a video from google deepmind - github pageswangleiphy.github.io/talks/rbm_seattle.pdfrecommender...
TRANSCRIPT
![Page 1: A Video from Google DeepMind - GitHub Pageswangleiphy.github.io/talks/RBM_Seattle.pdfRecommender Systems Learn preferences Recommendations Restricted Boltzmann Machine E (x, h)= XN](https://reader035.vdocument.in/reader035/viewer/2022062920/5f0243a37e708231d40365aa/html5/thumbnails/1.jpg)
A Video from Google DeepMind
http://www.nature.com/nature/journal/v518/n7540/fig_tab/nature14236_SV2.html
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Can machine learning teach us cluster updates ?
Lei Wang Institute of Physics, CAS https://wangleiphy.github.io
Li Huang and LW, 1610.02746 LW, 1702.08586
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Local vs Cluster algorithms
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Local vs Cluster algorithms
is slower than
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Local vs Cluster algorithms
Algorithmic innovation outperforms Moore’s law!
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Recommender Systems
Learn preferences
Recommendations
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Recommender Systems
Learn preferences
Recommendations
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Restricted Boltzmann Machine
E (x,h) = �NX
i=1
aixi �MX
j=1
bjhj �NX
i=1
MX
j=1
xiWijhj
x 2 {0, 1}N
h 2 {0, 1}M
Energy based model
x1 x2 . . .
xN
h1 h2 h3 . . .
hM
Smolensky 1986 Hinton and Sejnowski 1986
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Restricted Boltzmann Machine
E (x,h) = �NX
i=1
aixi �MX
j=1
bjhj �NX
i=1
MX
j=1
xiWijhj
x 2 {0, 1}N
h 2 {0, 1}M
Energy based model
x1 x2 . . .
xN
h1 h2 h3 . . .
hM
Smolensky 1986 Hinton and Sejnowski 1986
![Page 10: A Video from Google DeepMind - GitHub Pageswangleiphy.github.io/talks/RBM_Seattle.pdfRecommender Systems Learn preferences Recommendations Restricted Boltzmann Machine E (x, h)= XN](https://reader035.vdocument.in/reader035/viewer/2022062920/5f0243a37e708231d40365aa/html5/thumbnails/10.jpg)
Restricted Boltzmann Machine
E (x,h) = �NX
i=1
aixi �MX
j=1
bjhj �NX
i=1
MX
j=1
xiWijhj
x 2 {0, 1}N
h 2 {0, 1}M
Energy based model
p(x) =X
h
p(x,h)
p(x,h) ⇠ e�E(x,h)
p(h|x) = p(x,h)/p(x)
Probabilities
x1 x2 . . .
xN
h1 h2 h3 . . .
hM
Smolensky 1986 Hinton and Sejnowski 1986
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Restricted Boltzmann Machine
E (x,h) = �NX
i=1
aixi �MX
j=1
bjhj �NX
i=1
MX
j=1
xiWijhj
x 2 {0, 1}N
h 2 {0, 1}M
Energy based model
p(x) =X
h
p(x,h)
p(x,h) ⇠ e�E(x,h)
p(h|x) = p(x,h)/p(x)
Probabilities
x1 x2 . . .
xN
h1 h2 h3 . . .
hM
Universal approximator of probability distributions . Freund and Haussler, 1989 . Le Roux and Bengio, 2008
Smolensky 1986 Hinton and Sejnowski 1986
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Generative LearningLearning: Fit to the target distribution
Generating: Blocked Gibbs sampling
Hinton 2002Learn the model from data
Generate more data from the learned model
x
h
x
0
p(h|x) p(x0|h)
x
h
h
0
x
0
p(h|x) min
⇥1,
p(h0)p(h)
⇤p(x0|h0)
target probability p(x) ⇠ ⇡(x)
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MNIST database of handwritten digits
learned weight Wij
http://www.deeplearning.net/tutorial/rbm.html#rbmTheano deep learning tutorial
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MNIST database of handwritten digits
learned weight Wij
http://www.deeplearning.net/tutorial/rbm.html#rbmTheano deep learning tutorial
784 100x1 x2 . . .
