# Towards a Theory of Quantum Gravity from Neural Networks

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## Abstract

**:**

## 1. Introduction

## 2. Neural Networks

- $\mathbf{x}$, column state vector of boundary (i.e., input/output) and bulk (i.e., hidden) neurons,
- $\widehat{P}$, boundary projection operator to subspace spanned by boundary neurons,
- ${p}_{\partial}\left(\widehat{P}\mathbf{x}\right)$, probability distribution which describes the training dataset,
- $\widehat{w}$, weight matrix which describes connections and interactions between neurons,
- $\mathbf{b}$, column bias vector which describes bias in the inputs of individual neurons,
- $\mathbf{f}\left(\mathbf{y}\right)$, activation map which describes a non-linear part of the dynamics,
- $H(\mathbf{x},\mathbf{b},\widehat{w})=H(\mathbf{x},\mathbf{q})$, loss function where $\mathbf{q}$ denotes collectively both $\mathbf{b}$ and $\widehat{w}$.

## 3. Madelung Equations

## 4. Schrodinger Equation

## 5. Lorentz Symmetry

## 6. Emergent Space-Time

## 7. Geodesic Equation

## 8. Einstein Equations

## 9. Discussion

## Funding

## Acknowledgments

## Conflicts of Interest

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Vanchurin, V.
Towards a Theory of Quantum Gravity from Neural Networks. *Entropy* **2022**, *24*, 7.
https://doi.org/10.3390/e24010007

**AMA Style**

Vanchurin V.
Towards a Theory of Quantum Gravity from Neural Networks. *Entropy*. 2022; 24(1):7.
https://doi.org/10.3390/e24010007

**Chicago/Turabian Style**

Vanchurin, Vitaly.
2022. "Towards a Theory of Quantum Gravity from Neural Networks" *Entropy* 24, no. 1: 7.
https://doi.org/10.3390/e24010007