1 / 29

Deep Learning and Holographic QCD

Explore the usefulness of deep learning in solving inverse problems in holographic QCD and its resemblance to quantum gravity. Use QCD data to train a neural network to learn the metric and predict other physical quantities.

harmony
Télécharger la présentation

Deep Learning and Holographic QCD

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Nordita workshop on holographic QCD, July 24 2019 QCD club, Keio U., July 8 2019; Arnold Sommerfeld Center, Munich, LMU, June 13 2019; Max Planck Institute for gravitational Physics, June 11 2019 Microsoft research, 25 April 2019; U. Washington, seminar, 24 April 2019; AdS/CFT workshop at OIST, 3 April 2019; “Machine learning landscape” workshop, ICTP Trieste, 10 Dec 2018; East Asian string workshop, KIAS, Seoul, 7 Nov 2018; KMI colloquium, Nagoya U, 25 Oct 2018; “QG meets lattice QCD workshop”, ECT*, Trento, 3 Sep 2018; APCTP focus program, Hanyang U, Seoul, 15 Aug 2018; QFT workshop, YITP, Kyoto, 31 July 2018; Machine learning workshop, TSiMF, China, 15 June, 2018; Paris QCD workshop, 11 June, 2018; DLAP2018 workshop, Osaka, 1 June, 2018; MPI, AEI, virtual seminar, 13 Apr, 2018; MIT, CTP, seminar, 4 Apr, 2018; CQuest, Sogang u., seminar, 29 March, 2018; KIAS, seminar, 26 March, 2018 Deep Learningand Holographic QCD Koji Hashimoto (Osaka u) ArXiv:1907.????? w/ T.Akutagawa, T.Sumimoto (Osaka u) ArXiv:1903.04951 ArXiv:1802.08313, 1809.10536 w/ S. Sugishita (Kentucky), A. Tanaka, A. Tomiya (RIKEN)

  2. 4 pages 1. Is deep learning useful? 5pages AdS/DL 2. 8 pages 3. Deeply learning QCD

  3. 1-1 • Is deep learning useful? 3 reasons. 1. Holographic QCD is an inverse problem, and the deep learning is good at it. Normal problem: System “f” given, calculate A for given B. Inverse problem: For given many data (A,B), find “f”. 2. Quantum gravity is a network optimization, and so is the deep learning. 3. Deep learning architecture resembles holography.

  4. 1-2 • Holographic QCD is an inverse problem Gravity Model Metric Prediction Prediction Experiment data Experiment data

  5. 1-2 • Holographic QCD is an inverse problem Gravity Model Metric Q Qbar potential Lattice QCD data: chiral condensate VS quark mass Prediction Deep Learning Experiment data Experiment data [RBC-Bielefeld collaboration, 2008] (Courtesy of W.Unger) [Petreczky, 2010]

  6. 1-3 • Quantum gravity = Network optimization Quantum codes for holography Regge calculus [Regge 1961] Causal dynamical triangulation [Ambjorn, Loll 1998] AdS/MERA [Swingle `09] [Pastawski, Yoshida, Harlow, Preskill `15]

  7. http://www.asimovinstitute.org/neural-network-zoo/

  8. 1-4 • Resemblance of the architecture [KH `19] [You,Yang,Qi `18] (See also [Gan,Shu `17][Howard `18]) Deep Boltzmann machine AdS/CFT [Maldacena 1997] [Salakhutdinov, Hinton 2009]

  9. 4 pages 1. Is deep learning useful? 5pages AdS/DL 2. 8 pages 3. Deeply learning QCD

  10. 2-1 • Holography as a classifier AdS/CFT [Maldacena ‘97] Deep neural network Black hole AdS (Emergent spacetime) CFT

  11. 2-2 • Deep learning : optimized sequential map Layer N Layer 2 Layer 1 “Activation function” (fixed nonlinear fn.) “Weights” (variable linear map) Prepare many sets : input + output Train the network (adjust ) by lowering “Loss function”

  12. 2-3 • AdS/CFT: quantum response from geometry [Klebanov,Witten] Classical scalar field theory in (d+1) dim. geometry AdS boundary ( ) : Black hole horizon ( ) : Solve EoM, get response . Boundary conditions: AdS boundary ( ) : Black hole horizon ( ) :

