Further consideration on pattern separability in a random neural net with inhibitory connections

A two-layer random neural net with inhibitory connections composing of threshold elements has been regarded as a model of the cerebellar cortex. Many properties of pattern separation with the model have been disclosed through consideration on the degree of pattern separation. However, we have not shown yet that the degree of pattern separation is given by some different functions which are decided by the relation between the firing rates of input patterns. The present study is intended to reveal that the functions of the degree of pattern separation are synthesized with some different partial functions, and they are differently given on the relation between the firing rates of input patterns. Simultaneously, it is proved that the number of the functions also depend on the number of connections between two layers in the model. We also disclose the properties of the degree of pattern separation, and give some suggestions on the sizes of the firing rates of mossy fibers and granule cells under the knowledge about them.