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Holography as deep learning · Around

2017

Holography as deep learning

Gan, Wen-Cong, Shu, Fu-Wen

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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.

Built on

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Similar

S. Ryu, T. Takayanagi, “Holographic derivation of entanglement entropy from the anti-de sitter space/conformal field theory correspondence”, Phys. Rev. Lett. 96
2006
Cited alongside, same era.
G. Vidal, “Entanglement renormalization”, Phys. Rev. Lett. 99
2008
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J. McGreevy, “Holographic duality with a view toward many-body physics”, Adv. High Energy Phys. 2010
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2010
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B. Swingle, “Entanglement Renormalization and Holography”, Phys. Rev. D
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2012
Cited alongside, same era.
P. Mehta, D. J. Schwab, “An exact mapping between the Variational Renormalization Group and Deep Learning”, [arXiv:1410.3831]
Original
Cited in the paper.
G. ’t Hooft, “Dimensional Reduction in Quantum Gravity”, THU-93/26, [gr-qc/9310026]
Cited in the paper.
Y. Huang, J. E. Moore, “Neural network representation of tensor network and chiral states”, [arXiv:1701.06246]
Original
Cited in the paper.
X. Gao, L.-M. Duan, “Efficient Representation of Quantum Many-body States with Deep Neural Networks”, [arXiv:1701.05039]
Original
Cited in the paper.

Then

C. Bény, “Causal structure of the entanglement renormalization ansatz”, New J. Phys. 15
Original
2013
Later among the works it cites.
G. Torlai, R. G. Melko, “Learning Thermodynamics with Boltzmann Machines”, Phys. Rev. B
Original
2016
Later among the works it cites.
G. Carleo, M. Troyer, “Solving the quantum many-body problem with artificial neural networks”, Science 355
Original
2017
Closest in time.
D.-L. Deng, X. Li, S. D. Sarma, “Quantum Entanglement in Neural Network States”, Phys. Rev. X
Original
2017
Closest in time.

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