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AdS-CFT correspondence as a deep Boltzmann machine - 2019

Ads-Cft Correspondence As A Deep Boltzmann Machine

Research Area:  Machine Learning

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 Nc 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.

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Author(s) Name:  Koji Hashimoto

Journal name:  Physical Review D

Conferrence name:  

Publisher name:  American Physical Society

DOI:  10.1103/PhysRevD.99.106017

Volume Information:  Vol. 99, Iss. 10 — 15 May 2019