Before revision:  We use random matrix theory to show how gating robustly produces marginal stability and line attractors -- important mechanisms for biologically-relevant computations requiring long memory. The long-time behavior of the gated network is studied using its Lyapunov spectrum, and the DMFT is used to provide a novel analytical expression for the maximum Lyapunov exponent demonstrating its close relation to relaxation time of the dynamics.
After revision:  We show that gating leads to slow modes and a novel, marginally-stable state. The network in this marginally-stable state can function as a robust integrator, and unlike previous approaches, gating permits this function without parameter fine-tuning or special symmetries. We study the long-time behavior of the gated network is studied using its Lyapunov spectrum, and the DMFT is used to provide a novel analytical expression for the maximum Lyapunov exponent demonstrating its close relation to relaxation time of the dynamics.