Before revision: Statistical field theory captures collective non-equilibrium dynamics of neuronal networks , but it does not address the inverse problem of searching the connectivity to implement a desired dynamics. We here show for an analytically solvable network model that the effective action in statistical field theory is identical to the rate function in large deviation theory;
After revision: We here unify the field theoretical approach to neuronal networks with large deviation theory. For a prototypical random recurrent network model with continuous-valued units, we show that the effective action in statistical field theory is identical to the rate function in large deviation theory;