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IEEE-INNS-ENNS International Joint Conference on Neural Networks (IJCNN'00)-Volume 3   p. 3195
On the Properties of Time Trajectories Learned by the Cerebellar Cortex
A. Garenne, Université d'Angers
P. Chauvet, Institut de Mathématiques Appliquées
G.A. Chauvet, Université d'Angers and University of Southern California

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DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/IJCNN.2000.861303
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Abstract
The cerebellum is known to have a main role in motion control and coordination. However, centuries after this observation [1], and although the high level of modeling and experimental research, we are still unable to explain the mechanisms of the coordination of movement. There are several approaches to the modeling of the cerebellum [2,3] based on the numerical techniques or the type of neural network used. The neuromimetic quantitative approach allows (i) understanding certain aspects of the cerebellar function, and (ii) conceiving tools like the CMAC [4] or, more recently, the FOX [5] systems, which are helpful, e.g. in robotics. However, most often, the connexionist computing approach numerically provides the behavior of an obvious noticeable feature using optimization between the output and the target, i.e. the ability of doing a precise task. We now have certainly enough physiological data on the cerebellar cortex to build a more realistic, however reasonable, model of its function.Our own interpretation [6], hierarchically and mathematically oriented, gave an answer to the main issue outlined by, e.g. Bloedel [7], for the functional relation between the regular, homogeneous observed neural tissue and the high capacity of movement regulation. This approach, published in a series of papers, led to a mathematical definition of the functional unit of the cerebellum based on the stability of its dynamics. Here, we extend an ancient work from Chapeau-Blondeau and Chauvet [8], to explore the efficiency and the capacity of the cerebellar cortex to learn and memorize trajectories, i. e. time series patterns, taking into account its anatomical features. This is important because the field theory we have conceived involves the whole geometry of the system [9], thus the role of the delays of propagation between any cells, and because we have not yet any idea of the number of possible learned patterns.Using the most recent anatomical data on the cerebellum [10,11], the aim in this paper is: (i) to build an element of the cerebellar cortex using a semi-real neural network and an object-oriented implementation, (ii) to study the role of the most important parameters on the capacity of the cerebellar cortex to learn and retrieve temporal patterns, and (iii) to see in which extent the previous results [8] may be usable.
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Citation:  A. Garenne, P. Chauvet, G.A. Chauvet, "On the Properties of Time Trajectories Learned by the Cerebellar Cortex," ijcnn, p. 3195,  IEEE-INNS-ENNS International Joint Conference on Neural Networks (IJCNN'00)-Volume 3,  2000