Mutual Information, Neural Networks and the Renormalization Group
This work addresses a challenge in theoretical physics by enabling automated extraction of universal properties, though it is incremental as it builds on existing renormalization group concepts with machine learning integration.
The authors tackled the problem of identifying relevant degrees of freedom in physical systems by developing a machine learning algorithm that performs renormalization group steps without prior knowledge, applying it to classical statistical physics problems and extracting the Ising critical exponent.
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.