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Discrete Neural Network of Bidirectional Associative Memory

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Current Problems in Applied Mathematics and Computer Science and Systems (APAMCS 2022)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 702))

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Abstract

The paper considers bidirectional associative memory, which is one of the known neural network paradigms. To simplify the implementation of the calculation of this paradigm, a discrete mathematical model of its functioning is proposed. Reducing the complexity is achieved by switching to integer calculations because Integer multiplication is several times simpler than real multiplication. The known neural network of bidirectional associative memory neural network was compared with the proposed one. The simulation was carried out in the VHDL language. For comparative evaluation, Spartan3E, Spartan6 and XC9500 chips were used. In the experimental part, it was shown that the hardware costs for the implementation of the neural network of bidirectional associative memory have decreased by more than 3 times compared to the known one. The proposed discrete model of BAM functioning does not narrow the scope of its application in comparison with the known model and can be used to build memory devices and restore distorted or noisy information.

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References

  1. Kosko, B.: Bidirectional associative memories. IEEE Trans. Syst. Man Cybern. 18(1), 49–60 (1988)

    Google Scholar 

  2. Cao, J.D., Wang, L.: Exponential stability and periodic oscillatory solution in BAM networks with delays. IEEE Trans. Neural Netw. 13(2), 457–463 (2002)

    Article  Google Scholar 

  3. Sakthivel, R., et al.: Design of state estimator for bidirectional associative memory neural networks with leakage delays. Inf. Sci. 296, 263–274 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  4. Xu, C.: Local and global Hopf bifurcation analysis on simplified bidirectional associative memory neural networks with multiple delays. Math. Comput. Simul. 149, 69–90 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  5. Park, J.H., et al.: A new stability criterion for bidirectional associative memory neural networks of neutral-type. Appl. Math. Comput. 199(2), 716–722 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Shaposhnikov, A., Orazaev, A., Eremenko, E., Malakhov, D.: Hamming neural network in discrete form. In: Tchernykh, A., Alikhanov, A., Babenko, M., Samoylenko, I. (eds.) MANCS 2021. LNCS, vol. 424, pp. 11–17. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97020-8_2

  7. Ratnavelu, K., Manikandan, M., Balasubramaniam, P.: Synchronization of fuzzy bidirectional associative memory neural networks with various time delays. Appl. Math. Comput. 270, 582–605 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  8. Aouiti, C., Sakthivel, R., Touati, F.: Global dissipativity of high-order hopfield bidirectional associative memory neural networks with mixed delays. Neural Comput. Appl. 32(14), 10183–10197 (2020)

    Article  Google Scholar 

  9. Zhao, H.: Global stability of bidirectional associative memory neural networks with distributed delays. Phys. Lett. A 297(3–4), 182–190 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. Cao, J., Liang, J., Lam, J.: Exponential stability of high-order bidirectional associative memory neural networks with time delays. Physica D 199(3–4), 425–436 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kosko, B.: Adaptive bidirectional associative memories. Appl. Opt. 26(23), 4947–4960 (1987)

    Google Scholar 

  12. Aouiti, C., Sakthivel, R., Touati, F.: Global dissipativity of fuzzy bidirectional associative memory neural networks with proportional delays. Iranian J. Fuzzy Syst. 18(2), 65–80 (2021)

    MathSciNet  MATH  Google Scholar 

  13. Humphries, U., et al.: Global stability analysis of fractional-order quaternion-valued bidirectional associative memory neural networks. Mathematics 8(5), 801 (2020)

    Article  MathSciNet  Google Scholar 

  14. Makhzani, A., Frey, B.J.: Winner-take-all autoencoders. Adv. Neural Information Processing Systems, vol. 28 (2015)

    Google Scholar 

  15. Ionisyan, A.S.: Investigation of FPGA utilization of continues and discrete bidirectional associative memory neural networks. https://github.com/anserion/bidirmem_VHDL. Accessed 16 June 2022

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Acknowledgments

The authors would like to thank the North Caucasus Federal University for supporting the contest of projects competition of scientific groups and individual scientists of the North Caucasus Federal University. The work is supported by the North-Caucasus Center for Mathematical Research under agreement â„– 075-02-2021-1749 with the Ministry of Science and Higher Education of the Russian Federation and by Russian Foundation for Basic Research project 1907-00130.

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Authors and Affiliations

  1. Department of Mathematical Modeling, North-Caucasus Federal University, Stavropol, Russia

    Aleksey V. Shaposhnikov & Andrey S. Ionisyan

  2. North-Caucasus Center for Mathematical Research, North-Caucasus Federal University, Stavropol, Russia

    Anzor R. Orazaev

Authors
  1. Aleksey V. Shaposhnikov
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  2. Andrey S. Ionisyan
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  3. Anzor R. Orazaev
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Corresponding author

Correspondence to Anzor R. Orazaev .

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Editors and Affiliations

  1. Information Systems Department, Stavropol State Agrarian University, Stavropol, Russia

    Anatoly Alikhanov

  2. Information Systems Department, Stavropol State Agrarian University, Stavropol, Russia

    Pavel Lyakhov

  3. Information Systems Department, Stavropol State Agrarian University, Stavropol, Stavropol Territory, Russia

    Irina Samoylenko

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Shaposhnikov, A.V., Ionisyan, A.S., Orazaev, A.R. (2023). Discrete Neural Network of Bidirectional Associative Memory. In: Alikhanov, A., Lyakhov, P., Samoylenko, I. (eds) Current Problems in Applied Mathematics and Computer Science and Systems. APAMCS 2022. Lecture Notes in Networks and Systems, vol 702. Springer, Cham. https://doi.org/10.1007/978-3-031-34127-4_32

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  • DOI: https://doi.org/10.1007/978-3-031-34127-4_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-34126-7

  • Online ISBN: 978-3-031-34127-4

  • eBook Packages: EngineeringEngineering (R0)

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