  We discuss the effects of common synaptic inputs in a recurrent neural
network. Because of the effects of these common synaptic inputs, the
correlation between neural inputs cannot be ignored, and thus the network
exhibits sample dependence. Networks of this type do not have well-defined
thermodynamic limits, and self-averaging breaks down. We therefore need to
develop a suitable theory without relying on these common properties. While the
effects of the common synaptic inputs have been analyzed in layered neural
networks, it was apparently difficult to analyze these effects in recurrent
neural networks due to feedback connections. We investigated a sequential
associative memory model as an example of recurrent networks and succeeded in
deriving a macroscopic dynamical description as a recurrence relation form of a
probability density function.
