Constructing Generative Models via the Functional Renormalization Group

Inference problems invert the traditional flow of statistical physics requiring the construction of a probability distribution given a limited set of observations. The fundamental challenge of inverse problems is separating the true couplings between variables from correlations that measure interactions between variables mediated by the entire system. We consider, for cases were additional measurements are possible, the functional renormalization group (fRG) as a tool for such a separation. Standard fRG flows start with a model Hamiltonian modified with a regulator that suppresses all interactions below a certain scale. As the flow proceeds the regulator slowly moves down through all scales until we converge to the fully interacting system. We invert this program and systematically freeze and remove long range correlations from a fully interacting system. We apply this inverted fRG scheme to the Ising and XY models. Finally, we address the required set of observables to make an fRG reconstruction a viable scheme.