Mean-field theory of the three-level associative memory and its synthesis

The single layer neural network with feedback and discrete-time, synchronous dynamics serves as an associative memory for bi-valued patterns. A three-level function instead of the normally used signum-function as output function of the neurons decreases the regions of attraction of the spurious states considerably. The mean-field theory is applied to this kind of system. Results of the theoretical investigation explain its behavior and provide expressions for the choice of the function parameters. The theory is in agreement with results obtained from simulations.