Advertisement

Design of Synthesizing Multi-valued High-Capacity Auto-associative Memories Based on Complex-Valued Networks

  • Chunlin Sha
  • Hongyong Zhao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11301)

Abstract

This paper presents a novel design method which is aimed to synthesize arbitrary multi-valued auto-associative memories via complex-valued neural networks. Globally exponential stable criteria are obtained to guarantee that the unique storage prototype can be retrieved. The proposed procedure enables auto-associative memories to be synthesized by satisfying the constraints of inequalities rather than the learning procedure. The main emphasis of the research presented here is on multi-valued high-capacity auto-associative memories via complex-valued networks. The designed auto-associative memories with \((2r+2)^n\) high memory capacities are robust with respect to design parameter selection and extend the scope of application of complex-valued neural networks. The approach of external inputs via complex-valued neural networks avoids spurious equilibria and retrieves the stored patters accurately. Some applicable experiments are given to illustrate the effectiveness and superiority.

Keywords

Multi-valued associative memories Network dynamics Design methods Real-imaginary-type activation External inputs 

Notes

Acknowledgement

The authors would like to thank the anonymous referees and editors for their helpful suggestions, which have improved the quality of this paper. This work was supported by National Natural Science Foundation of China (Grant nos. 11571170 and 11501290).

References

  1. 1.
    Aghajari, Z., Teshnehlab, M., Motlagh, M.: A novel chaotic hetero-associative memory. Neurocomputing 167, 352–358 (2015)CrossRefGoogle Scholar
  2. 2.
    Hirose, A.: Complex-Valued Neural Networks: Theories and Applications. World Scientific, Singapore (2003)CrossRefGoogle Scholar
  3. 3.
    Suzuki, Y., Kitahara, M., Kobayashi, M.: Dynamic complex-valued associative memory with strong bias terms. In: Lu, B.-L., Zhang, L., Kwok, J. (eds.) ICONIP 2011. LNCS, vol. 7062, pp. 509–518. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-24955-6_61CrossRefGoogle Scholar
  4. 4.
    Kitahara, M., Kobayashi, M.: Fundamental abilities of rotor associative memory. In: 9th IEEE International Conference on Computer and Information Science (ICIS), pp. 497–502 (2010)Google Scholar
  5. 5.
    Grassi, G.: A new approach to design cellular neural networks for associative memories. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 44, 835–838 (1997)CrossRefGoogle Scholar
  6. 6.
    Grassi, G.: On discrete-time cellular neural networks for associative memories. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 48, 107–111 (2001)CrossRefGoogle Scholar
  7. 7.
    Zeng, Z., Wang, J.: Design and analysis of high-capacity associative memories based on a class of discrete-time recurrent neural networks. IEEE Trans. Syst. Man Cybern Part B Cybern. 38, 1525–1536 (2008)CrossRefGoogle Scholar
  8. 8.
    Zeng, Z., Wang, J.: Associative memories based on continuous-time cellular neural networks designed using space-invariant cloning templates. Neural Netw. 22, 651–657 (2009)CrossRefGoogle Scholar
  9. 9.
    Han, Q., Liao, X., Huang, T., et al.: Analysis and design of associative memories based on stability of cellular neural networks. Neurocomputing 97, 192–200 (2012)CrossRefGoogle Scholar
  10. 10.
    Zhang, H., Huang, Y., Wang, B., et al.: Design and analysis of associative memories based on external inputs of delayed recurrent neural networks. Neurocomputing 136, 337–344 (2014)CrossRefGoogle Scholar
  11. 11.
    Zhou, C., Zeng, X., Yu, J., et al.: A unified associative memory model based on external inputs of continuous recurrent neural networks. Neurocomputing 186, 44–53 (2016)CrossRefGoogle Scholar
  12. 12.
    Sha, C., Zhao, H.: Design and analysis of associative memories based on external inputs of continuous bidirectional associative networks. Neurocomputing 266, 433–444 (2017)CrossRefGoogle Scholar
  13. 13.
    Xiu, C., Liu, C., Cheng, Y.: Associative memory network and its hardware design. Neurocomputing 158, 204–209 (2015)CrossRefGoogle Scholar
  14. 14.
    Chartier, S., Proulx, R.: NDRAM: nonlinear dynamic recurrent associative memory for learning bipolar and nonbipolar correlated patterns. IEEE Trans. Neural Netw. 16(6), 1393–1400 (2005)CrossRefGoogle Scholar
  15. 15.
    Chen, X., Zhao, Z., Song, Q., et al.: Multistability of complex-valued neural networks with time-varying delays. Appl. Math. Comput. 294, 18–35 (2017)MathSciNetGoogle Scholar
  16. 16.
    Song, Q., Yan, H., Zhao, Z., et al.: Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays. Neural Netw. 81, 1–10 (2016)CrossRefGoogle Scholar
  17. 17.
    Zhao, Z., Song, Q., Zhao, Y.: Stability of complex-valued neural networks with two additive time-varying delay components. In: Cong, F., Leung, A., Wei, Q. (eds.) ISNN 2017. LNCS, vol. 10261, pp. 564–571. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-59072-1_66CrossRefGoogle Scholar
  18. 18.
    Zhou, C., Zeng, X., Luo, C., et al.: A new local bipolar autoassociative memory based on external inputs of discrete recurrent neural networks with time delay. IEEE Trans. Neural Netw. Learn. Syst. 28(11), 2479–2489 (2016)CrossRefGoogle Scholar
  19. 19.
    Zheng, P., Tang, W., Zhang, J.: Efficient continuous-time asymmetric Hopfield networks for memory retrieval. Neural Comput. 22, 1597–1614 (2010)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Zheng, P.: Threshold complex-valued neural associative memory. IEEE Trans. Neural Netw. Learn. Syst. 25, 1714–1718 (2014)CrossRefGoogle Scholar
  21. 21.
    Huang, Y., Wang, X., Long, H., et al.: Synthesization of high-capacity auto-associative memories using complex-valued neural networks. Chin. Phys. B 25, 120701 (2016)CrossRefGoogle Scholar
  22. 22.
    Nie, X., Zheng, W., Cao, J.: Multistability of memristive Cohen-Grossberg neural networks with non-monotonic piecewise linear activation functions and time-varying delays. Neural Netw. 71, 27–36 (2015)CrossRefGoogle Scholar
  23. 23.
    Wang, L.: Dynamical analysis on the multistability of high-order neural networks. Neurocomputing 110, 137–144 (2013)CrossRefGoogle Scholar
  24. 24.
    Zeidler, E.: Nonlinear Functional Analysis and its Applications I: Fixed-Point Theorems. Springer, Heidelberg (1986)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsNanjing University of Aeronautics and AstronauticsNanjingChina

Personalised recommendations