Neural networks with low levels of activity: Ising vs. McCulloch-Pitts neurons

The performance of neural networks used as associative memory for uncorrelated patterns with prescribed mean activity is analyzed within the replica symmetric mean field theory. The optimal representation of the possible states of the neutrons, active or inactive, is found to depend on the mean activity. For activity equal one half Ising neurons and for low activities McCulloch-Pitts neurons are optimal. In this optimal representation the noise due to noncondensed patterns is reduced.