Sparsely Encoded Hopfield Model with Unit Replacement

摘要

We investigate a sparsely encoded Hopfield model with unit replacement by using a statistical mechanical method called self-consistent signal-to-noise analysis. We theoretically obtain a relation between the storage capacity and the number of replacement units for each sparseness a. Moreover, we compare the unit replacement model with the forgetting model in terms of the network storage capacity. The results show that the unit replacement model has a finite value of the optimal sparseness on an open interval 0 (1/2 coding) < a < 1 (the limit of sparseness) to maximize the storage capacity for a large number of replacement units, although the forgetting model does not.