Sequence processing neural network with a non-monotonic transfer function

We investigate storage capacity and retrieval property for a synchronous fully connected neural network with a non-monotonic transfer function which retrieves sequences of patterns, by an analytic method and also by numerical simulations. Because of asymmetry of interactions and non-monotonicity of the transfer function, it is difficult to use conventional methods of the equilibrium statistical mechanics in order to investigate the network. We then use a generating function method of path-integral representation, and obtain equations for dynamical order parameters in the stationary state. We clarify that the network with the non-monotonic transfer function retrieves more sequences of patterns than that with a monotonic transfer function at zero temperature when non-monotonicity of the transfer function is selected optimally. It is also clarified that some chaotic behavior appears in solutions for the equations of the dynamical order parameters when non-monotonicity of the transfer function increases. The analytic results are in excellent agreement with the results obtained by numerical simulations.