The Inverse of Exact Renormalization Group Flows as Statistical Inference

Understand

We build on the view of the Exact Renormalization Group (ERG) as an instantiation of Optimal Transport described by a functional convection-diffusion equation.

• We provide a new information theoretic perspective for understanding the ERG through the intermediary of Bayesian Statistical Inference.
• This connection is facilitated by the Dynamical Bayesian Inference scheme, which encodes Bayesian inference in the form of a one parameter family of probability distributions solving an integro-differential equation derived from Bayes' law.
• In this note, we demonstrate how the Dynamical Bayesian Inference equation is, itself, equivalent to a diffusion equation which we dub Bayesian Diffusion.