Abstract

Physical systems differing in their microscopic details often display
strikingly similar behaviour when probed at macroscopic scales. Those
universal properties, largely determining their physical
characteristics, are revealed by the renormalization group (RG)
procedure, which systematically retains ‘slow’ degrees of freedom and
integrates out the rest. We demonstrate a machine-learning algorithm
based on a model-independent, information-theoretic characterization of
real-space RG, capable of identifying the relevant degrees of freedom
and executing RG steps iteratively without any prior knowledge about
the system. We apply it to classical statistical physics problems in 1 and
2D: we demonstrate RG flow and extract critical exponents. We also
prove results about optimality of the procedure.