Abstract
In this paper we study a neural network model of self-organization. This model uses a variation of a Hebb rule for updating its synaptic weights, and surely converges to the equilibrium status. The key point of the convergence is the update rule that constrains the total synaptic weight and this seems to make the model stable. We investigate the role of the constraint and show that it is the constraint that makes the model stable. For analyzing this setting, we propose a simple probabilistic game that abstracts the neural network and the self-organization process. Then, we investigate the characteristics of this game, namely, the probability that the game becomes stable and the number of the steps it takes.
Supported by ESPRIT LTR Project no. 20244 - ALCOM-IT and CICYT Project TIC97-1475-CE.
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
C. Domingo, O. Watanabe, T. Yamazaki, A role of constraint in self-organization, Research Report C-124, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 1998; http://www.is.titech.ac.jp/research/technical-report/C/index.html.
W. Feller, An Introduction to Probability Theory and its Applications, volume I, third edition. John Wiley, 1968.
Japanese Standards Association ed., Statistical Tables and Formulas with Computer Applications, JSA-1972, Japanese Standards Association, Tokyo, 1972.
C. von der Malsburg, Self-organization of orientation sensitive cells in the striate cortex, Kybernetik 14 (1973), 85–100.
K. Miller and D. MacKay, The role of constrains in Hebbian learning, Neural Computation 16 (1994), 100–126.
N. Swindale, The development of topography in the visual cortex: a review of models, Network 7 (1996), 161–247.
S. Tanaka, Theory of self-organization of cortical maps: mathematical framework, Neural Networks, 3 (1990), 625–640.
T. Wiesel and D. Hubel, Effects of visual deprivation on morphology and physiology of cells in cat’s lateral geniculate body, J. Neurophysiology, 26 (1963), 978–993.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Domingo, C., Watanabe, O., Yamazaki, T. (1998). A Role of Constraint in Self-Organization. In: Luby, M., Rolim, J.D.P., Serna, M. (eds) Randomization and Approximation Techniques in Computer Science. RANDOM 1998. Lecture Notes in Computer Science, vol 1518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49543-6_24
Download citation
DOI: https://doi.org/10.1007/3-540-49543-6_24
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65142-0
Online ISBN: 978-3-540-49543-7
eBook Packages: Springer Book Archive