Abstract
In this chapter we introduce a biologically plausible model of the neural integrator model based on recurrent neural networks. Its original features are: fixed sign synaptic weights for all the network connections; and artificial transmission delays between the units. These improvements lead to the emergence of clusters in the weight structure of the lateral inhibitory connection layer. We will demonstrate that these clusters are not an artifact of computation.
We will see that this spontaneous emergence of clusters in artificial neural networks, performing a well defined physico—mathematical task (a temporal integration) is owed to computational constraints, with a restricted space of solutions. Thus information processing constraints could be a plausible factor inducing the emergence of iterated patterns in biological neural networks.
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
Abbott, F.: Integrating with action potential. Neuron, 26:3–4 (2000).
Anastasio, T.: Neural network models of velocity storage in the horizontal vestibulo-ocular reflex. Biol Cybern, 64:187–196 (1991).
Arnold, D. B. and Robinson, D. A.: A learning model of the neural integrator of the oculomotor system. Biol Cybern, 64:447–454 (1991).
Baker, R. and Berthoz, A.: Is the prepositus hypoglossi nucleus the source of another vestibular ocular pathway ? Brain Res, 86:366–371 (1975).
Becker, W. and Klein, H.: Accuracy of saccadic eye movements and maintenance of eccentric eye position in the dark. Vision Res, 13:1021–1034 (1973).
Bliss, T. V. P. and Lomo, T.: Long-lasting potentiation of synaptic transmission in the dendate area of the anaesthetized rabbit following stimulation of the perforant path. J Physiol, 232:331–356 (1973).
Cannon, S. C. and Robinson, D. A.: A proposed neural network for the integrator of the oculomotor system. Biol Cybern, 49:127–136 (1983).
Cannon, S. C. and Robinson, D. A.: An improved neural-network model for the neural integrator of the oculomotor system: more realistic neuron behavior. Biol Cybern, 53:93–108 (1985).
Cannon, S. and Robinson, D. A.: Loss of the neural integrator of the oculomotor system from brain stem lesions in monkey. J Neurophysiol, 53:93–108 (1987).
Cheron, G. and Godaux, E.: Self-terminated fast movement of the forearm in man: amplitude dependence of the triple burst pattern. Journal of Biophysics and Biomechanics, 10(3): 109–117 (1986).
Cheron, G. and Godaux, E.: Disabling of the oculomotor integrator by kainic acid injections in the prepositus-vestibular complex of the cat. J Physiol (London), 394:267–290 (1987).
Cheron, G., Mettens, R and Godaux, E.: Gaze holding defect induced by injections of ketamine in the cat brainstem. NeuroReport, 3:97–100 (1992).
Crawford, J., Cadera, W. and Vilis, T.: Generation of torsional and vertical eye position signals by the interstitial nucleus of Cajal. Science, 252:1551–1553 (1991).
Delgado-Garcia, J., Vidal, J., Gomez, C. and Berthoz, A.: A neurophysiological study of the prepositus hypoglossi neurons projecting to oculomotor and preoculomotor nuclei in the alert cat. Neuroscience, 29:291–307 (1989).
Draye, J., Cheron, G., Libert, G. and Godaux, E.: Supervised neural network simulation of the integrator of the oculomotor system. Journal of Biomechanics, 27(6):775 (1994).
Eccles, J. C.: Chemical transmission and Dale’s principle. In Neuropeptides in central nervous system. Hokfelt T., Fuxe K. and Bjorklund A., eds (1986).
Escudero, M., de la Cruz, R. and Delgado-Garcia, J.: A physiological study of vestibular and prepositus hypoglossi neurones projecting to the abducens nucleus in the alert cat. J Physiol, 458:539–560 (1992).
Fukushima, K.: The interstitial nucleus of Cajal and its role in control of movements of head and eyes. Prog Neurobiol, 29:107–192 (1987).
Fuster, J.: Memory in the cerebral cortex. Cambridge, MA:MIT Press (1995).
Gill, R E., Murray, W. and Wright, M. H.: Practical Optimization. Academic Press (1981).
Godaux, E. and Cheron, G.: The hypothesis of the uniqueness of the oculomotor integrator: direct experimental evidence in the cat. Journal of Physiology, 492(2):517–527 (1996).
Hale, J.: Ordinary Differential Equations. Krieger, New York (1980).
Hoyle, F.: On the fragmentation of gas clouds into galaxies and stars. Astrophysical J, 118:513–528 (1953).
Ikeda, N.: Distributed and cerebellar projections of cholinergic and cortiotropin-releasing factor-containing neurons in the caudal vestibular nuclear complex and adjacent brainstem. Neuroscience, 49(3):635–651 (1992).
