Skip to main content
Springer Nature Link
Log in

Small-world Hopfield neural networks with weight salience priority and memristor synapses for digit recognition

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

A novel systematic design of associative memory networks is addressed in this paper, by incorporating both the biological small-world effect and the recently acclaimed memristor into the conventional Hopfield neural network. More specifically, the original fully connected Hopfield network is diluted by considering the small-world effect, based on a preferential connection removal criteria, i.e., weight salience priority. The generated sparse network exhibits comparable performance in associative memory but with much less connections. Furthermore, a hardware implementation scheme of the small-world Hopfield network is proposed using the experimental threshold adaptive memristor (TEAM) synaptic-based circuits. Finally, performance of the proposed network is validated by illustrative examples of digit recognition.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Driessche PVD, Zou X (1998) Global attractivity in delayed Hopfield neural network models. SIAM J Appl Math 58(6):1878–1890

    Article  MathSciNet  MATH  Google Scholar 

  2. Sporns O, Honey CJ (2006) Small worlds inside big brains. Proc Natl Acad Sci 103:19219–19220

    Article  Google Scholar 

  3. Humphries MD, Gurney K, Prescott TJ (2006) The brainstem reticular formation is a small-world, not scale-free, network. Proc R Soc B Biol Sci 273(1585):503–511

    Article  Google Scholar 

  4. Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small world’ networks. Nature 393:440–442

    Article  Google Scholar 

  5. Bassett DS, Bullmore ED (2006) Small-world brain networks. Neuroscientist 12:512–523

    Article  Google Scholar 

  6. Hu X, Feng G, Li H, Chen Y, Duan S (2014) An adjustable memristor model and its application in small-world neural networks. In: 2014 international joint conference on neural networks (IJCNN). Beijing, China

  7. Fekete T, Beacher FDCC, Cha J, Rubin D, Mujica-Parodi LR (2014) Small-world network properties inprefrontal cortex correlate with predictors of psychopathology risk in young children: a NIRS study. Neuroimage 85:345–353

    Article  Google Scholar 

  8. Taylor NR (2013) Small world network strategies for studying protein structures and binding. Comput Struct Biotechnol J 5(6):1–7

    Article  Google Scholar 

  9. Tkačik G, Marre O, Mora T et al (2013) The simplest maximum entropy model for collective behavior in a neural network. J Stat Mech Theory Exp 2013(03):P03011

    MathSciNet  Google Scholar 

  10. Chua LO (1971) Memristors: the missing circuit element. IEEE Trans Circuit Theory 18(5):507–519

    Article  Google Scholar 

  11. Strukov DB, Snider GS, Stewart DR, Williams RS (2008) The missing memristor found. Nature 453:80–83

    Article  Google Scholar 

  12. Williams RS (2008) How we found the missing memristor. IEEE Spectr 45:28–35

    Article  Google Scholar 

  13. Shin S, Kim K, Kang S-M (2013) Resistive computing: memristors enabled signal multiplication. IEEE Trans Circuits Syst I 60(5):1241–1249

    Article  MathSciNet  Google Scholar 

  14. Hu X, Chen G, Duan S, Geng G (2014) A memristor-based chaotic system with boundary conditions. In: Adamatzky A, Chua LO (eds) Memristor networks. International Publishing, New York, pp 351–364

    Chapter  Google Scholar 

  15. Cong J, Xiao B (2011) mrFPGA: A novel FPGA architecture with memristor-based reconfiguration. In: Proc. IEEE/ACM Int. Symp. Nanoscale Architectures, 1–8

  16. Mouttet B (2009) Proposal for memristors in signal processing. In: Proc. 3rd Int. ICST Conf., NanoNet 2008, Boston, MA. Revised Selected Papers, 11–13

  17. Duan S, Hu X, Wang L, Li C, Mazumder P (2012) Memristor-based RRAM with applications. Sci China Inf Sci. 55(6):1446–1460

    Article  Google Scholar 

  18. Thomas A (2013) Memristor-based neural networks. J Phys D Appl Phys 46(9):093001

    Article  Google Scholar 

  19. Pickett MD, Strukov DB, Borghetti JL, Yang JJ, Snider GS, Stewart DR, Williams RS (2009) Switching dynamics in titanium dioxide memristive devices. J Appl Phys 106(7):074508

