Capacity of the associative memory using the Boltzmann machine learning

In the present paper, the capacity of an associative memory using the Boltzmann machine learning is evaluated by numerical experiments in the case where the size of the network is small. The authors consider the capacity as the upper bound of the ratio of the number of the nominal patterns to the number of the units, where the network can recall any of such patterns correctly as well as every nominal pattern has the basin of attraction of some proper size. It is shown that this capacity is around 0.6 in both cases where the recalling algorithm is asynchronous and synchronous. It exceeds the well-known capacity by the simple correlation learning, 0.15. The authors also examine what combination of the nominal patterns generates spurious memories. It is shown that there are some particular combinations of the patterns generating spurious memories by any of the different learning methods.