xN
h1 h2 h3 . . .
hM
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MNIST database of handwritten digits
learned weight Wij
http://www.deeplearning.net/tutorial/rbm.html#rbmTheano deep learning tutorial
784 100x1 x2 . . .
xN
h1 h2 h3 . . .
hM
![Page 16: A Video from Google DeepMind - GitHub Pageswangleiphy.github.io/talks/RBM_Seattle.pdfRecommender Systems Learn preferences Recommendations Restricted Boltzmann Machine E (x, h)= XN](https://reader035.vdocument.in/reader035/viewer/2022062920/5f0243a37e708231d40365aa/html5/thumbnails/16.jpg)
Which one is written by human ?
Good$Genera=ve$Model?$MNIST$HandwriEen$Digit$Dataset$
Challenge
Salakhutdinov, 2015 Deep learning summer school
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Idea
Model the QMC data with an RBM, then sample !om the RBM
Li Huang and LW, 1610.02746
cf. Liu, Qi, Meng, Fu,1610.03137Liu, Shen, Qi, Meng, Fu,1611.09364
Xu, Qi, Liu, Fu, Meng,1612.03804
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Why is it useful ?• When the fitting is perfect, we can completely
bypass the “quantum” part of the QMC
• Even with an imperfect fitting, the RBM can still guide the QMC sampling
RBM is a recommender system for the QMC simulations
cf. Torlai, Melko,1606.02718
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Why is it useful ?• When the fitting is perfect, we can completely
bypass the “quantum” part of the QMC
• Even with an imperfect fitting, the RBM can still guide the QMC sampling
Bonus: it is also fun to see what it discovers for the physical model
RBM is a recommender system for the QMC simulations
cf. Torlai, Melko,1606.02718
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Learned Weight
of a 8*8 Falicov-Kimball model
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Accept or not?
The art of Monte Carlo methods
A(x ! x
0) = min
1,
T (x0 ! x)
T (x ! x
0)
⇡(x0)
⇡(x)
�
Sample the RBM, and propose the move to QMCx
h
x
0
p(h|x) p(x0|h)
x
h
h
0
x
0
p(h|x) min
⇥1,
p(h0)p(h)
⇤p(x0|h0)
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Accept or not?
A(x ! x
0) = min
1,
T (x0 ! x)
T (x ! x
0)
⇡(x0)
⇡(x)
�
Sample the RBM, and propose the move to QMC
T (x0 ! x)
T (x ! x
0)=
p(x)
p(x0)Detailed balance condition for the RBM
x
h
x
0
p(h|x) p(x0|h)
x
h
h
0
x
0
p(h|x) min
⇥1,
p(h0)p(h)
⇤p(x0|h0)
![Page 23: A Video from Google DeepMind - GitHub Pageswangleiphy.github.io/talks/RBM_Seattle.pdfRecommender Systems Learn preferences Recommendations Restricted Boltzmann Machine E (x, h)= XN](https://reader035.vdocument.in/reader035/viewer/2022062920/5f0243a37e708231d40365aa/html5/thumbnails/23.jpg)
Accept or not?
A(x ! x
0) = min
1,
p(x)
p(x0)· ⇡(x
0)
⇡(x)
�Li Huang and LW, 1610.02746
Acceptance rate of recommended update
R. M. Neal, Bayesian learning for neural networks, 1996 . J. S. Liu, Monte Carlo strategies in scientific computing, 2008
S. Zhang, Auxiliary-field QMC for correlated electron systems, 2013
“surrogate function”
“force bias”
RBM Physical model
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Can Boltzmann Machines Discover Cluster Updates ?
LW, 1702.08586
Question
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Cluster Update in a Nutshell
Swendsen and Wang,1987
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Cluster Update in a NutshellSample auxiliary bond variables
Swendsen and Wang,1987
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Cluster Update in a NutshellBuild clusters
Swendsen and Wang,1987
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Cluster Update in a NutshellFlip clusters randomly
Swendsen and Wang,1987
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Cluster Update in a Nutshell
Rejection free cluster update!
