Abstract
Self-organizing computational models with specific intracortical connections can explain many functional features of visual cortex, such as topographic orientation and ocular dominance maps. However, due to their computational requirements, it is difficult to use such detailed models to study large-scale phenomenal like object segmentation and binding, object recognition, tilt illusions, optic flow, and fovea-periphery differences. This article introduces two techniques that make large simulations practical. First, we show how parameter scaling equations can be derived for laterally connected self-organizing models. These equations result in quantitatively equivalent maps over a wide range of simulation sizes, making it possible to debug small simulations and then scale them up only when needed. Parameter scaling also allows detailed comparison of biological maps and parameters between individuals and species with different brain region sizes. Second, we use parameter scaling to implement a new growing map method called GLISSOM, which dramatically reduces the memory and computational requirements of large self-organizing networks. With GLISSOM, it should be possible to simulate all of human V1 at the single-column level using current desktop workstations. We are using these techniques to develop a new simulator Topographica, which will help make it practical to perform detailed studies of large-scale phenomena in topographic maps.
Similar content being viewed by others
References
Amari, S. I. (1980) Topographic organization of nerve fields. Bulletin Math. Bio. 42, 339–364.
Anderson, J. A. and Rosenfeld, E., eds. (1988) Neurocomputing: Foundations of Research. MIT Press, Cambridge, MA.
Bednar, J. A. (2002) Learning to See: Genetic and Environmental Influences on Visual Development. PhD thesis, Department of Computer Sciences, The University of Texas at Austin. Technical Report AI-TR-02-294.
Bednar, J. A., Kelkar, A., and Miikkulainen, R. (2002) Modeling large cortical networks with growing self-organizing maps. Neurocomputing 44–46, 315–321. (Special issue containing the proceedings of the CNS*01 conference.)
Bednar, J. A. and Miikkulainen, R. (2000) Tilt after-effects in a self-organizing model of the primary visual cortex. Neural Computation 12, 1721–1740.
Bednar, J. A. and Miikkulainen, R. (2003a) Learning innate face preferences. Neural Computation 15, 1525–1557.
Bednar, J. A. and Miikkulainen, R. (2003b) Selforganization of spatiotemporal receptive fields and laterally connected direction and orientation maps. Neurocomputing 52–54, 473–480.
Bednar, J. A. and Miikkulainen, R. (2004) Prenatal and postnatal development of laterally connected orientation maps. Neurocomputing, in press.
Blasdel, G. G. (1992) Orientation selectivity, preference, and continuity in monkey striate cortex. J. Neurosc. 12, 3139–3161.
Bosking, W. H., Zhang, Y., Schofield, B., and Fitzpatrick, D. (1997) Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. J. Neurosc. 17, 2112–2127.
Bower, J. M. and Beeman, D. (1998) The Book of GENESIS: Exploring Realistic Neural Models with the GEneral NEural SImulation System. Telos, Santa Clara, CA.
Burger, T. and Lang, E.W. (1999) An incremental Hebbian learning model of the primary visual cortex with lateral plasticity and real input patterns. Zeitschrift für Naturforschung C—A J. Biosc., 54, 128–140.
Chang, L. C. and Chang, F. J. (2002) An efficient parallel algorithm for LISSOM neural network. Parallel Computing 28, 1611–1633.
Chapman, B., Stryker, M. P., and Bonhoeffer, T. (1996) Development of orientation preference maps in ferret primary visual cortex. J. Neurosc. 16, 6443–6453.
Choe, Y. and Miikkulainen, R. (1998) Self-organization and segmentation in a laterally connected orientation map of spiking neurons. Neurocomputing 21, 139–157.
Cover, T. M. and Thomas, J. (1991). Elements of Information Theory. Wiley, pp. 247–249.
Dittenbach, M., Merkl, D., and Rauber, A. (2000). The growing hierarchical self-organizing map. In Amari S., Giles C.L., Gori M., and Puri V., eds., Proc of the International Joint Conference on Neural Networks (IJCNN 2000), volume VI, 15–19. IEEE Computer Society.
Erwin, E., Obermayer, K., and Schulten, K. (1992) Self-organizing maps: Ordering, convergence properties and energy functions. Biological Cybernetics 67, 47–55.
Erwin, E., Obermayer, K., and Schulten, K. (1995) Models of orientation and ocular dominance columns in the visual cortex: A critical comparison. Neural Computation 7(3), 425–468.
Fritzke, B. (1995) Growing grid: A self-organizing network with constant neighborhood range and adaptation strength. Neural Proc. Lett. 2, 9–13.
Gilbert, C. D., Das, A., Ito, M., Kapadia, M., and Westheimer, G. (1996) Spatial integration and cortical dynamics. Proc. Nat. Acad. Sci., USA 93, 615–622.
Gilbert, C. D., Hirsch, J. A., and Wiesel, T. N. (1990) Lateral interactions in visual cortex. In Cold Spring Harbor Symposia on Quantitative Biology, Volume LV, pp.663–677. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY.
Gould, E., Reeves, A. J., Graziano, M. S. A., and Gross, C. G. (1999) Neurogenesis in the neocortex of adult primates. Science 286, 548–552.
Grinvald, A., Lieke, E. E., Frostig, R. D., and Hildesheim, R. (1994) Cortical point-spread function and long-range lateral interactions revealed by real-time optical imaging of macaque monkey primary visual cortex. J. Neurosc. 14, 2545–2568.
Grossberg, S. (1976) On the development of feature detectors in the visual cortex with applications to learning and reaction-diffusion systems. Biol. Cybernet. 21, 145–159.
Hines, M. L. and Carnevale, N. T. (1997) The NEURON simulation environment. Neural Computation 9, 1179–1209.
