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Attractor Landscapes and the Invariants of Behavior

  • Mario NegrelloEmail author
Chapter
  • 504 Downloads
Part of the Springer Series in Cognitive and Neural Systems book series (SSCNS, volume 1)

Abstract

This chapter introduces an explanatory middleman, the concept of an attractor landscape. It is used to show what is an invariant of behavior: an abstract representation of a functional mechanism. With an experiment in the evolution of active tracking, recurrent neural networks are evolved that enable agents to track a moving object in a simulated environment. The invariant behavior, i.e., the functional mechanism implemented by agents, is a two-dimensional version of the well-known – from cybernetics – negative feedback, which subsumes an ample range of both simple and complex organismic functions. I will (1) show how, despite extreme variability in network structures, constancy of behavior reflects invariant features of the attractor landscapes, (2) show that behavioral function only exists as a potential, until it is evoked, and (3) show that even networks with radically different attractors may implement the same embodied function, as long as these networks possess certain invariant features of the attractor landscape. This chapter also addresses constancy arising from level crossing, convergence, as variable activity patterns have their dimensions effectively reduced at the level of actuators. I will show how attractors are made equivalent through convergence. How the ongoingness of behavior appears as the attractor landscape is explored through organism–environment interaction. This will lead to the concept of a “metatransient,” with respect to which we show effectively what it means for an organism, to implicitly represent the coupling between the organism and its environment.

