Machine learning techniques to probe theoretical physics Intro In - PowerPoint PPT Presentation

Akinori Tanaka (RIKEN AIP/iTHEMS) Machine learning techniques to probe theoretical physics

Intro In inSPIRE, search find t machine learning OR deep learning and date 20xx->20xx+1

year number of results Intro Mainly experimental, a few theoretical “Deep learning shock” in ILSVRC

Agenda II. Reviews on selected papers I. Reviews on Machine Learning III. Summary

I. Reviews on Machine Learning “supervised” “un-supervised” “reinforcement” ● Rough classification

I. Reviews on Machine Learning “supervised” “un-supervised” “reinforcement” ● Rough classification

I. Reviews on Machine Learning “supervised” ● Rough classification “machine” 2 “machine” 5 “machine” 0 ↑MNIST dataset

I. Reviews on Machine Learning “supervised” ● Rough classification well trained machine 6 bad machine 5 I wrote it f : X → Y In general, trying to learn a “concept”   

I. Reviews on Machine Learning “supervised” “un-supervised” “reinforcement” ● Rough classification

I. Reviews on Machine Learning ● Rough classification “un-supervised” “machine” “machine” “machine” No answer given

I. Reviews on Machine Learning ● Rough classification “un-supervised” well trained machine 1. Feature extraction “local coupling consts” (called features ) “RBM”

I. Reviews on Machine Learning ● Rough classification “un-supervised” well trained machine 2. Generating data

I. Reviews on Machine Learning ● Rough classification (2016) in hep-th All titles Using machine 2. Generating data well trained “un-supervised” towards a non-perturbative corrections to quantum gravity emergent entanglement entropy for 4d superconformal theory Joking demo 😝 chiral transport and Bowman, et al. (2015) entanglement entropy in general relativity

I. Reviews on Machine Learning “supervised” “un-supervised” “reinforcement” ● Rough classification

I. Reviews on Machine Learning ● Rough classification “reinforcement” ������������� ������ ��������� “machine” environment

I. Reviews on Machine Learning ● Rough classification “reinforcement” ������������� ������ ��������� “machine” environment

I. Reviews on Machine Learning ● Shock of Deep Learning “supervised” “un-supervised” “reinforcement” Super fine generated images ％ ↓DL AlphaGo zero ILSVRC top errors T. Karras, et al. (2017) D. Silver, et al. (2017)

I. Reviews on Machine Learning ● Deep Learning “machine” 2 ＝ Multi layered perceptron

I. Reviews on Machine Learning ● Deep Learning “machine” 2 ＝ Linear ∈ tunable params

I. Reviews on Machine Learning ● Deep Learning “machine” 2 ＝ Non Linear

I. Reviews on Machine Learning ● Deep Learning “machine” ＝ ~ ~ y x

I. Reviews on Machine Learning “Error function” input ● Deep Learning ~ ~ y x answer ~ ~ d d y, ~ y − ~ d | 2 E ( ~ d ) = | ~

I. Reviews on Machine Learning input params “Error function” ● Deep Learning E ~ ~ y x answer ~ ~ d d y, ~ E ( ~ d )

I. Reviews on Machine Learning ● Deep Learning Data ~ ~ d x E W ← W − ✏@ W E

I. Reviews on Machine Learning ● Deep Learning easy to start TensorFlow Keras Chainer … Many users … Easy to write … Pythonic and others… https://developer.nvidia.com/deep-learning-frameworks

I. Reviews on Machine Learning ● Deep Learning Comments: For more details: The most famous DL book DL book by a string theorist 1. DL works very well. 2. MLP ≠ DL. 3. MLP + tips = DL.

I. Reviews on Machine Learning ● hep-th & machine learning ? 1. applications 2. proposals = 3. ?? hep-th stat.ML

Agenda 1. TH ← ML 2. TH → ML 3. TH = ML II. Reviews on I. Reviews on Machine Learning

1. TH ← ML ● Drawing phase diagrams ● ML Landscape ● Supporting MC simulations

1. TH ← ML ● Drawing phase diagrams “machine” Idea ↑ Configurations generated by MC simulations ~ ~ y x

1. TH ← ML ● Drawing phase diagrams input ・Cold Cold Hot Carrasquilla, Melko (2016) 1 . 72 5 . 00 2 . 50 output ・Hot 3 . 84 T 2 . 27

1. TH ← ML ● Drawing phase diagrams Cold Hot Test acc > 90% ←Given explicitly Carrasquilla, Melko (2016) T 2 T c = 2) = 2 . 27 . . . √ log(1 +

1. TH ← ML ● Drawing phase diagrams Training Known Model Application Other (similar) Models Carrasquilla, Melko (2016) T 4 T c = log(3) = 3 . 64 . . .

1. TH ← ML Data Update F, W ● Drawing phase diagrams draw AT, Tomiya (2016) 1 . 72 5 . 00 2 . 50 3 . 84 T ... W = F a ... T ...

