Modeling and Invariance

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


Further in the analysis of invariants and their explanatory roles, this chapter introduces models of computational neuroscience that elucidate the interplay between constancy and variability, and illustrate the appearance of invariances. These models rely on the interplay between the structure of the input and rules of structural modification, in which a malleable structure organizes by assimilating the regularities in input. In analogy, organisms learning and adapting to their bodies and environments also self-organize function. Although powerful, empirical assessment of invariances and models thereof present partial pictures. To assemble this mosaic of models, it is necessary to have a theory that is able to cover the causal levels of behavioral phenomena. Dynamical systems is proposed as such a theory.


Recurrent Neural Network Place Cell Hebbian Learning Spiral Pattern Computational Neuroscience 
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.


  1. 1.
    Abbott L, Blum K (1996) Functional significance of ltp for sequence learning and prediction. Cereb Cortex (6):406–416PubMedCrossRefGoogle Scholar
  2. 2.
    Abbott LF, Blum KI (1996) Functional significance of long-term potentiation between hippocampal place cells. Cereb Cortex 6:406–416. URL Google Scholar
  3. 3.
    Abbott LF, Nelson SB (2000) Synaptic plasticity: Taming the beast. Nat Neurosci 3:1178–1183PubMedCrossRefGoogle Scholar
  4. 4.
    Blum KI, Abbott LF (1999) A model of spatial map formation in the Hippocampus of the rat. Neural codes and distributed representations. MIT Press, CambridgeGoogle Scholar
  5. 5.
    Domany E, van Hemmen J, Schulten K (1995) Models of neural networks, vol I, 2nd edn. (updated). Springer, New YorkGoogle Scholar
  6. 6.
    Franzius M, Sprekeler H, Wiskott L (2007) Slowness and sparseness lead to place, head-direction, and spatial-view cells. PLoS Comput Biol 3(8):e166PubMedCrossRefGoogle Scholar
  7. 7.
    Goodwin B (2001) The evolution of complexity: How the leopard changed its spots. Princeton Academic, PrincetonGoogle Scholar
  8. 8.
    Harris K, Csicsvari J, Hirase H, Dragoi G, Buzsáki G (2003) Organization of cell assemblies in the hippocampus. Nat a-z index 424(6948):552–556CrossRefGoogle Scholar
  9. 9.
    Hartley T, Maguire E, Spiers H, Burgess N (2003) The well-worn route and the path less traveled distinct neural bases of route following and wayfinding in humans. Neuron 37(5): 877–888PubMedCrossRefGoogle Scholar
  10. 10.
    Hebb D (1949) Organization of behavior. Wiley, New YorkGoogle Scholar
  11. 11.
    Heylighen F, Joslyn C (2001) Cybernetics and second-order cybernetics. In: Meyers R (ed) Encyclopedia of physical science and technology, 3rd edn. Academic, New YorkGoogle Scholar
  12. 12.
    Hopfield JJ (1982) Neural networks and physical systems with collective emergent computational abilities. Proc Natl Acad Sci (Biophysics) 79:2554–2558CrossRefGoogle Scholar
  13. 13.
    Izhikevich EM (2004) Which model to use for cortical spiking neurons. IEEE Trans Neural Netw 15(5):1063–1070PubMedCrossRefGoogle Scholar
  14. 14.
    Kohonen T (1982) Self-organized formation of topologically correct feature maps. In: von der Malsburg C (ed) Kybernetik 14(2), pp 59–69Google Scholar
  15. 15.
    Körding K, König P (2001) Supervised and unsupervised learning with two sites of synaptic integration. J Comput Neurosci 11(3):207–215PubMedCrossRefGoogle Scholar
  16. 16.
    von der Malsburg C (1973) Self-organization of orientation sensitive cells in the striate cortex. Kybernetik 14(2):85–100PubMedCrossRefGoogle Scholar
  17. 17.
    Metha M, Quirk M, Wilson M (2000) Experience-dependent, assymetric shape of hippocampal receptive fields. Nature 25:707–715Google Scholar
  18. 18.
    Philipona D, O’Regan J (2004) Perception multimodale de l’espace. Philosophie de la nature aujourd’hui?, MSH, BostonGoogle Scholar
  19. 19.
    Philipona D, O’Regan J, Nadal J (2003) Is there something out there? inferring space from sensorimotor dependencies. Neural Comput 15(9):2029–2049PubMedCrossRefGoogle Scholar
  20. 20.
    Ritter H, Kohonen T (1989) Self-organizing semantic maps. Biol Cybern 61(4):241–254CrossRefGoogle Scholar
  21. 21.
    Sandstede B, Scheel A, Wulff C (1998) Bifurcations and dynamics of spiral waves. J Nonlinear Sci 9(4):439–478CrossRefGoogle Scholar
  22. 22.
    Wiskott L, Sejnowski TJ (2002) Slow feature analysis: Unsupervised learning of invariances. Neural Comput 14:715–770PubMedCrossRefGoogle Scholar
  23. 23.
    Wyss R, Verschure PFMJ (2003) Bounded invariance and the formation of place fields. In proceedings: NIPSGoogle Scholar
  24. 24.
    Wyss R, König P, Verschure PFMJ (2002) Invariant encoding of spatial stimulus topology in the temporal domain. Neurocomputing 44–46:703–708CrossRefGoogle Scholar
  25. 25.
    Wyss R, König P, Verschure PFMJ (2003) Invariant representations of visual patterns in a temporal population code. Proc Natl Acad Sci 108(1):324–329CrossRefGoogle Scholar
  26. 26.
    Wyss R, König P, Verschure PFMJ (2006) A model of the ventral visual system based on temporal stability and local memory. PLoS Biol 4(5)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Okinawa Institute of Science and TechnologyOkinawaJapan

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