In this paper, an associative memory model with a forgetting process proposed by Mezard et al. is investigated as a means of storing sparsely encoded patterns by the SCSNA proposed by Shiino and Fukai. Similar to the case of storing non-sparse (non-biased) patterns as analyzed by Mezard et al., this sparsely encoded associative memory model is also free from a catastrophic deterioration of the memory caused by memory pattern overloading. We theoretically obtain a relationship between the storage capacity and the forgetting rate, and find that there is an optimal forgetting rate leading to the maximum storage capacity. We call this the optimal storage capacity rate. As the memory pattern firing rate decreases, the optimal storage capacity increases and the optimal forgetting rate decreases. Furthermore, we shown that the capacity rate (i.e. the ratio of the storage capacity for the conventional correlation learning rule to the optimal storage capacity) is almost constant with respect to the memory pattern firing rate.

An associative memory model with a forgetting process a la Mezard et al. is investigated for a piecewise nonmonotonic output function by the SCSNA proposed by Shiino and Fukai. Similar to the formal monotonic two-state model analyzed by Mezard et al. , the discussed nonmonotonic model is also free from a catastrophic deterioration of memory due to overloading. We theoretically obtain a relationship between the storage capacity and the forgetting rate, and find that there is an optimal value of forgetting rate, at which the storage capacity is maximized for the given nonmonotonicity. The maximal storage capacity and capacity ratio (a ratio of the storage capacity for the conventional correlation learning rule to the maximal storage capacity) increase with nonmonotonicity, whereas the optimal forgetting rate decreases with nonmonotonicity.