Skip to main content
SpringerLink
Log in

A Winner-Take-All Neural Networks of N Linear Threshold Neurons without Self-Excitatory Connections

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

Multistable neural networks have attracted much interests in recent years, since the monostable networks are computationally restricted. This paper studies a N linear threshold neurons recurrent networks without Self-Excitatory connections. Our studies show that this network performs a Winner-Take-All (WTA) behavior, which has been recognized as a basic computational model done in brain. The contributions of this paper are: (1) It proves by mathematics that the proposed model is Non-Divergent. (2) An important implication (Winner-Take-All) of the proposed network model is studied. (3) Digital computer simulations are carried out to validate the performance of the theory findings.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hartline HK, Ratliff F (1958) Spatial summation of inhibitory influence in the eye of limulus and the mutual interaction of receptor units. J Gen Physiol 41: 1049–1066

    Article  Google Scholar 

  2. Salinas A, Abbott LF (1996) A model of multiplicative responses in parietal cortex. Proc Nat Acad Sci USA 93: 11956–11961

    Article  Google Scholar 

  3. Adorjan P, Levitt LB, Lund JS, Obermayer K (1999) A model for the intracortical origin of orientation preference and tuning in macaque striate cortex. Vis Neurosci 16: 303–318

    Article  Google Scholar 

  4. Hahnloser RLT, Sarpeshkar R, Mahowald MA, Douglas R, Seung H (2000) Digital selection and analogue amplification coexist in a cortexinsired silicon circuits. Nature 405: 947–951

    Article  Google Scholar 

  5. Wersing H, Beyn WJ, Ritter H (2001) Dynamical stability conditions for recurrent neural networks with unstarturating piecewise linear transfer functions. Neural comput 13: 1811–1825

    Article  MATH  Google Scholar 

  6. Hopfield JJ, Tank DW (1985) Neural computation of decisions in optimization problems. Biol Cybern 52: 141–152

    MATH  MathSciNet  Google Scholar 

  7. Chua LO, Yang L (1998) Cellular neural networks: theory. EEE Trans Circuits Syst 35(12): 1257–1272

    MathSciNet  Google Scholar 

  8. Feng J, Pan H, Roychowdhury VP (1996) On neurodynamics with limiter function and Linsker’s development model. Neural comput 8: 1003–1019

    Article  Google Scholar 

  9. Douglas R, Koch C, Mahowald M, Martin K, Suarez H (1995) Recurrent excitation in neocortical circuits. Science 269: 981–985

    Article  Google Scholar 

  10. Feng J, Hadeler K (1996) Qualitative behaviour of some simple networks. J Phys A 29: 5019–5033

    Article  MATH  MathSciNet  Google Scholar 

  11. Kuhn D, Loehwen R (1987) Piecewise affine bijections of R n, and the equation Sx + − Tx − =  y. Linear Algebra Appl 96: 109–129

    Article  MATH  MathSciNet  Google Scholar 

  12. Yi Z, Tan KK (2002) Dynamic stability conditions for Lotka-Volterra recurrent neural networks with delays. Phys Rev E 66: 1–8

    Google Scholar 

  13. Wersing H, Steil JJ, Ritter H (2001) A competitive-layer model for feature binding and sensory segmentation. Neural comput 13: 357–387

    Article  MATH  Google Scholar 

  14. Yi Z, Tan KK, Lee TH (2003) Multistability analysis for recurrent neural networks with unsaturating piecewise linear transfer functions. Neural Comput 15: 639–662

    Article  MATH  Google Scholar 

  15. Yi Z, Tan KK (2004) Multistability of discrete-time recurrent neural networks with unsaturating piecewise linear transfer functions. IEEE Trans Neural Netw 15(2): 329–336

    Article  Google Scholar 

  16. Tan KC, Tang HJ, Zhang WN (2004) Qualitative analysis for recurrent neural networks with linear threshold transfer functions. IEEE Trans Circuits Syst 52(5): 1003–1012

    MathSciNet  Google Scholar 

  17. Tang HJ, Tan KC, Zhang WN (2005) Analysis of cyclic dynamics for networks of linear threshold neurons. Neural Comput 17: 97–114

    Article  MATH  MathSciNet  Google Scholar 

  18. Hahnloser RLT (1998) On the piecewise analysis of networks of linear threshold neurons. Neural Netw 11: 691–697

    Article  Google Scholar 

  19. Song P, Wang XJ (2005) Angular path integration by moving hill of activity: a spiking neuron model without recurrent excitation of the head-direction system. J Comput Neurosci 25(4): 1002–1014

    MathSciNet  Google Scholar 

  20. Shi BE (2000) A low-power orientation-selective vision sensor. IEEE Trans Circuits Syst II 47(5): 435–440

    Article  Google Scholar 

  21. Shi BE, Boahen K (2002) Competitively coupled orientation selective cellular neural networks. IEEE Trans Circuits Syst I 49(3): 388–394

    Article  Google Scholar 

  22. Shimonomura K, Yagin T (2005) A Multichip aVLSI system emulating orientation selectivity of primary visual cortical cells. IEEE Trans Neural Netw 16(4): 972–979

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, People’s Republic of China

    Hong Qu, Zhang Yi & Xiaobin Wang

Authors
  1. Hong Qu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhang Yi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaobin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hong Qu.

Additional information

This work was supported by Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant 200806141049.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Qu, H., Yi, Z. & Wang, X. A Winner-Take-All Neural Networks of N Linear Threshold Neurons without Self-Excitatory Connections. Neural Process Lett 29, 143–154 (2009). https://doi.org/10.1007/s11063-009-9100-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-009-9100-x

Keywords

Search

Navigation