Holography as deep learning

2017/05/16 by Wen-Cong Gan, Fu-Wen Shu · 1 voice · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th #quant-ph

paper · pdf · doi:10.1142/s0218271817430209

arxiv published 2017/05/16 · arxiv updated 2017/05/27 · openalex publication_date 2017/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Quantum many-body problem with exponentially large degrees of freedom can be reduced to a tractable computational form by neural network method [G. Carleo and M. Troyer, Science 355 (2017) 602, arXiv:1606.02318.] 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 paper, 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 DNN 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.

Citations

• Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
• The world as a hologram

Cited by

• Geometrization of deep networks for the interpretability of deep learning systems

Discussions

• Holography as deep learning [hn, 3 points, 0 comments]

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