Before revision:   For the second class of networks,  we provide a procedure to identify transiently amplified inputs and the corresponding readouts for arbitrary connectivity matrices. We then exploit our approach to build the minimalconnectivity which robustly implements trajectories that map a specific input onto a specific output state , and we demonstrate that the capacity of the obtained networks increases proportionally with their size.
After revision:  For the second class of networks, we provide a procedure to identify transiently amplified inputs and the corresponding readouts . We first apply these results to standard randomly-connected and two-population networks. We then build minimal, low-rank networks that robustly implement trajectories mapping a specific input onto a specific output state , and we demonstrate that the capacity of the obtained networks increases proportionally with their size.