1. TH ← ML ● Drawing phase diagrams Tc ~ 2.27 AT, Tomiya (2016) ... W F a = ... T ... ... ... T

1. TH ← ML ● Drawing phase diagrams of 3D TI → 2D image 4-layered MLP phases training consistent w/ result by transfer matrix Ohtsuki, Ohtsuki (2016) | ψ ( x, y, z ) | 2

1. TH ← ML ● Drawing phase diagrams ● ML Landscape ● Supporting MC simulations

1. TH ← ML ● Supporting MC simulations Integrable Aut(X) ⊃ “good” symmetry otherwise (usually) Non-integrable → Z dx P ( x ) O ( x ) X 😃 MC 😄 😅

1. TH ← ML ● Supporting MC simulations How? Z dx P ( x ) O ( x ) X Sampling x [ i ] ∼ P ( x )( i.i.d. ) N 1 X N O ( x [ i ]) ∼ i =1

1. TH ← ML ● Supporting MC simulations change ～ P(x) … N 1 X N O ( x [ i ]) ∼ i =1 x [0] x [1] x [ N ] x [ i ] x [ i + 1] ˜ x [ i + 1] Metropolis Test( x [ i ] , ˜ x [ i + 1]) =

1. TH ← ML ● Supporting MC simulations … similar similar similar N 1 X N O ( x [ i ]) ∼ i =1 x [0] x [1] x [ N ]

1. TH ← ML ● Supporting MC simulations Ising Model : one spin random flip Autocorrelation ⇣ ⇣ (similarity) : Γ ( τ ) τ

1. TH ← ML ● Supporting MC simulations Ising Model : one spin random flip ↑∃ Faster update Big picture: ML → Fast update ? ⇣ ⇣

1. TH ← ML ● Supporting MC simulations Self Learning Monte Carlo MC w/ global update ML Liu, Qi, Meng, Fu (2016) H e ff H

1. TH ← ML ● Supporting MC simulations Self Learning Monte Carlo … … Liu, Qi, Meng, Fu (2016) x [0] x [1] x [ N ] x [1] ˜ x [0] ˜ x [ n ] ˜ ↑update by H e ff ˜ Metropolis Test(˜ x [0] , ˜ x [ n ]) = x [ i + 1]

1. TH ← ML ● Supporting MC simulations Self Learning Monte Carlo Liu, Qi, Meng, Fu (2016)

1. TH ← ML ● Supporting MC simulations choose j1 s.t. decreases. (QMC, S = vertices on imaginary time circle) Self Learning Monte Carlo Using MLP Liu, Qi, Meng, Fu (2016) X X H e ff ( S ) = E 0 − j 1 S i S j − j 2 S i S j − . . . <ij> 1 <ij> 2 | H e ff ( S data ) − H ( S data ) | 2 Nagai, Okumura, AT (2018) H e ff ( S ) = MLP ( S )

1. TH ← ML … ● Supporting MC simulations usual update Using Boltzmann Machines Huang, Wang (2016) AT, Tomiya (2017) x [0] x [1] x [ N ] x 0 [ i ] x [ i ] x [ i + 1] ˜ x [ i + 1] Metropolis Test( x [ i ] , ˜ x [ i + 1]) =

1. TH ← ML ● Supporting MC simulations Using Boltzmann Machines Scalar lattice QFT Huang, Wang (2016) AT, Tomiya (2017)

1. TH ← ML ● Drawing phase diagrams ● ML Landscape ● Supporting MC simulations

1. TH ← ML ● ML Landscape topic diagram,… polytope, … Invariants ↑ geometric data ↑ Idea “machine” Landscape → SM-like theory ~ ~ y x h 1 , 2 h 2 , 1 χ

1. TH ← ML ● ML Landscape ・Usage of Mathematica package ・CY3s ∈ WP^4, CICY3s, CICY4s, Quivers MLP not MLP ・F-theory compactifications MLP ・Toric diagram → min(vol(SE)) He (2017) Carifio, Halverson, Krioukov, Nelson (2017) Krefl, Seong (2017)

Agenda 1. TH ← ML 2. TH → ML 3. TH = ML II. Reviews on I. Reviews on Machine Learning

2. TH → ML ● Boltzmann machines Machine” “Boltzmann … Design H Imitate Hinton, Sejnowski (1983) n n P hand-written ( x ) P ising ( x ) = e − H ( x ) Z n n ⇢ +1 = − 1

2. TH → ML ● Boltzmann machines Naive BM How to train W ? → Maximize relative entropy ↑hard to compute (for non-local H) Hinton, Sejnowski (1983) X H = x i W ij x j i,j h log e − H Z i P

2. TH → ML ● Boltzmann machines Restricted BM h integrate out ～ ～ Hinton, Sejnowski (1983) P true ( x ) P ( x ) ↑ ～ P ( x, h ) = e − H ( x,h ) h ∈ Z 2 Z H ( x, h ) = x T Wh + x T B x + B T h h

2. TH → ML ● Boltzmann machines Riemann-Theta BM ～ ～ h integrate out Hinton, Sejnowski (1983) Krefl, Carrazza, Haghighat, Kahlen (2016) θ ( x T W | σ − 1 ) ∝ ˜ P true ( x ) P ( x ) ↑ ～ P ( x, h ) = e − H ( x,h ) h ∈ Z Z H ( x, h ) = x T Wh + x T Σ − 1 x + h T σ − 1 h

Agenda 1. TH ← ML 2. TH → ML 3. TH = ML II. Reviews on I. Reviews on Machine Learning