Pattern separability in a random neural net with inhibitory connections

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Abstract
Some interesting properties on pattern separation have been shown through researches by neural models of cerebellar cortex. It seems to us that those results are a part of the properties of pattern separation. A two layer random nerve net with inhibitory connections is given as a model of the cerebellar cortex. The model is composed of threshold elements there. A more general theory of pattern separation than those studied earlier is given, and the pattern separability of the model is considered. It is revealed that the standard deviation of threshold values of threshold elements has a great effect on the pattern separability and the control of the firing rate. The present study is also intended to investigate the pattern separability in such a case that the firing rate of input patterns are not equal, and a pattern includes the other pattern. It is assumed there that the standard deviation is small. Some properties of the degree of pattern separation are cleaned up.