  13. 2-4 • Neural network of AdS scalar BulkEoM metric Discretization, Hamilton form Neural-Network representation

  14. 2-5 • Dictionary of AdS/DL correspondence

  15. 4 pages 1. Is deep learning useful? 5pages AdS/DL 2. 8 pages 3. Deeply learning QCD

  16. Holographic QCD is an inverse problem Gravity Model Metric Q Qbar potential Lattice QCD data: chiral condensate VS quark mass Prediction Deep Learning Experiment data Experiment data [RBC-Bielefeld collaboration, 2008] (Courtesy of W.Unger) [Petreczky, 2010]

  17. 3-1 • Deeply learning QCD • Use a QCD data. • Let the network learn a metric. • Calculate other physical quantities.

  18. 3-2 • Deeply learning QCD • Use a QCD data. • Let the network learn a metric. • Calculate other physical quantities. Chiral condensate VS quark mass. Pick up β=3.33 data Positive data Negative data β=3.30  T=196[MeV] [RBC-Bielefeld collaboration, 2008] (Courtesy of W.Unger)

  19. 3-3 • Deeply learning QCD • Use a QCD data. • Let the network learn a metric. • Calculate other physical quantities. Map it to asymptotic scalar configuration. [Klebanov,Witten] [DaRold,Pomarol][Karch,Katz,Son,Stephanov] [Cherman,Cohen,Werbos] • Conformal dimension of is 3. • Sub-leading contribution, present. • Everything measured in unit of AdS radius.

  20. 3-4 • Deeply learning QCD • Use a QCD data. • Let the network learn a metric. • Calculate other physical quantities. asymptotic AdS horizon Klebanov-Witten decomposition Unspecified metric , coupling (to be trained)

  21. 3-5 • Deeply learning QCD • Use a QCD data. • Let the network learn a metric. • Calculate other physical quantities. QCD lattice data

  22. 3-6 • Deeply learning QCD • Use a QCD data. • Let the network learn a metric. • Calculate other physical quantities. Learned value of (AdS radius)-1 : 1/L = 237(3)[MeV] bulk coupling : λ/L = 0.0127(6)

  23. 3-7 • Deeply learning QCD • Use a QCD data. • Let the network learn a metric. • Calculate other physical quantities. Learned metric Cf) Bottom-up model [Andreev, Zakharov, `06, `07] Bump Quantum gravity effect? Cf[Hyakutake`14]

  24. 3-7 • Deeply learning QCD • Use a QCD data. • Let the network learn a metric. • Calculate other physical quantities. Q Qbar potential Learned metric Procedures based on [Maldacena] [Rey,Theisen,Yee] Bump Quantum gravity effect? Cf[Hyakutake 2014]

  25. 3-8 • Deeply learning QCD • Use a QCD data. • Let the network learn a metric. • Calculate other physical quantities. Q Qbar potential [Petreczky, `10] [T.Ishikawa et al., `08, CPPACS + JLQCD collaboration]

  26. 4 pages 1. Is deep learning useful? 5pages AdS/DL 2. 8 pages 3. Deeply learning QCD

  27. Summary: Neural network as a spacetime Deep neural network Black hole AdS (Emergent spacetime) CFT

  28. A • What do we learn? Strategy for a universal modeling? - Consistency with more observables: 1-pt, 2-pt, 3-pt, … and spacetime dependence? - Hadron spectroscopy. [Akutagawa,Sumimoto,KH in progress] - Rather, observable-oriented modeling? Consistency with top-down approach? - Supergravity as a regularization for learning Quantum gravity path-integral?

  29. A • Emergent geometry? Emergence of AdS radial direction? Bulk reconstruction and locality. [Heemskerk, Penedones, Polchinski, Sully 09] Entanglement entropy reconstruction. [Balasubramanian, Chowdhury, Czech, deBoer, Heller 13] [Myers, Rao, Sugishita 14] Optimization of boundary path integral. [Caputa,Kundu,Miyaji,Takayanagi,Watanabe 17] Renormalization and effective LG theory. [Ki-Seok Kim, Chanyong Park 16] AdS/MERA. [Swingle 12] Emergence of smooth neural network space? Statistical neural network. [Amari et al.]

More Related