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Recursive Nodes with Rich Dynamics as Modeling Tools for Cognitive Functions

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Neurodynamics of Cognition and Consciousness

Part of the book series: Understanding Complex Systems ((UCS))

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Abstract

This chapter addresses artificial neural networks employing processing nodes with complex dynamics and the representation of information through spatiotemporal patterns. These architectures can be programmed to store information through cyclic collective oscillations, which can be explored for the representation of stored memories or pattern classes. The nodes that compose the network are parametric recursions that present rich dynamics, bifurcation and chaos. A blend of periodic and erratic behavior is explored for the representation of information and the search for stored patterns. Several results on these networks have been produced in recent years, some of them showing their superior performance on pattern storage and recovery when compared to traditional neural architectures. We discuss tools of analysis, design methodologies and tools for the characterization of these RPEs networks (RPEs - Recursive Processing Elements, as the nodes are named).

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References

  1. Aihara, K., Takabe, T., Toyoda, M.: Chaotic Neural Networks. Physica Letters A, Vol. 144(6,7 1990), 333–340

    Article  Google Scholar 

  2. Adachi, M., Aihara, K.: Associative Dynamics in a Chaotic Neural Network. Neural Networks, Vol. 10(1997), 83–98

    Article  Google Scholar 

  3. Caianiello, E. R.: Outline of a Theory of Thought-Processes and Thinking Machines. Journal on Theoretical Biology, Vol. 2(1961), 204–235

    Article  Google Scholar 

  4. Del-Moral-Hernandez, E.: Bifurcating Pulsed Neural Networks, Chaotic Neural Networks and Parametric Recursions: Conciliating Different Frameworks in Neuro-like Computing. In: International Joint Conference on Neural Networks 2000, Vol. 6, 423–428, Como, Italy

    Google Scholar 

  5. Del-Moral-Hernandez, E.: A Novel Time-Based Neural Coding for Artificial Neural Networks with Bifurcating Recursive Processing Elements. In: International Joint Conference on Neural Networks 2001, Vol. 1, 44–49, Washington, USA

    Google Scholar 

  6. Del-Moral-Hernandez, E.: Neural Networks with Chaotic Recursive Nodes: Techniques for the Design of Associative Memories, Contrast with Hopfield Architectures, and Extensions for Time-dependent Inputs. Neural Networks, Vol. 16(2003) 675–682

    Article  Google Scholar 

  7. Del-Moral-Hernandez, E., Gee-Hyuk Lee, Farhat, N.: Analog Realization of Arbitrary One Dimensional Maps. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 50(Dec.2003), 1538–1547

    Article  Google Scholar 

  8. Del-Moral-Hernandez, E.: Contrasting Coupling Strategies in Associative Neural Networks with Chaotic Recursive Processing Elements. In: Neural networks and Computational Intelligence IASTED Conference, NCI 2004, Grindelwald, Switzerland

    Google Scholar 

  9. Del-Moral-Hernandez, E., Silva, L. A.: A New Hybrid Neural Architecture (MLP+RPE) for Hetero Association: Multi Layer Perceptron and Coupled Recursive Processing Elements Neural Networks. In: International Joint Conference on Neural Networks 2004, Budapest

    Google Scholar 

  10. Del-Moral-Hernandez, E., Sandmann, H., Silva, L. A.: Pattern Recovery in Networks of Recursive Processing Elements with Continuous Learning. In: International Joint Conference on Neural Networks 2004, Budapest

    Google Scholar 

  11. Del-Moral-Hernandez, E.: Non-Homogenous Structures in Neural Networks with Chaotic Recursive Nodes: Dealing with Diverse Multi-assemblies Architectures, Connectivity and Arbitrary Bifurcating Nodes. In: International Joint Conference on Neural Networks 2005, Montreal

    Google Scholar 

  12. Del-Moral-Hernandez, E.: Non-homogenous Neural Networks with Chaotic Recursive Nodes: Connectivity and Multi-assemblies Structures in Recursive Processing Elements Architectures, Neural Networks, Vol. 18(n.5–6, 2005), 532–540

    Article  Google Scholar 

  13. Del-Moral-Hernandez, E.: Fragmented Basins of Attraction of Recursive Processing Elements in Associative Neural Networks and its Impact on Pattern Recovery Performance. In: International Joint Conference on Neural Networks 2006, Vancouver

    Google Scholar 

  14. Del-Moral-Hernandez, E.: Chaotic Searches and Stable Spatio-temporal Patterns as a Naturally Emergent Mixture in Networks of Spiking Neural Oscillators with Rich Dynamics. In: International Joint Conference on Neural Networks 2006, Vancouver

    Google Scholar 

  15. Farfan-Pelaez, A., Del-Moral-Hernandez, E., Navarro, J. S. J., Van Noije, W.: A CMOS Implementation of the Sine-circle Map. In: 48th IEEE International Midwest Symposium on Circuits & Systems, Cincinnatti, 2005

    Google Scholar 

  16. 16. Farhat, N. H., S-Y Lin, Eldelfrawy, M.: Complexity and Chaotic Dynamics in Spiking Neuron Embodiment, SPIE Critical Review, Vol. CR55 (1994), 77-88, SPIE, Bellingham,Washington

    Google Scholar 

  17. Farhat, N. H. Del-Moral-Hernandez, E.: Logistic Networks with DNA-Like Encoding and Interactions. Lecture Notes in Computer Science, Vol. 930 (1995), 214–222. Berlin: Springer-Verlag

