<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>AdS</mml:mi><mml:mo>/</mml:mo><mml:mi>CFT</mml:mi></mml:mrow></mml:math>correspondence as a deep Boltzmann machine

Hashimoto, Koji

doi:10.1103/physrevd.99.106017

Cited by 49 publications

(26 citation statements)

References 48 publications

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“…In the growing subject (see Ref. [26] for a recent summary of data science application to string theory), the idea of equating a holographic spacetime with neural network [11,12,16,17,[27][28][29] may be intertwined with machine learning string landscapes initiated by Refs. [30][31][32][33].…”

Section: Discussionmentioning

confidence: 99%

Deep learning and AdS/QCD

2020

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We propose a deep learning method to build an AdS/QCD model from the data of hadron spectra. A major problem of generic AdS/QCD models is that a large ambiguity is allowed for the bulk gravity metric with which QCD observables are holographically calculated. We adopt the experimentally measured spectra of ρ and a 2 mesons as training data, and perform a supervised machine learning which determines concretely a bulk metric and a dilaton profile of an AdS/QCD model. Our deep learning (DL) architecture is based on the AdS/DL correspondence [K. Hashimoto, S. Sugishita, A. Tanaka, and A. Tomiya, Phys. Rev. D 98, 046019 (2018)] where the deep neural network is identified with the emergent bulk spacetime.

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Section: Discussionmentioning

confidence: 99%

Deep learning and AdS/QCD

2020

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“…These topics will be left for our future studies. During the preparation of our manuscript, we notice that a related work was made available [56].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Although many progress of RBM states has been made, the DBM states are less investigated [30]. There are several crucial reasons why we need deep neural network rather than shallow one: (i) the representational power of shallow network is limited, there exist states which can be efficiently represented by deep neural network while the shallow one can not represent [30]; (ii) aAny Boltzmann machine (BM) can be reduced into a DBM, this also makes some limits in usage of shallow BM (with just one hidden layer, viz, RBM) [30]; (iii) the hierarchy structure of deep neural is more suitable for encoding holography [49,55,56] and for procedure such as renormalization [57]. Now let us take a close look at the geometry of a DBM neural network.…”

Section: Entanglement Features Of Deep Neural Network Statesmentioning

confidence: 99%

Entanglement area law for shallow and deep quantum neural network states

Jia

et al. 2020

New J. Phys.

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A study of the artificial neural network representation of quantum many-body states is presented. The locality and entanglement properties of states for shallow and deep quantum neural networks are investigated in detail. By introducing the notion of local quasi-product states, for which the locally connected shallow feed-forward neural network states and restricted Boltzmann machine states are special cases, we show that Rényi entanglement entropies of all these states obey the entanglement area law. Besides, we also investigate the entanglement features of deep Boltzmann machine states and show that locality constraints imposed on the neural networks make the states obey the entanglement area law. Finally, as an application, we apply the notion of Rényi entanglement entropy to understand the power of neural networks, and show that image classification problems can be efficiently solved must obey the area law.

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“…The non-gaussianity of the training process has been related to renormalisation group flow, with different trained networks acting alike fixed points in the flow [132,133] (q.v. [134]). Cementing these ideas is an interesting topic for further work.…”

Section: A Digression: Machine Learningmentioning

confidence: 99%

Some Open Questions in Quiver Gauge Theory

Bao,

Hanany,

et al. 2021

Preprint

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Quivers, gauge theories and singular geometries are of great interest in both mathematics and physics. In this note, we collect a few open questions which have arisen in various recent works at the intersection between gauge theories, representation theory, and algebraic geometry. The questions originate from the study of supersymmetric gauge theories in different dimensions with different supersymmetries. Although these constitute merely the tip of a vast iceberg, we hope this guide can give a hint of possible directions in future research.This is an invited contribution to a special volume of Proyecciones, E. Gasparim, Ed., and it is the hope that the questions are specific enough for research projects aimed at PhD students.

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AdS/CFTcorrespondence as a deep Boltzmann machine

Cited by 49 publications

References 48 publications

Deep learning and AdS/QCD

Deep learning and AdS/QCD

Entanglement area law for shallow and deep quantum neural network states

Some Open Questions in Quiver Gauge Theory

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