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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.
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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)
4 pages 1. Is deep learning useful? 5pages AdS/DL 2. 8 pages 3. Deeply learning QCD
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.
1-2 • Holographic QCD is an inverse problem Gravity Model Metric Prediction Prediction Experiment data Experiment data
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]
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]
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]
4 pages 1. Is deep learning useful? 5pages AdS/DL 2. 8 pages 3. Deeply learning QCD
2-1 • Holography as a classifier AdS/CFT [Maldacena ‘97] Deep neural network Black hole AdS (Emergent spacetime) CFT
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”
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 ( ) :
2-4 • Neural network of AdS scalar BulkEoM metric Discretization, Hamilton form Neural-Network representation
2-5 • Dictionary of AdS/DL correspondence
4 pages 1. Is deep learning useful? 5pages AdS/DL 2. 8 pages 3. Deeply learning QCD
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]
3-1 • Deeply learning QCD • Use a QCD data. • Let the network learn a metric. • Calculate other physical quantities.
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)
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.
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)
3-5 • Deeply learning QCD • Use a QCD data. • Let the network learn a metric. • Calculate other physical quantities. QCD lattice data
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)
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]
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]
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]
4 pages 1. Is deep learning useful? 5pages AdS/DL 2. 8 pages 3. Deeply learning QCD
Summary: Neural network as a spacetime Deep neural network Black hole AdS (Emergent spacetime) CFT
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?
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.]