# AdS/CFT as a deep Boltzmann machine

## TL;DR

This paper introduces a deep Boltzmann machine model for the AdS/CFT correspondence, linking neural networks with bulk spacetime geometry and providing a new computational framework for holography.

## Contribution

It presents a novel neural network architecture that models the bulk spacetime in AdS/CFT, including black hole horizons and Einstein action regularization, bridging holography and machine learning.

## Key findings

- DBM models bulk scalar fields in curved geometries
- Training weights encode the bulk metric
- Holographic renormalization implemented in autoencoder

## Abstract

We provide a deep Boltzmann machine (DBM) for the AdS/CFT correspondence. Under the philosophy that the bulk spacetime is a neural network, we give a dictionary between those, and obtain a restricted DBM as a discretized bulk scalar field theory in curved geometries. The probability distribution as training data is the generating functional of the boundary quantum field theory, and it trains neural network weights which are the metric of the bulk geometry. The deepest layer implements black hole horizons, and an employed regularization for the weights is an Einstein action. A large $N_c$ limit in holography reduces the DBM to a folded feed-forward architecture. We also neurally implement holographic renormalization into an autoencoder. The DBM for the AdS/CFT may serve as a platform for studying mechanisms of spacetime emergence in holography.