  The ability of discrete-time nonlinear recurrent neural networks to store
time-varying small input signals is investigated by mean-field theory. The
combination of a small input strength and mean-field assumptions makes it
possible to derive an approximate expression for the conditional probability
density of the state of a neuron given a past input signal. From this
conditional probability density, we can analytically calculate short-term
memory measures, such as memory capacity, mutual information, and Fisher
information, and determine the relationships among these measures, which have
not been clarified to date to the best of our knowledge. We show that the
network contribution of these short-term memory measures peaks before the edge
of chaos, where the dynamics of input-driven networks is stable but
corresponding systems without input signals are unstable.
