Abstract
Dynamical system theory offers approaches towards cognitive modeling and computation inspired by self-organization and pattern formation in open systems operating far from thermodynamical equilibrium. In this spirit we propose a functional architecture for the emergence of complex functions such as sequential motor behaviors. We model elementary functions as Structured Flows on Manifolds (SFM) that provide an unambiguous deterministic description of the functional dynamics, while still remaining compatible with the intrinsically low dimensionality of elementary behaviors. Pattern competition processes (operating on a hierarchy of time scales) provide the means to compose complex functions out of simpler constituent ones. Our underlying hypothesis is that complex functions can be decomposed in functional modes (simpler building blocks). Simulations of generating cursive handwriting provide proof of concept and suggest exciting avenues towards extending the current framework to other human functions including learning and language.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kelso, S.: Dynamic Patterns: The Self-Organization of Brain and Behavior. A Bradford Book, The MIT Press, Cambridge (1995)
Kozma, R., Freeman, W.: The KIV model of intentional dynamics. Neural Networks 22(3), 277–285 (2009)
Friston, K., Kilner, J., Harrison, L.: A free energy principle for the brain, pp. 70–87 (2006)
Harris, C., Wolpert, D.: Signal-dependent noise determines motor planning. Nature 394, 780–784 (1998)
Newel, A.: Unified theories of cognition. Harvard University Press, Cambridge (1990)
Kremer, S.: Spatiotemporal connectionist networks: A taxonomy and review. Neural Computation 13, 249–306 (2001)
Sun, R., Alexandre, F.: Connectionist-symbolic integration: From unified to hybrid approaches. Lawrence Erlbaum Associates, Mahwah (1997)
Rabinovich, M., Muezzinoglu, M.: Mutual emotion-cognition dynamics (September 2009), arXiv:0909.1144
Rabinovich, M., Huerta, R., Verona, P., Afraimovich, V.: Transient cognitive dynamics, metastability, and decision making. PLoS Comp. Biol. 4(5) (2008)
Kolen, J., Kremer, S.: A field guide to dynamical recurrent networks. Wiley-IEEE Press, New York (2001)
Carpenter, G., Grossberg, S.: Adaptive resonance theory. In: Arbib, M. (ed.) The handbook of brain theory and neural networks, 2nd edn., pp. 87–90. The MIT Press, Cambridge (2003)
Maass, W., Natschlager, T., Markram, H.: Real-time computing without stable states: A new framework for neural computation based on perturbations. Neural Computation 14, 2531–2560 (2002)
Schmidt, R., Lee, T.: Motor control and learning: a behavioral emphasis, 4th edn. Human Kinetics, Leeds (2005)
Mussa-Ivaldi, F., Bizzi, E.: Motor learning through the combination of primitives. Phil. Trans. R. Soc. Lond. B 355, 1755–1769 (2000)
Morasso, P., Mussa-Ivaldi, F.: Trajectory formation and handwriting: A computational model. Biological Cybernetics 45, 131–142 (1982)
Tuller, B., Kelso, S.: The production and perception of syllable structure. Journal of Speech and Hearing Research 34, 501–508 (1991)
Poeppel, D., Idsardi, W., van Wassenhove, V.: Speech perception at the interface of neurobiology and linguistics. Phil. Trans. R. Soc. B 363(1493), 1071–1086 (2007)
Lakoff, G.: Women, fire, and dangerous things: What categories reveal about the mind. University of Chicago Press, Chicago (1987)
Feldman, J.: From molecule to metaphor: A neural theory of language. A Bradford Book, The MIT Press, Cambridge (2006)
Jirsa, V., Mersmann, J.: Neuronal network structure and method to operate a neuronal network structure. International Patent Application WO 2009/037526 A1 (2009)
Pillai, A.: Structured Flows on Manifolds: Distributed functional architectures. PhD thesis, Florida Atlantic University (2008)
Haken, H.: Synergetics: introduction and advanced topics. Springer, Heidelberg (2004)
Kelso, S., Jirsa, V.: Coordination dynamics: issues and trends. Springer, Heidelberg (2004)
Guckenheimer, J., Holmes, P.: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Springer, New York (2002)
Constantin, P., Foias, C., Nicolaenko, B., Teman, R.: Intergral manifolds and inertial manifolds for dissipative partial differential equations, 1st edn. Springer, New York (1989)
Jirsa, V., Kelso, S.: The excitator as a minimal model for the coordination dynamics of discrete and rhythmic movement generation. J. Mot. Behav. 37(1), 35–51 (2005)
Huys, R., Fernandez, L., Bootsma, R., Jirsa, V.: Fitts’ law is not continuous in reciprocal aiming, pp. 1179–1184 (2009)
Fink, P., Kelso, S., Jirsa, V.: Perturbation-induced false starts as a test of the Jirsa-Kelso excitator model, pp. 147–157 (2009)
Huys, R., Jirsa, V., Studenka, B., Rheaume, N., Zelaznik, H.: Human trajectory formation: Taxonomy of movement based on phase flow topology. In: Fuchs, A., Jirsa, V. (eds.) Coordination: neural, behavioral and social dynamics. Springer, Heidelberg (2007)
Perdikis, D., Jirsa, V.: How to control complex movements. Poster in Progress in Motor Control, Marseille (2009)
Friston, K.: Hierarchical models in the brain. PLoS Comput. Biol. 4(11) (2008)
Kiebel, S., von Kriegstein, K., Daunizeau, J., Friston, K.: Recognizing sequences of sequences. PLoS Comput. Biol. 5(8) (2009)
Haken, H.: Synergetic computers and cognition: a top-down approach to neural nets, 2nd edn. Springer, Heidelberg (2004)
Grossberg, S.: Biological competition: Decision rules, pattern formation and oscillations. Proc. Natl. Acad. Sci. USA 77(4), 2338–2342 (1980)
Bullock, D., Rhodes, B.: Competitive queuing for planning and serial performance. In: Arbib, M. (ed.) Handbook of brain theory and neural networks, 2nd edn., pp. 241–244. The MIT Press, Cambridge (2003)
Maturana, H., Varela, F.: The tree of knowledge: The biological roots of human understanding Revised edn. Shambhala, Boston (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Perdikis, D., Woodman, M., Jirsa, V. (2010). Functional Architectures and Hierarchies of Time Scales. In: Diamantaras, K., Duch, W., Iliadis, L.S. (eds) Artificial Neural Networks – ICANN 2010. ICANN 2010. Lecture Notes in Computer Science, vol 6353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15822-3_43
Download citation
DOI: https://doi.org/10.1007/978-3-642-15822-3_43
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15821-6
Online ISBN: 978-3-642-15822-3
eBook Packages: Computer ScienceComputer Science (R0)