    Google Scholar 

  18. Freeman, W. J.: Tutorial on Neurobiology: From Single Neuron to Brain Chaos. International Journal of Bifurcation and Chaos, Vol. 2(3, 1992), 451–482

    Article  MATH  Google Scholar 

  19. Gerstner,W., Kistler,W.M.: Spiking NeuronModels: Single Neurons, Populations, Plasticity, Cambridge University Press, Cambridge, UK (2002)

    MATH  Google Scholar 

  20. Haykin, S.: Neural Networks: a Comprehensive Foundation, 2nd edn., Prentice Hall, NJ: Upper Saddle River (1999)

    MATH  Google Scholar 

  21. Hilborn, R.C.: Chaos and Nonlinear Dynamics: an Introduction for Scientists and Engineers, New York, Oxford University Press (1994)

    MATH  Google Scholar 

  22. Hopfield, J. J.: Neural Networks and Physical Systems with Emergent Collective Computational Abilities. Proceedings of the National Academy of Sciences, USA, Vol. 79(1982),2554–2558

    Article  Google Scholar 

  23. Hopfield, J. J.: Pattern Recognition Computation Using Action Potential Timing for Stimulus Representation. Nature, Vol. 376 (1995), 33–36

    Article  Google Scholar 

  24. Ishii, S. et al.: Associative Memory Using Spatiotemporal Chaos. In: International Joint Conference on Neural Networks 1993, Vol. 3, 2638–2641, Nagoya

    Google Scholar 

  25. Kaneko, K.: Overview of Coupled Map Lattices. Chaos, Vol. 2(3, 1992), 279–282

    Article  MATH  Google Scholar 

  26. Kaneko, K.: The Coupled Map Lattice: Introduction, Phenomenology, Lyapunov Analysis, Thermodynamics and Applications. In Theory and Applications of Coupled Map Lattices, 1–49. John Wiley – Sons, Chichester (1993)

    Google Scholar 

  27. Kaneko, K., Tsuda, I.: Complex Systems: Chaos and Beyond: a Constructive Approach with Applications in Life Sciences, Springer-Verlag (2001)

    Google Scholar 

  28. Kandel, E. R., Schwartz, J. H., Jessell, T.M.: Principles of Neural Science, Appleton & Lange, Norwalk, Connecticut (1991)

    Google Scholar 

  29. Kelso, J. A. S.: Dynamic Patterns - the Self-Organization of Brain Behavior, The MIT Press, MA: Cambridge (1995)

    Google Scholar 

  30. Kosko, B.: Bidirectional Associative Memories. IEEE Transactions on Systems, Man, and Cybernetics, Vol. 18 (Jan-Feb 1988), 49–60

    Article  Google Scholar 

  31. Kozma, R., Freeman, W.J.: Encoding and Recall of Noisy Data as Chaotic Spatio-Temporal Memory Patterns in the Style of the Brains. In: International Joint Conference on Neural Networks 2000, Vol. 5, 33–38, Como, Italy

    Google Scholar 

  32. Kozma, R., Freeman, W.J.: Control of Mesoscopic/Intermediate-Range Spatio-TemporalChaos in the Cortex. In: American Control Conference 2001, Vol. 1, 263–268

    Google Scholar 

  33. Lysetskiy, M., Zurada, J.M., Lozowasky, A.: Bifurcation-Based Neural Computation. In: International Joint Conference on Neural Networks 2002, Vol. 3, 2716–2720

    Google Scholar 

  34. McEliece, R., E., Posner, E., Venkatesh, S.: The Capacity of the Hopfield Associative Memory. IEEE Transactions on Information Theory, Vol. 33(4, Jul.1987), 461–482

    Article  MATH  Google Scholar 

  35. Nagumo, J., Sato, S.: On a Response Characteristic of a Mathematical Neuron Model. Kybernetic, Vol. 10(1972), 155–164, 1972

    Google Scholar 

  36. Principe, J. C., Tavares, V. G., Harris J. G, Freeman, W. J.: Design and Implementation of a Biologically Realistic Olfactory Cortex in Analog VLSI. Proceedings of the IEEE, Vol.89(2001), 1030–1051

    Article  Google Scholar 

  37. Siegelmann, H. T.: Computation Beyond the Turing Limit. Science, Vol. 268(1995), 545–548

    Article  Google Scholar 

  38. Wang, L.: Heteroassociations of Spatio-Temporal Sequences with the Bidirectional Associative Memory. IEEE Transactions on Neural Networks, Vol. 11(2000), 1503–1505

    Article  Google Scholar 

  39. Wang, D.: A Comparison of CNN and LEGION Networks. International Joint Conference on Neural Networks 2004, 1735–1740

    Google Scholar 

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Authors
  1. Emilio Del-Moral-Hernandez
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Editor information

Editors and Affiliations

  1. School of Engineering and Applied Sciences, Harvard University, 33 Oxford St, Cambridge, MA 02138, USA

    Leonid I. Perlovsky

  2. Computational Neurodynamics Laboratory 373 Dunn Hall, Department of Computer Science University of Memphis, Memphis, TN 38152, USA

    Robert Kozma

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Del-Moral-Hernandez, E. (2007). Recursive Nodes with Rich Dynamics as Modeling Tools for Cognitive Functions. In: Perlovsky, L.I., Kozma, R. (eds) Neurodynamics of Cognition and Consciousness. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73267-9_13

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