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On Structures with Emergent Computing Properties. A Connectionist versus Control Engineering Approach

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9094))

Abstract

This paper starts by revisiting some founding, classical ideas for Neural Networks as Artificial Intelligence devices. The basic functionality of these devices is given by stability related properties such as the gradient-like and other collective qualitative behaviors. These properties can be linked to the structural – connectionist – approach. A version of this approach is offered by the hyperstability theory which is presented in brief (its essentials) in the paper. The hyperstability of an isolated Hopfield neuron and the interconnection of these neurons in hyperstable structures are discussed. It is shown that the so-called “triplet” of neurons has good stability properties with a non-symmetric weight matrix. This suggests new approaches in developing of Artificial Intelligence devices based on the triplet interconnection of elementary systems (neurons) in order to obtain new useful emergent collective computational properties.

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References

  1. Răsvan, V.: Reflections on neural networks as repetitive structures with several equilibria and stable behavior. In: Rojas, I., Joya, G., Cabestany, J. (eds.) IWANN 2013, Part II. LNCS, vol. 7903, pp. 375–385. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  2. Graupe, D.: Principles of Artificial Neural Networks, Advanced Series on Circuits and Systems, vol. 6, 2nd edn. World Scientific, Singapore (2007)

    Google Scholar 

  3. Grossberg, S.: Self-organizing neural networks for stable control of autonomous behavior in a changing world. In: Taylor, J.G. (ed.) Mathematical Approaches to Neural Networks, pp. 139–197. Elsevier (1993)

    Google Scholar 

  4. Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 79(1), 2554–2558 (1982)

    Article  MathSciNet  Google Scholar 

  5. Hopfield, J.: Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. USA 81(5), 3088–3092 (1984)

    Article  Google Scholar 

  6. Neymark, Y.I.: Dynamical systems and controlled processes (in Russian). Nauka, Moscow (1978)

    Google Scholar 

  7. Danciu, D., Răsvan, V.: Dynamics of neural networks - some qualitative properties. In: Sandoval, F., Prieto, A.G., Cabestany, J., Graña, M. (eds.) IWANN 2007. LNCS, vol. 4507, pp. 8–15. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Danciu, D., Răsvan, V.: Gradient like behavior and high gain design of KWTA neural networks. In: Cabestany, J., Sandoval, F., Prieto, A., Corchado, J.M. (eds.) IWANN 2009, Part I. LNCS, vol. 5517, pp. 24–32. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  9. Danciu, D.: Dynamics of neural networks as nonlinear systems with several equilibria. In: Porto, A.B., Pazos, A., Buno, W. (eds.) Advancing Artificial Intelligence Through Biological Process Applications, pp. 331–357. IGI Global Publisher (2009)

    Google Scholar 

  10. Danciu, D., Răsvan, V.: Systems with slope restricted nonlinearities and neural networks dynamics. In: Cabestany, J., Rojas, I., Joya, G. (eds.) IWANN 2011, Part II. LNCS, vol. 6692, pp. 565–572. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  11. Danciu, D.: Systems with several equilibria. Applications to neural networks (in Romanian). Universitaria, Craiova Romania (2006)

    Google Scholar 

  12. Danciu, D.: Neural networks. Stability, synchronization, delays (in Romanian). Universitaria, Craiova Romania (2010)

    Google Scholar 

  13. Forti, M.: On global asymptotic stability of a class of nonlinear systems arising in neural network theory. J. Differ. Equ. 113(1), 246–264 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  14. Forti, M., Tesi, A.: A new method to analyze complete stability of pwl Cellular Neural Networks. Int. J. Bifurcation Chaos 11(3), 655–676 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  15. Marco, M.D., Forti, M., Grazzini, M., Pancioni, L.: Limit set dichotomy and convergence of cooperative piecewise linear neural networks. IEEE Trans. on Circuits and Systems I 58(5), 1052–1062, May 2011

    Google Scholar 

  16. Atencia, M., Joya, G., Sandoval, F.: Spurious minima and basins of attraction in higher-order Hopfield networks. In: Mira, J., Álvarez, J.R. (eds.) IWANN 2003. LNCS, vol. 2686, pp. 350–357. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  17. Qin, S., Xue, X.: Dynamical analysis of neural networks of subgradient systems. IEEE Trans. on Aut. Contr. 55(10), 2347–2352 (2010)

    Article  MathSciNet  Google Scholar 

  18. Lu, W., Wang, J.: Convergence analysis of a class of nonsmooth gradient systems. IEEE Trans. on Circuits and Systems I 55(11), 3514–3527, December 2008

    Google Scholar 

  19. Gelig, A.K., Leonov, G.A., Yakubovich, V.A.: Stability of systems with non-unique equilibria (in Russian). Nauka, Moscow (1978)

    Google Scholar 

  20. Leonov, G.A., Reitmann, V., Smirnova, V.B.: Non-Local Methods for Pendulum-Like Feedback Systems, Teubner-Texte zur Mathematik, vol. 132. B.G. Teubner Verlagsgeselllschaft, Stuttgart (1992)

    Book  Google Scholar 

  21. Yakubovich, V.A., Leonov, G.A., Gelig, A.K.: Stability of Stationary Sets in Control Systems with Discontinuous Nonlinearities, Stability, Vibration and Control of Systems, Series A, vol. 14. World Scientific, Singapore (2004)

    Google Scholar 

  22. Halanay, A., Răsvan, V.: Applications of Liapunov Methods in Stability, Mathematics and its Applications, vol. 245. Kluwer Academic Publishers, Dordrecht (1993)

    Book  Google Scholar 

  23. Răsvan, V.: Dynamical systems with several equilibria and natural Liapunov functions. Archivum Mathematicum 34(1), 207–215 (1998)

    MATH  MathSciNet  Google Scholar 

  24. Brockett, R.W.: Dynamical systems that sort lists, diagonalize matrices and solve linear programming problems. In: Proc. IEEE Conference on Decision and Control, pp. 799–803. IEEE Press (1988)

    Google Scholar 

  25. Cohen, M.: The construction of arbitrary stable dynamics in nonlinear neural networks. Neural Networks 5, 83–103 (1992)

    Article  Google Scholar 

  26. Warwick, K., Zhu, Q., Ma, Z.: A hyperstable neural network for the modelling and control of nonlinear systems. Sādhanā 25(2), 169–180 (2000)

    MATH  MathSciNet  Google Scholar 

  27. Popov, V.M.: Hyperstability of Control Systems, Die Grundlehren der mathematischen Wissenschaften, vol. 204. Springer Verlag, Berlin (1973)

    Google Scholar 

  28. Popov, V.M.: An analogue of electrical network synthesis in hyperstability (in Romanian). In: Proc. Symposium on Analysis and Synthesis of Electrical Networks. p. 9.1. No. III, Power Institute of Romanian Academy (1967)

    Google Scholar 

  29. Kurosh, A.G.: Lectures in General Algebra. Pure and Applied Mathematics Monographs. Pergamon Press, London (1965)

    MATH  Google Scholar 

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Correspondence to Daniela Danciu or Vladimir Răsvan .

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Danciu, D., Răsvan, V. (2015). On Structures with Emergent Computing Properties. A Connectionist versus Control Engineering Approach. In: Rojas, I., Joya, G., Catala, A. (eds) Advances in Computational Intelligence. IWANN 2015. Lecture Notes in Computer Science(), vol 9094. Springer, Cham. https://doi.org/10.1007/978-3-319-19258-1_35

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  • DOI: https://doi.org/10.1007/978-3-319-19258-1_35

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19257-4

  • Online ISBN: 978-3-319-19258-1

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