# Is Deep Learning a Renormalization Group Flow?

## TL;DR

This paper explores the analogy between deep learning and the renormalization group (RG) by comparing a trained RBM on the Ising model to RG transformations, revealing RG-like patterns in neural network correlations.

## Contribution

It demonstrates that correlation functions in trained RBMs can exhibit RG-like coarse graining, providing a theoretical link between deep learning and RG.

## Key findings

- Correlation functions show RG-like patterns in RBMs
- Differences between RG and deep learning are identified
- RBMs can mimic RG coarse graining processes

## Abstract

Although there has been a rapid development of practical applications, theoretical explanations of deep learning are in their infancy. Deep learning performs a sophisticated coarse graining. Since coarse graining is a key ingredient of the renormalization group (RG), RG may provide a useful theoretical framework directly relevant to deep learning. In this study we pursue this possibility. A statistical mechanics model for a magnet, the Ising model, is used to train an unsupervised restricted Boltzmann machine (RBM). The patterns generated by the trained RBM are compared to the configurations generated through an RG treatment of the Ising model. Although we are motivated by the connection between deep learning and RG flow, in this study we focus mainly on comparing a single layer of a deep network to a single step in the RG flow. We argue that correlation functions between hidden and visible neurons are capable of diagnosing RG-like coarse graining. Numerical experiments show the presence of RG-like patterns in correlators computed using the trained RBMs. The observables we consider are also able to exhibit important differences between RG and deep learning.