A free-energy principle for representation learning

This paper employs a formal connection of machine learning with thermodynamics to characterize the quality of learned representations for transfer learning. We discuss how information-theoretic functionals such as rate, distortion and classification loss of a model lie on a convex, so-called, equilibrium surface. We prescribe dynamical processes to traverse this surface under specific constraints; in particular we develop an iso-classification process that trades off rate and distortion to keep the classification loss unchanged. We demonstrate how this process can be used for transferring representations from a source task to a target task while keeping the classification loss constant. Experimental validation of the theoretical results is provided on image-classification datasets.