Illing, S.: Association of efferent neurons to the compartmental architecture of the superior colliculus. Proc Natl Acad Sci USA, 89:10900–10904 (1992).
Ito, M.: Long-term depression. Ann Rev Neurosci, 12:85–102 (1989).
Kamath, B. and Keller, E.: A neurological integrator for the oculomotor system. Math Biosci, 30:341–352 (1976).
Kaneko, C.: Eye movement deficits following ibotenic acid lesions of the nucleus prepositus hypoglossi in monkeys. i. saccades and fixation. J Neurophysiol, 78:1753–1768 (1997).
Kaneko, C.: Eye movement deficits following ibotenic acid lesions of the nucleus prepositus hypoglossi in monkeys. ii. pursuit, vestibular. J Neurophysiol, 81:668–681 (1999).
King, W. and Leigh, R.: Physiology of vertical gaze. In Lennerstrand, G., Zee, D.S. and Keller, E., editors, Physiology of vertical gaze in functional basis of ocular motility disorders, pages 267–272. Pergamon Press, Oxford (1982).
LaSalle, J.: The stability of dynamical systems. In SIAM Regional Conferences Series in Applied Mathematics, volume 25. SIAM (1976).
Mandelbrot, B.: Les objets fractals: Survol du langage fractal. Flammarion (1989).
McFarland, J. and Fuchs, A.: Discharge patterns in nucleus prepositus hypoglossi and adjacent medial nucleus during horizontal eye movements in behaving macaques. J Neurophysiol, 68:319–332 (1992).
Mettens, P., Godaux, E., Cheron, G. and Galiana, H.: Effect of muscimol microinjections into the prepositus hypoglossi and the medial vestibular nuclei on cat eye movements. J Neurophysiol, 72:785–802 (1994).
Pastor, A., De La Cruz, R. and Baker, R.: Eye position and eye velocity integrators reside in separate brainstem nuclei. Proceedings of the National Academy of Science USA, 91:807–811 (1994).
Pearlmutter, B.: Learning state space trajectories in recurrent neural networks. Neural Computation, 1:263–269 (1989).
Purves, D., Riddle, D. R. and LaMantia, A.-S.: Iterated patterns of brain circuitry (or how the cortex gets its spots). Trends in Neurosciences, 15:362–368 (1992).
Quinn, K. J., Schmajuk, N., Jain, A., Baker, J. F. and Peterson, B. W.: Vestibu-loocular reflex arc analysis using an experimentally constrained neural network. Biol Cybern, 67:113–122 (1992).
Robinson, D. A.: Eye movement control in primates. Science, 161:1219–1224 (1968).
Robinson, D. A.: Implications of neural networks for how we think about brain function. Behavioral and Brain Sciences, 15:644–655 (1992).
Robinson, D. A.: Integrating with neurons. Ann Rev Neurosci, 12:33–45 (1989).
Rumelhart, D. E., Hinton, G. E. and Williams, R. J.: Learning internal representations by error propagation. In Parallel Distributed Processing: Ex-plorations of the Micro structure of Cognition, volume I. Cambridge MA, Bradford Books (1986).
Schroeder, M.: Fractals, Chaos, Power Laws. W. H. Freeman and Company (1991).
Seung, H.: How the brain keeps the eyes still. Proceedings of the National Academy of Science USA, 93:13339–13344 (1996).
Seung, H., Lee, D., Reis, B. and Tank, D.: Stability of the memory of eye position in a recurrent network of conductance-based model neurons. Neuron, 26:259–271 (2000).
Wang, X. and Blum, E. K.: Discrete-time versus continuous-time models of neural networks. Journal of Computer and System Sciences, 45:1–19 (1992).
Weissman, B., DiScenna, A. and Leigh, R.: Maturation of the vestibulo-ocular reflex in normal infants during the first two monts of life. Neurology, 39:534–538 (1989).
Williams, R. J. and Zipser, D.: A learning algorithm for continually running fully recurrent neural networks. Neural Computation, 1:270–280 (1989).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Draye, JP., Cheron, G. (2001). Simulation of the Human Oculomotor Integrator Using a Dynamic Recurrent Neural Network. In: Mastebroek, H.A.K., Vos, J.E. (eds) Plausible Neural Networks for Biological Modelling. Mathematical Modelling: Theory and Applications, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0674-3_5
Download citation
DOI: https://doi.org/10.1007/978-94-010-0674-3_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-3864-5
Online ISBN: 978-94-010-0674-3
eBook Packages: Springer Book Archive