Abstract
In this work, a neural network model for the development of variable sized receptive fields is presented. The system self-organizes under simple rules such as correlation of activity, signal diffusion, and competitive synaptic growth. The network model has one input and one output layer. They are fully connected by an excitatory weight matrix. In addition, the neurons of the output layer are interconnected by inhibitory weights. The set of differential equations for the time evolution of the system is calculated. Numerical integration shows that according to the set of network parameters the system reaches either a non-organized steady state, where all the connections have the same value, or any of two organized states, one of them having connections that represent mexican hat shaped receptive fields of variable size.
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References
Carlson, A. 1990. Anti-Hebbian learning in a non-linear neural network. Biol. Cybern., 64, 171–176
Földiak, P. 1990. Forming sparse representations by local anti-Hebbian learning. Biol. Cybern. 64, 165–170
Frégnac, Y. and M. Imbert. 1984. Development of neuronal selectivity in primary visual cortex of cat. Physiol. Rev. 64, 325–434
Gizzi, M.S., E. Katz, R.A. Schumer, J.A. Movshon. 1990. Selectivity for orientation and directon of motion of single neurons in cat striate and extrastriate visual cortex. J. Neurophysiology. 63, 1529–1543
Hebb, D.O. 1949. Organization of Behavior John Wiley & Sons, New York
Hubel, D.H. and T.N. Wiesel. 1963. Receptive fields of cells in striate cortex of very young visually inexperienced kittens. J. Neurophysiol. 26, 994–1002
Kuffler, S.W., J.G. Nicholls, A.R. Martin. 1984. From Neuron to Brain. Sinauer Associates Inc. Publishers.
Le Vay, S., M.P. Stryker and C.J. Shatz. 1978. Ocular dominance columns and their development in layer IV of the cat's visual cortex: a quantitative study. J. Comp. Neurol. 179, 223–224
Miller, K.D., J.B. Keller and M.P. Stryker. 1989. Ocular dominance columnar development: analysis and simulation. Science. 245, 605–615
Miyashita, M. and S. Tanaka. A mathematical model for the self-organizaton of orientation columns in visual cortex. NeuroReport. 3, 69–72
Orban, G.A. 1984. Neuronal Operations in the Visual Cortex. Springer-Verlag.
Singer, W. 1987. Activity-dependent self-organization of synaptic connections as a substrate of learning. In: The Neural and Molecular Bases of Learning, eds. J.-P. Changeaux y M. Konishi, pp 239–262. Dahlem Konferenzen. Chichester: John Wiley & Sons Ltd.
Spillman, L. and J.S. Werner. 1990. Visual Perception. The Neurophysiological Foundations. Academic Press, Inc.
Stent, G.S. 1973. Physiological mechanism for Hebb's postulate of learning. Proc. Natl. Acad. Sci. USA 70, 997–1001
Stryker, M.P. 1986. The role of neural activity in rearranging connections in the central visual system. In The Biology of Change in Otolaryngology, Elsevier Science Publishers B V, R.W. Ruben et al eds., pp 211–224
Tootell, R.B., M.S. Silverman and R.L. de Valois. 1981. Spatial frequency columns in primary visual cortex. Science. 214, 813–815
von der Malsburg, C. 1987. Synaptic plasticity as basis of brain self-organization. In: The Neural and Molecular Bases of Learning, eds. J.-P. Changeaux and M. Konishi, pp 411–431. Dahlem Konferenzen. Chichester: John Wiley & Sons Ltd.
von der Malsburg, C., and W. Singer. 1988. Principles of cortical network organization, in Neurobiology of Neocortex, eds. P Rakic y W Singer, pp 69–99
Weitzenfeld, A. 1992. A Unified Computational Model for Schemas and Neural Networks in Concurrent Object-Oriented Programming. Technical Report 92-03. Center for Neural Engineering. University of Southern California.
Wörgotter, F. and G. Holt. 1991. Spatiotemporal mechanisms in receptive fields of visual cortical simple cells: a model. J. Neurophysiology. 65, 494–510
Yuille, A.L., M.D. Kammen, and D.S. Cohen. 1989. Quadrature and the development of orientation selective cortical cells by Hebb rules. Biol. Cybern. 61, 183–194
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Andrade, M.A., Morán, F. (1993). A model for the development of neurons selective to visual stimulus size. In: Mira, J., Cabestany, J., Prieto, A. (eds) New Trends in Neural Computation. IWANN 1993. Lecture Notes in Computer Science, vol 686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56798-4_119
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DOI: https://doi.org/10.1007/3-540-56798-4_119
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