Retrieval process of an associative memory with a general input-output function

The retrieval process of an associative memory with a general input-output function is studied by means of a signal-to-noise ratio analysis. We derive a set of recursion relations for macroscopic variables to describe the time development of the network. By taking the equilibrium limit of the recursion relations, we find that a certain type of nonmonotonic input-output relation of a single neuron yields an enhanced memory capacity of the network compared with the conventional monotonic relation. This behavior is in agreement with the prediction of Morita et al. who used numerical simulations as well as geometrical arguments to reach their conclusion. Our method reveals the relation between the type of the input-output function and the memory capacity in a generic associative memory.