Hirsch, J. A. and Gilbert, C. D. (1991) Synaptic physiology of horizontal connections in the cat’s visual cortex. J. Neurosc. 11, 1800–1809.
Kaas, J. H. (2000) Why is brain size so important: Design problems and solutions as neocortex gets bigger or smaller. Brain and Mind 1, 7–23.
Kalarickal, G. J. and Marshall, J. A. (2002) Rearrangement of receptive field topography after intracortical and peripheral stimulation: The role of plasticity in inhibitory pathways. Network: Comput. Neural Sys. 13, 1–40.
Kohonen, T. (1989) Self-Organization and Associative Memory. Springer, Berlin; New York, Third edition.
Kolen, J. F. and Pollack, J. B. (1990) Scenes from exclusive-OR: Back propagation is sensitive to initial conditions. In Proceedings of the 12th Annual Conference of the Cognitive Science Society, 868–875. Hillsdale, NJ: Erlbaum.
Luttrell, S. P. (1988) Self-organizing multilayer topographic mappings. In Proceedings of the IEEE International Conference on Neural Networks (San Diego, CA). Piscataway, NJ: IEEE.
Marshall, J. A. (1995) Adaptive perceptual pattern recognition by self-organizing neural networks: Context, uncertainty, multiplicity, and scale. Neural Networks 8, 335–362.
Miikkulainen, R., Bednar, J. A., Choe, Y., and Sirosh, J. (1997) Self-organization, plasticity, and low-level visual phenomena in a laterally connected map model of the primary visual cortex. In Goldstone R.L., Schyns P.G., and Medin D.L., eds., Perceptual Learning, volume 36 of Psychology of Learning and Motivation, 257–308. Academic Press, San Diego, CA.
Mundel, T., Dimitrov, A., and Cowan, J. D. (1997) Visual cortex circuitry and orientation tuning. In Mozer M. C., Jordan M. I., and Petsche T., eds., Advances in Neural Information Processing Systems 9, 887–893. Cambridge, MA: MIT Press.
Obermayer, K., Ritter, H. J., and Schulten, K. J. (1990) A principle for the formation of the spatial structure of cortical feature maps. Pro. Nat. Acad. Sci., USA 87, 8345–8349.
Osan, R. and Ermentrout, B. (2002) Development of joint ocular dominance and orientation selectivity maps in a correlation-based neural network model. In Bower J.M., ed., Computational Neuroscience: Trends in Research, 2002. New York: Elsevier.
Purves, D. (1988) Body and Brain: A Trophic Theory of Neural Connections. Harvard University Press, Cambridge, MA.
Rall, W. (1962) Theory of physiological properties of dendrites. Ann. NY Acad. Sci. 96, 1071–1092.
Rockel, A. J., Hiorns, R. W., and Powell, T. P. S. (1980) The basic uniformity in structure of the neocortex. Brain 103, 221–244.
Rodriques, J. S. and Almeida, L. B. (1990) Improving the learning speed in topological maps of patterns. In Proceedings of the International Neural Networks Conference (Paris, France), 813–816. Kluwer, Dordrecht; Boston.
Roque Da Silva Filho, A. C. (1992) Investigation of a Generalized Version of Amari’s Continuous Model for Neural Networks. PhD thesis, University of Sussex at Brighton, Brighton, UK.
Sirosh, J. (1995) A Self-Organizing Neural Network Model of the Primary Visual Cortex. PhD thesis, Department of Computer Sciences, The University of Texas at Austin, Austin, TX. Technical Report A195-237.
Sirosh, J. and Miikkulainen, R. (1994) Cooperative self-organization of afferent and lateral connections in cortical maps. Biol. Cybernet. 71, 66–78.
Sirosh, J., Miikkulainen, R., and Bednar, J. A. (1996) Self-organization of orientation maps, lateral connections, and dynamic receptive fields in the primary visual cortex. In Sirosh J., Miikkulainen R., and Choe Y., eds., Lateral Interactions in the Cortex: Structure and Function. The UTCS Neural Networks Research Group, Austin, TX. Electronic book, ISBN 0-9647060-0-8, http://www.cs.utexas.edu/users/nn/webpubs/htmlbook96.
Swindale, N. V. (1992) A model for the coordinated development of columnar systems in primate striate cortex. Biol. Cybernet. 66, 217–230.
Swindale, N. V. (1996) The development of topography in the visual cortex: A review of models. Network — Comput. Neural Sys. 7, 161–247.
Turrigiano, G. G., Leslie, K. R., Desai, N. S., Rutherford, L. C., and Nelson, S. B. (1998). Activity-dependent scaling of quantal amplitude in neocortical neurons. Nature 391, 845–846.
van Praag, H., Schinder, A. F., Christie, B. R., Toni, N., Palmer, T. D., and Gage, F. H. (2002) Functional neurogenesis in the adult hippocampus. Nature 415, 1030–1034.
von der Malsburg, C. (1973) Self-organization of orientation-sensitive cells in the striate cortex. Kybernetik 15,85–100. Reprinted in Anderson and Rosenfeld, 1988.
Wandell, B. A. (1995) Foundations of Vision. Sinauer Associates, Inc., Sunderland, MA.
Weliky, M., Kandler, K., Fitzpatrick, D., and Katz, L.C. (1995) Patterns of excitation and inhibition evoked by horizontal connections in visual cortex share a common relationship to orientation columns. Nature 15, 541–552.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bednar, J.A., Kelkar, A. & Miikkulainen, R. Scaling self-organizing maps to model large cortical networks. Neuroinform 2, 275–301 (2004). https://doi.org/10.1385/NI:2:3:275
Issue Date:
DOI: https://doi.org/10.1385/NI:2:3:275