Mixed state on a sparsely encoded associative memory model

We analyzed symmetric mixed states corresponding to the so-called concept formation on a sparsely encoded associative memory model with 0-1 neurons. Three types of mixed states--OR, AND, and a majority decision--are described as typical examples. Each element of the OR mixed state is composed of corresponding memory pattern elements by means of the OR operation. The other two types are similarly defined. By analyzing their equilibrium properties through self-consistent signal-to-noise analysis and computer simulation, we found that the storage capacity of the OR mixed state diverges in a sparse limit, but that the other states do not diverge. In addition, we found that the optimal threshold values, which maximize the storage capacity for the memory pattern and the OR mixed state, coincide with each other in the spare limit. We conclude that the OR mixed state is a reasonable representative of mixed state in the sparse limit.