A Mathematical Model of Cerebellar Cortex as a Pattern Categorizer

We regard the cerebellar cortex as a pattern categorizer, and construct a mathematical model of it as the pattern categorizer under many physiological evidences. The model is a four-layer neural net consisting of threshold elements with two inhibitory elements. Then, a pattern class is defined as a set of patterns having large overlapping rate with a learning pattern of its class. The property of the pattern class is considered in detail. In order to make the model work as the pattern categorizer, a set of equations for learning is given, and the process of learning is considered. On the basis of the above consideration, an equation giving the ability of pattern classification of this pattern categorizer is derived in the case of two pattern classes. Furthermore, it is shown that the number of connections between the first and second layer has a great effect on the ability of pattern classification. As the result, it is revealed that the pattern categorizer has the property and ability of pattern classification serving the practical application. Simultaneously, some applicable examples for this pattern categorizer are picked up, and the prospect of success for the applications is discussed.