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The ability of discrete-time nonlinear recurrent neural networks to storetime-varying small input signals is investigated by mean-field theory. Thecombination of a small input strength and mean-field assumptions makes itpossible to derive an approximate expression for the conditional probabilitydensity of the state of a neuron given a past input signal. From thisconditional probability density, we can analytically calculate short-termmemory measures, such as memory capacity, mutual information, and Fisherinformation, and determine the relationships among these measures, which havenot been clarified to date to the best of our knowledge. We show that thenetwork contribution of these short-term memory measures peaks before the edgeof chaos, where the dynamics of input-driven networks is stable butcorresponding systems without input signals are unstable.

Optimal short-term memory before the edge of chaos in driven random recurrent networks