On the Information Required for Feedback Control

What the math gives to ML

The paper derives an information-theoretic lower bound on the feedback information rate required to steer a noisy stochastic system toward a target steady state. Its most transferable mechanism is a performance-information Pareto frontier, together with an explicit probabilistic time-reversal protocol that saturates the bound for state-independent passive dynamics. This can be transferred to recurrent controllers and state-space models by adding a causal information bottleneck and regularizing the controller toward the reverse passive transition kernel. The central falsifiable prediction is a monotone control-cost versus information-rate frontier, with a measurable advantage for reverse-dynamics initialization at equal information rate.