# Holography as deep learning

## TL;DR

This paper explores the connection between deep neural networks, renormalization group processes, and holographic principles, suggesting that neural network structures encode hyperbolic geometry and entanglement patterns akin to holographic dualities.

## Contribution

It demonstrates that RG-reflecting networks inherently possess hyperbolic geometry and encode entanglement structures similar to holographic theories, linking deep learning to quantum gravity.

## Key findings

- Neural networks reflecting RG processes have intrinsic hyperbolic geometry.
- Deep neural network entanglement structure follows Ryu-Takayanagi form.
- Holographic gravitational emergence relates to deep learning of quantum fields.

## Abstract

Quantum many-body problem with exponentially large degrees of freedom can be reduced to a tractable computational form by neural network method \cite{CT}. The power of deep neural network (DNN) based on deep learning is clarified by mapping it to renormalization group (RG), which may shed lights on holographic principle by identifying a sequence of RG transformations to the AdS geometry. In this essay, we show that any network which reflects RG process has intrinsic hyperbolic geometry, and discuss the structure of entanglement encoded in the graph of DNN. We find the entanglement structure of deep neural network is of Ryu-Takayanagi form. Based on these facts, we argue that the emergence of holographic gravitational theory is related to deep learning process of the quantum field theory.