Keywords

Hide Layer Input Pattern Chaotic Attractor Motor Output Structural Coupling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Arbib MA (1972) The metaphorical brain, an introduction to cybernetics and brain theory. MIT, Cambridge, CAGoogle Scholar
  2. 2.
    Ashby W (1960) Design for a brain: The origin of adaptive behavior, 2nd edn. Chapman & Hall, LondonCrossRefGoogle Scholar
  3. 3.
    Banerjee A (2001) The roles played by external input and synaptic modulations in the dynamics of neuronal systems. Behav Brain Sci 24(5):811–812CrossRefGoogle Scholar
  4. 4.
    Barandiaran X, Moreno A (2006) On what makes certain dynamical systems cognitive: A minimally cognitive organization program. Adaptive Behavior 14(2):171–185. DOI 10.1177/105971230601400208, URL http://adb.sagepub.com/cgi/content/abstract/14/2/171, http://adb.sagepub.com/cgi/reprint/14/2/171.pdf
  5. 5.
    Beer R (2009) Beyond control: The dynamics of brain-body-environment interaction in motor systems. In: Sternad D (ed) Progress in motor control V: A multidisciplinary perspective. Springer, New YorkGoogle Scholar
  6. 6.
    Beer R, Gallagher J (1992) Evolving dynamical neural networks for adaptive behavior. Adapt Behav 1(1):91–122CrossRefGoogle Scholar
  7. 7.
    Beer RD (1995) A dynamical systems perspective on agent-environment interaction. Artif Intell (72):173–215CrossRefGoogle Scholar
  8. 8.
    Berry H, Quoy M (2006) Structure and dynamics of random recurrent neural networks. Adapt Behav 14(2):129–137. DOI 10.1177/105971230601400204, URL http://adb.sagepub.com/cgi/content/abstract/14/2/129, http://adb.sagepub.com/cgi/reprint/14/2/129.pdf
  9. 9.
    Boeddeker N, Egelhaaf M (2005) A single control system for smooth and saccade-like pursuit in blowflies. J Exp Biol (208):1563–1572PubMedCrossRefGoogle Scholar
  10. 10.
    Edelman GM (1989) The remembered present. Basic Books, New YorkGoogle Scholar
  11. 11.
    Freeman W (2000) Mesoscopic neurodynamics: From neuron to brain. J Physiol Paris 94(5–6):303–322PubMedCrossRefGoogle Scholar
  12. 12.
    Harvey I, Paolo ED, Wood R, Quinn M, Tuci E (2005) Evolutionary robotics: A new scientific tool for studying cognition. Artif Life 11(1–2):79–98. URL http://www.mitpressjournals.org/doi/abs/10.1162/1064546053278991 Google Scholar
  13. 13.
    von Holst VE, Mittelstaedt H (1950) Das Reafferenzprinzip. Die Naturwissenschaften 37(20):464–476CrossRefGoogle Scholar
  14. 14.
    Homberg U, Paech A (2002) Ultrastructure and orientation of ommatidia in the dorsal rim area of the locust compound eye. Arthropod Struct Dev 30(4):271–280PubMedCrossRefGoogle Scholar
  15. 15.
    Hülse M (2006) Multifunktionalität rekurrenter neuronaler netze – synthese und analyse nichtlinearer kontrolle autonomer roboter. PhD thesis, Universität OsnabrückGoogle Scholar
  16. 16.
    Hülse M, Ghazi-Zahedi K, Pasemann F (2002) Dynamical neural schmitt trigger for robot control. In: Dorronsoro JR (ed) ICANN, Springer, vol ICANN 2002, LNCS 2415, pp 783–788Google Scholar
  17. 17.
    Ijspeert AJ, Nakanishi J, Schaal S (2003) Learning attractor landscapes for learning motor primitives. In: Advances in neural information processing systems, MIT, Cambridge, CAGoogle Scholar
  18. 18.
    Ikegami T, Tani J (2002) Chaotic itinerancy needs embodied cognition to explain memory dynamics. Behav Brain Sci 24(05):818–819Google Scholar
  19. 19.
    Jaegger H, Maas W, Markram H (2007) special issue: Echo state networks and liquid state machines. Neural Netw 20(3):290–297CrossRefGoogle Scholar
  20. 20.
    Kaneko K (1990) Clustering, coding, switching, hierarchical ordering, and control in network of chaotic elements. Physica D 41(37)Google Scholar
  21. 21.
    Kaneko K, Tsuda I (2003) Chaotic itinerancy. Chaos 13(3):926–936PubMedCrossRefGoogle Scholar
  22. 22.
    Merleau-Ponty M (1963 (translation), 1942) The structure of behavior. Duquesne University Press, Philadelphia, PAGoogle Scholar
  23. 23.
    Molter C, Salihoglu U, Bersini H (2007) The road to chaos by time-asymmetric hebbian learning in recurrent neural networks. Neural Comput 19:80–110PubMedCrossRefGoogle Scholar
  24. 24.
    Pasemann F (1993) Discrete dynamics of two neuron networks. Open Syst Inf Dyn 2(1):49–66CrossRefGoogle Scholar
  25. 25.
    Philipona D, O’Regan J, Nadal J, Coenen OM (2004) Perception of the structure of the physical world using unknown multimodal sensors and effectors. Adv Neural Inf Process Syst 16:945–952Google Scholar
  26. 26.
    Rossel S, Corlija J, Schuster S (2002) Predicting three-dimensional target motion: how archer fish determine where to catch their dislodged prey. J Exp Biol 205(21):3321–3326. URL http://jeb.biologists.org/cgi/content/abstract/205/21/3321, http://jeb.biologists.org/cgi/reprint/205/21/3321.pdf
  27. 27.
    Sterelny K (2005) Thought in a hostile world. MIT, Cambridge, CAGoogle Scholar
  28. 28.
    Tani J (1998) An interpretation of the ‘self’ from the dynamical systems perspective: A constructivist approach. J Conscious Stud 5(5–6):516–542Google Scholar
  29. 29.
    Taylor C (1999) The atomists leucippus and democritus: Fragments: A text and translation. University of Toronto Press, TorontoGoogle Scholar
  30. 30.
    Tsuda I (1991) Chaotic itinerancy as a dynamical basis of hermeneutics in brain and mind. In: Microcomputers and attention. Manchester University Press, ManchesterGoogle Scholar
  31. 31.
    Tsuda I (2001) Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems. Behav Brain Sci 24:793–847PubMedCrossRefGoogle Scholar
  32. 32.
    von Uexküll J (1934) Bedeutungslehre / Streifzüge durch die Umwelten von Tieren und Menschen, 1956th edn. Rowohlt HamburgGoogle Scholar
  33. 33.
    Varela F (1979) Principles of biological autonomy. North Holland, New YorkGoogle Scholar
  34. 34.
    Varela F, Maturana H, Uribe R (1974) Autopoiesis: The organization of living systems, its characterization and a model. Curr Model Biol 5(4):187–96Google Scholar
  35. 35.
    Von Foerster H (2003) Understanding understanding: Essays on cybernetics and cognition. Springer, New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Okinawa Institute of Science and TechnologyOkinawaJapan

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