Holography as deep learning

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.

Received an Honorable Mention on the Gravity Research Foundation's 2017 Essay Competition; v2: typos corrected

References in corpus (12)

• Gauge Theory Correlators from Non-Critical String Theory
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• The World as a Hologram
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Entanglement renormalization
• A class of quantum many-body states that can be efficiently simulated
• Entanglement Renormalization and Holography
• Holographic duality with a view toward many-body physics
• Quantum Entanglement in Neural Network States
• Learning Thermodynamics with Boltzmann Machines
• Neural network representation of tensor network and chiral states
• Causal structure of the entanglement renormalization ansatz

Cited by in corpus (31)

• Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure
• Quantum Neural Network States: A Brief Review of Methods and Applications
• Deep Learning and AdS/CFT
• Machine Learning Spatial Geometry from Entanglement Features
• Deep DIH : Statistically Inferred Reconstruction of Digital In-Line Holography by Deep Learning
• Deep Learning and Holographic QCD
• AdS/CFT as a deep Boltzmann machine
• Deep Learning and AdS/QCD
• Machine Learning Holographic Mapping by Neural Network Renormalization Group
• The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning
• Deep learning black hole metrics from shear viscosity
• Machine learning for complete intersection Calabi-Yau manifolds: a methodological study
• Learning the black hole metric from holographic conductivity
• Deep learning the holographic black hole with charge
• Machine Learning Statistical Gravity from Multi-Region Entanglement Entropy
• Quantum bit threads of MERA tensor network in large $c$ limit
• Surface growth scheme for bulk reconstruction and tensor network
• Quantum computing with classical bits
• RG-Flow: A hierarchical and explainable flow model based on renormalization group and sparse prior
• Gravitational Duals from Equations of State
• Entanglement Area Law for Shallow and Deep Quantum Neural Network States
• Bending the Bruhat-Tits Tree I:Tensor Network and Emergent Einstein Equations
• Thread/State correspondence: from bit threads to qubit threads
• Inferring relevant features: from QFT to PCA
• Quantum fields as deep learning
• Geometrization of deep networks for the interpretability of deep learning systems
• Neural-network Quantum State of Transverse-field Ising Model
• Deep learning-based holography for T-linear resistivity
• Deep-Learning in Search of Light Charged Higgs
• Time-dependent variational principle for open quantum systems with artificial neural networks
• Self-regularizing restricted Boltzmann machines