# Mutual Information, Neural Networks and the Renormalization Group

## TL;DR

This paper presents a neural network-based machine learning algorithm that autonomously identifies relevant degrees of freedom and performs renormalization group steps in physical systems, successfully applying it to classical models and extracting critical exponents.

## Contribution

It introduces a model-independent, information-theoretic neural network approach to perform real-space RG without prior knowledge, advancing the integration of machine learning into theoretical physics.

## Key findings

- Successfully applied to 1D and 2D Ising models
- Extracted critical exponents consistent with known values
- Demonstrated the ability to identify relevant degrees of freedom

## Abstract

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.