh & Yu-Hsin Hsieh & Chia-Ling Huang, 2022. "Newly Developed Flexible Grid Trading Model Combined ANN and SSO algorithm," Papers 2211.12839, arXiv.org.
    17. Yin, Linfei & He, Xiaoyu, 2023. "Artificial emotional deep Q learning for real-time smart voltage control of cyber-physical social power systems," Energy, Elsevier, vol. 273(C).
    18. Omar Al-Ani & Sanjoy Das, 2022. "Reinforcement Learning: Theory and Applications in HEMS," Energies, MDPI, vol. 15(17), pages 1-37, September.
    19. Taejong Joo & Hyunyoung Jun & Dongmin Shin, 2022. "Task Allocation in Human–Machine Manufacturing Systems Using Deep Reinforcement Learning," Sustainability, MDPI, vol. 14(4), pages 1-18, February.
    20. Jikai Jin & Vasilis Syrgkanis, 2023. "Learning Causal Representations from General Environments: Identifiability and Intrinsic Ambiguity," Papers 2311.12267, arXiv.org, revised Feb 2024.

    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:gam:jmathe:v:12:y:2024:i:23:p:3704-:d:1530019. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.