1. Quantum fields as deep learning
Jae-Weon Lee (Jungwon univ.)
arXiv:

2. Brief History of Complexity
1920: Hilbert's program
Decision problem=asking for an algorithm to decide whether a given
statement is provable from the axioms using the rules of logic
1931:Kurt Gödel's incompleteness theorem
1936:Turing machine  computational complexity theory
Easy problem = in P, Hard problem = not in P
Church–Turing Thesis
= “All physically computable functions are Turing-computable”
1981: Feynman proposes Q. Computer (N spins need 2N coefficients)
Quantum Church–Turing thesis
=“A quantum Turing machine can efficiently simulate any realistic
model of computation.”
Church–Turing -Dutch principle 
The universe is equivalent to a Turing machine digital physics.

3. Machine learning
“A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E” -Tom M. Mitchell
(x)
Supervised Learning (data x-label y)
Classification
Regression
Unsupervised Learning (data x)
Clustering
Underlying Probability Density Estimation
Semisupervised learning
Reinforcement Learning – delayed reward problem
(y)
(x)
Algorithms: Gradient descent, Regression, Bayesian, HMM, SVM, ANN

4. Artificial neural networks (ANN)
O(1011) cells
with O(104) synapses
가중치 역치
Activation function
perceptron
1958 Rosenblatt

5. How DLs recognize a dog
Roger Parloff

6. WHY DOES DEEP LEARNING WORK?
RG?
Combination?
Simple physical laws
arXiv:
Pankaj Mehta, David J. Schwab
Lin, Tegmark

7. Hopfield network (energy based, deterministic)
Training a Hopfield net = lowering the energy
of states that the net should "remember" 1 3
1)wij = wji, 2) asynchronous 
associative memory

8. Boltzmann machine (BM)
 Stochastic(Monte Carlo), generative counterpart of Hopfield nets
Similar to Spin glass
Unsupervised learning
impractical

9. Restricted Boltzmann machine (RBM)
no two nodes of the same layer are linked
interaction

10. 차원감소
Autoencoder

11. Renormalization
Kadanoff h v
Boltzmann distribution
Variational RG

12. An exact mapping between the Variational Renormalization Group and Deep Learning
arXiv:
Pankaj Mehta, David J. Schwab

13. An exact mapping between the Variational Renormalization Group and Deep Learning

15. AdS/MERA gA CFTd A AdSd+1 Ryu-Takayanagi formula 2006 s steps L~ 2s
Swingle 2009
Ryu-Takayanagi formula 2006 A gA
CFTd
AdSd+1
s steps
L~ 2s
E.E ~ # of tracing out indices
~# of cuts ~ s ~ log(L)
 geodesic in AdS
 Redundancy, QEC, Holography…

16. Holography as deep learning
Wen-Cong Ganand Fu-Wen Shu,

17. Gravity from entanglement
Lee, Lee, Kim, JKPS 2013
Vacuum in Euclidean L R t x dE
Boost H. a
with proper time
Unruh effect
BH horizon too

18. Quantum fields as deep RBM
arXiv:
Higgs?

20. Conclusion Deep learning has physics in it
Quantum fields, and spacetime, could be deep learning
[Q] Can nature think? If yes, then why doesn’t it speak to us??

22. Machine Learning Spatial Geometry from Entanglement
Hayden etal
the random tensor network (RTN) states
satisfy the Ryu-Takayanagi formula
Yi-Zhuang You etal

23. Other ideas 1) Euclidean quantum fieeld theory in
d+1 dimensional at spacetime and the statistical mechanics in d+1 dimensional at space using an imaginary time
2) QNN

24. Entanglement entropy of a state
How broadly spread over, or Information in a density matrix A
Ex) Vacuum or ground
Partial trace
For pure states
Entanglement
Entropy
(vNE of subsystem)
More correlated, less we know about the subsystem alone.

25. Vanishing gradient problem
Multi-layer perceptron
기울기<1/4 출력 입력
Backpropagation
Backward:Hinton et al. (1986) Nature
Using chainrule

26. Tensor network
Orus
arXiv:
Tensor network: to find the ground states of critical quantum systems in an efficient manner. (MPS, PEPS, MERA…)
(Feynman’s original motivation for QC.)
Ex) N spin wave fn
ansatz
Ground
state
Vidal

27. aXiv:

28. MERA ( Multiscale entanglement renormalization ansatz) Vidal 2007
time RG
Removal UV
DOF
(preserves the inner product)
Removal UV
entanglement

29. Jacobson’s Great idea
Padmanabhan
1st law (assumption) R
Covariant form
where
Raychaudhuri equation
For all null
using contracted
Bianchi identity
Einstein equation is related to 1st law for local Rindler horizons!

30. Entanglement 1st law

31. Holographic Q. error correcting code
HaPPY
Perfect tensor with 2n indices:
Isometry
Maximally entangled n to n
2n-1 qubit EC for 1 qubit
The code can tolerate loss of 2 qubit
5 qubit code
Logical op. preserving code space reside
in the bulk
Geodesic line
= epr pairs
Quantum code on boundary

32. Activation function needs to be nonlinear (Logistic)
미분에 유리
(Logistic)
Rectified linear unit
Moujahid

33. Entanglement as spacetime glue
Raamsdonk A B L
Minimal surface
The smaller entanglement, the less ST connected gA
CFT
CFT
Two CFTs in HH states
=dual to eternal AdS black hole spacetime
(EE is equal to thermal entropy of BH)
Quantum superposition of disconnected spacetime
 Emergent spacetime
Maldacena, hepth/

34. Modern interpretationL R t x a