    Article  Google Scholar 

  20. Abdalla H, Pickett MD (2011) SPICE modeling of memristors. In: Circuits and Systems (ISCAS), IEEE International Symposium on, pp. 1832–1835

  21. Wang X, Chen Y, Xi H, Li H, Dimitrov D et al (2009) Spintronic memristor through spin-torque-induced magnetization motion. Elec Device Lett IEEE 30:294–297

    Article  Google Scholar 

  22. Strukov DB, Williams RS (2009) Exponential ionic drift: fast switching and low volatility of thin-film memristors. Appl Phys A Mater Sci Proc 94(3):515–519

    Article  Google Scholar 

  23. Corinto F, Alon A, Marco G (2012) Mathematical models and circuit implementations of memristive systems. In: Cellular Nanoscale Networks and Their Applications (CNNA), 2012 13th International Workshop on, IEEE, pp. 1–6

  24. Pino RE, Bohl JW, McDonald N et al. (2012) Compact method for modeling and simulation of memristor devices: ion conductor chalcogenide-based memristor devices. In: Nanoscale Architectures (NANOARCH), 2010 IEEE/ACM International Symposium on, 1–4

  25. Kvatinsky Shahar, Friedman Eby G, Kolodny Avinoam, Weiser Uri C (2013) TEAM: thrEshold adaptive memristor model. Circuits Syst I Regular Papers IEEE Trans 60(1):211–221

    Article  MathSciNet  Google Scholar 

  26. Ascoli A, Corinto F, Senger V, Tetzlaff R (2013) Memristor model comparison. IEEE Trans Circuit Syst 89–105

  27. Biolek Z, Biolek D, Biolková V (2009) SPICE model of memristor with nonlinear dopant drift. Radio Eng 18:210–214

    Google Scholar 

  28. Rojas R (1996) Neural Networks. Springer, Berlin

    Book  MATH  Google Scholar 

  29. Haykin S (1999) Neural networks: a comprehensive foundation. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  30. Liu B, Chen Y, Wysocki B et al (2012) The circuit realization of a neuromorphic computing system with memristor-based synapse design Neural Information Processing. Springer, Berlin Heidelberg, pp 357–365

    Google Scholar 

  31. Chartier S, Proulx R (2005) NDRAM: nonlinear dynamic recurrent associative memory for learning bipolar and nonbipolar correlated patterns. IEEE Transactions on Neural Network 16:6

    Article  Google Scholar 

Download references

Acknowledgments

The work was supported by Program for New Century Excellent Talents in University (Grant Nos.[2013]47), National Natural Science Foundation of China (Grant Nos. 61372139, 61101233, 60972155), ‘Spring Sunshine Plan’ Research Project of Ministry of Education of China (Grant No. z2011148), Technology Foundation for Selected Overseas Chinese Scholars, Ministry of Personnel in China (Grant No. 2012-186), University Excellent Talents Supporting Foundations in of Chongqing (Grant No. 2011-65), University Key Teacher Supporting Foundations of Chongqing (Grant No. 2011-65), Fundamental Research Funds for the Central Universities (Grant Nos. XDJK2014A009, XDJK2013B011).

Author information

Authors and Affiliations

  1. School of Electronics and Information Engineering, Southwest University, Chongqing, 400715, China

    Shukai Duan, Zhekang Dong & Lidan Wang

  2. Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Kowloon, Hong Kong

    Xiaofang Hu

  3. Department of Electrical and Computer Engineering, University of Pittsburgh, Pittsburgh, PA, 15261, USA

    Xiaofang Hu & Hai Li

Authors
  1. Shukai Duan
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Zhekang Dong
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Xiaofang Hu
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Lidan Wang
    View author publications

    You can also search for this author inPubMed Google Scholar

  5. Hai Li
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Xiaofang Hu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Duan, S., Dong, Z., Hu, X. et al. Small-world Hopfield neural networks with weight salience priority and memristor synapses for digit recognition. Neural Comput & Applic 27, 837–844 (2016). https://doi.org/10.1007/s00521-015-1899-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-015-1899-7

Keywords