Before revision:  We  explore how different types of cortical neurons may represent different variables , such as prior and posterior distributions and value functions, and what cortical dynamics may realize required computations.
After revision:  We first review the classic duality of inference and control in linear quadratic systems and then review the correspondence between dynamic Bayesian inference and optimal control. Based on the architecture of the canonical cortical circuit, we explore how different types of cortical neurons may represent different variables , such as prior and posterior distributions and value functions, and what cortical dynamics may realize required computations.