Stable computational dynamics for a class of circuits with O(N) interconnections capable of KWTA and rank extractions

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 52, Issue 5, 2005, Pages 949-959

  Marinov, Corneliu A ^a   Hopfield, John J ^b  

^a UNIVERSITY POLITEHNICA OF BUCHAREST   (Romania)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

Computational capability; Dynamic system; K winners take all (KWTA) circuits; Lyapunov function; Neural network; Ranking; Selection

Indexed keywords

AMPLIFIERS (ELECTRONIC); CONVERGENCE OF NUMERICAL METHODS; FEEDBACK; LYAPUNOV METHODS; MATHEMATICAL MODELS; NEURAL NETWORKS; THEOREM PROVING;

ANALOG CIRCUIT; COMPUTATIONAL CAPABILITY; DYNAMIC SYSTEM; LYAPUNOV FUNCTION;

CIRCUIT THEORY;

EID: 20144378649     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2005.846662     Document Type: Article

References (32)

1. J. J. Hopfield, "Neurons with graded response have collective computational properties like those of two state neurons," in Proc. Nat. Academy Sci., vol. 81, 1984, pp. 3088-3092.
2. J. J. Hopfield and D. W. Tank, "Neural computation of decisions optimization problems," Biol. Cybern., vol. 52, pp. 141-152, 1985.
3. D. W. Tank and J. J. Hopfield, "Simple 'Neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit," IEEE Trans. Circuits Syst., vol. CAS-33, pp. 533-541, May 1986.
4. J.-H. Li, A. N. Michel, and W. Porod, "Analysis and synthesis of a class of neural networks: Linear systems operating on a closed hypercube.," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 36, no. 11, pp. 1405-1422, Nov. 1989.
5. S. V. B. Aiyer, M. Niranjan, and F. Fallside, "A theoretical investigation into the performance of the Hopfield model," IEEE Trans. Neural Netw., vol. 1, no. 3, pp. 204-215, Jun. 1990.
6. F. M. A. Salam, Y. Wang, and M.-R. Chai, "On the analysis of dynamic feedaback neural nets," IEEE Trans. Circuits Syst., vol. 38, no. 2, pp. 196-201, Feb. 1991.
7. H. Yang and T. S. Dillon, "Exponential stability and oscillation of Hopfield graded response neural network," IEEE Trans. Neural Netw., vol. 5, no. 3, pp. 719-729, Sep. 1994.
8. N. Peterfreund and Y. Baram, "Second order bounds on the domain of attraction and the rate of convergence of nonlinear dynamical systems and neural networks," IEEE Trans. Neural Netw., vol. 5, no. 2, pp. 551-560, Jul. 1994.
9. M. Vidysagar, "Minimum-seeking properties of analog neural networks with multilinear objective functions," IEEE Trans. Autom. Contr., vol. 40, no. 8, pp. 1359-1375, Aug. 1995.
10. J. Cao, "Global exponential stability of Hopfield neural networks," Int. J. Syst. Sci, vol. 32, no. 2, pp. 233-236, Feb. 2001.
11. S. Hu and J. Wang, "Absolute exponential stability of a class of continuous time recurrent neural networks," IEEE Trans. Neural Netw., vol. 14, no. 1, pp. 35-45, Jan. 2003.
12. E. Majani, R. Erlanson, and Y. Abu-Mostafa, "On the K-winners-take-all network," in Advances in Neural Information Processing Systems, D. S. Touretzky, Ed. San Mateo, CA: Morgan-Kaufmann, 1989, vol. 1, pp. 634-642.
13. R. Erlanson and Y. Abu-Mostafa, "Analog neural networks as decoders," in Advances in Neural Information Processing systems, D. S. Touretzky, Ed. Los Angeles, CA: Morgan-Kaufmann, 1991, vol. 3, pp. 585-588.
14. M. Atkins, "Sorting by Hopfield nets," in Proc. Int. Joint Conf. Neural Networks, vol. 2, Washington, DC, 1992, pp. 65-68.
15. B. D. Calvert and C. A. Marinov, "Another K-winners-take-all analog neural network," IEEE Trans Neural Netw., vol. 11, no. 3, pp. 829-838, Jul. 2000.
16. C. A. Marinov and B. D. Calvert, "Performance analysis for a K-winners-take-all analog neural network: Basic theory," IEEE Trans. Neural Netw., vol. 14, no. 3, pp. 766-780, Jul. 2003.
17. C. A. Marinov and B. D. Calbert, "Sorting with dynamical systems of neural type," Math. Rep., vol. 5(55), no. 4, pp. 333-342, 2003.
18. J. Lazzaro, S. Ryckebush, M. A. Mahowald, and C. A. Mead, "Winner-take-all networks of O(n) complexity," in Advances in Neural Information Processing Systems, D. S. Touretzky, Ed. San Mateo, CA: Morgan-Kaufmann, 1989, vol. 1, pp. 703-711.
19. B. P. Tan and D. M. Wilson, "Semiparallel rank order filtering in analog VLSI," IEEE Trans. Circuits Syst. II: Analog Digit. Signal Process., vol. 48, no. 2, pp. 198-205, Feb. 2001.
20. I. E. Opris, "Analog rank extractors," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 44, no. 12, pp. 1114-1121, Dec. 1997.
21. Y. Fang, M. A. Cohen, and T. G. Kincaid, "Dynamics of a winner-take-all neural network," Neural Netw., vol. 9, no. 7, pp. 1141-1154, 1996.
22. B. Sekerkiran and U. Cilingiroglu, "A CMOS K-winners-take-all circuit with O(n) complexity," IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 46, no. 1, pp. 1-5, Jan. 1999.
23. R. P. Lippmann, "An introduction to computing with neural nets," IEEE ASSP Magazine, pp. 4-22, Apr. 1987.
24. T. S. Dranger and R. Priemer, "Collective process circuit that sorts," Proc. IEE, Circuits Devices Syst., vol. 144, pp. 145-148, Jun. 1997.
25. T. M. Kwon and M. Zervakis, "A parallel sorting network without comparators: A neural network approach," in Proc. Int. Joint Conf. Neural Networks, vol. 1, Baltimore, MD, 1992, pp. 701-706.
26. Y. Takefuji and K.-C. Lee, "A super-parallel sorting algorithm based on neural networks," IEEE Trans. Circuits Syst., vol. 37, no. 11, pp. 1425-1429, Nov. 1990.
27. J. Wang, "Analysis and design of an analog sorting network," IEEE Trans. Neural Netw., vol. 6, no. 3, pp. 962-971, Jul. 1995.
28. J. P. F. Sum, C.-S. Leung, P. K. S. Tam, G. H. Young, W. K. Kan, and L.-W. Chan, "Analysis for a class of winner-take-all model," IEEE Trans. Neural Netw., vol. 10, no. 1, pp. 64-71, Jan. 1999.
29. T. P. Troudet and S. M. Walters, "Neural network architecture for crossbar switch control," IEEE Trans. Circuits Syst., vol. 38, no. 1, pp. 42-56, Jan. 1991.
30. J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables. London, U.K.: Academic, 1970.
31. M. Vidyasagar, Nonlinear Systems Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1993.
32. H. K. Khalil, Nonlinear Systems. New York: Macmillan, 1992.