Mixed states in a sparsely encoded associative memory model storing ultrametric patterns

When mixed states are composed of s memory patterns, s types of mixed states, which can become equilibrium states of the model, can be generated. We previously reported that storage capacities for most mixed states composed of uncorrelated memory patterns do not diverge at the sparse limit of the firing rate, f -> 0. On the contrary to the uncorrelated case, we show that the storage capacities for all mixed states composed of correlated memory patterns diverge as 1/|f log f| even when the correlation of memory patterns is infinitestimal small. We also show that, when the firing rate is fixed, as the correlation coefficient increases, the storage capacities of the mixed states composed of all correlated memory patterns increase, while those of the mixed states composed of only some of the correlated memory patterns decrease.