  Physical systems differring 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 powerful renormalization group (RG) procedure, which systematically retains
"slow" degrees of freedom and integrates out the rest. However, the important
degrees of freedom may be difficult to identify. Here we demonstrate a machine
learning algorithm capable of identifying the relevant degrees of freedom and
executing RG steps iteratively without any prior knowledge about the system. We
introduce an artificial neural network based on a model-independent,
information-theoretic characterization of a real-space RG procedure, performing
this task. We apply the algorithm to classical statistical physics problems in
one and two dimensions. We demonstrate RG flow and extract the Ising critical
exponent. Our results demonstrate that machine learning techniques can extract
abstract physical concepts and consequently become an integral part of theory-
and model-building.