Swendsen and Wang,1987
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Ising spins Visible units
Auxiliary bond variables Hidden units
Build clusters Sample h given s
Flip clusters Sample s given h
Swendsen-Wang Boltzmann Machine
flip clusters
p(h|s)h` = 0, 1si = ±1
visible hidden
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Boltzmann Machine for cluster update
E(s,h) = �X
`
(Wsi`sj` + b)h`
si` sj`
h` = 1h 2 {0, 1}|Edge|
s 2 {�1,+1}|Vertex|
![Page 32: A Video from Google DeepMind - GitHub Pageswangleiphy.github.io/talks/RBM_Seattle.pdfRecommender Systems Learn preferences Recommendations Restricted Boltzmann Machine E (x, h)= XN](https://reader035.vdocument.in/reader035/viewer/2022062920/5f0243a37e708231d40365aa/html5/thumbnails/32.jpg)
Boltzmann Machine for cluster update
E(s,h) = �X
`
(Wsi`sj` + b)h`
si` sj`
h` = 0h 2 {0, 1}|Edge|
s 2 {�1,+1}|Vertex|
![Page 33: A Video from Google DeepMind - GitHub Pageswangleiphy.github.io/talks/RBM_Seattle.pdfRecommender Systems Learn preferences Recommendations Restricted Boltzmann Machine E (x, h)= XN](https://reader035.vdocument.in/reader035/viewer/2022062920/5f0243a37e708231d40365aa/html5/thumbnails/33.jpg)
Boltzmann Machine for cluster update
E(s,h) = �X
`
(Wsi`sj` + b)h`
si` sj`
h` = 0h 2 {0, 1}|Edge|
s 2 {�1,+1}|Vertex|
![Page 34: A Video from Google DeepMind - GitHub Pageswangleiphy.github.io/talks/RBM_Seattle.pdfRecommender Systems Learn preferences Recommendations Restricted Boltzmann Machine E (x, h)= XN](https://reader035.vdocument.in/reader035/viewer/2022062920/5f0243a37e708231d40365aa/html5/thumbnails/34.jpg)
Cluster Update in the BM language
![Page 35: A Video from Google DeepMind - GitHub Pageswangleiphy.github.io/talks/RBM_Seattle.pdfRecommender Systems Learn preferences Recommendations Restricted Boltzmann Machine E (x, h)= XN](https://reader035.vdocument.in/reader035/viewer/2022062920/5f0243a37e708231d40365aa/html5/thumbnails/35.jpg)
Sample hidden variables given visible units
Cluster Update in the BM language
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Inactive hidden units break the links
Cluster Update in the BM language
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Randomly flip clusters of visible units
Cluster Update in the BM language
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Voila!
Cluster Update in the BM language
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E(s,h) = �X
`
(Wsi`sj` + b)h`
si` sj`
h` = 0h 2 {0, 1}|Edge|
s 2 {�1,+1}|Vertex|
• Rejection free Monte Carlo updates when 1 + eb+W
1 + eb�W= e2�J
Boltzmann Machine for cluster update
![Page 40: A Video from Google DeepMind - GitHub Pageswangleiphy.github.io/talks/RBM_Seattle.pdfRecommender Systems Learn preferences Recommendations Restricted Boltzmann Machine E (x, h)= XN](https://reader035.vdocument.in/reader035/viewer/2022062920/5f0243a37e708231d40365aa/html5/thumbnails/40.jpg)
E(s,h) = �X
`
(Wsi`sj` + b)h`
si` sj`
h` = 0h 2 {0, 1}|Edge|
s 2 {�1,+1}|Vertex|
• Encompass general cluster algorithm frameworksNiedermeyer,1988 Kandel and Domany,1991 Kawashima and Gubernatis,1995
• Rejection free Monte Carlo updates when 1 + eb+W
1 + eb�W= e2�J
Boltzmann Machine for cluster update
![Page 41: A Video from Google DeepMind - GitHub Pageswangleiphy.github.io/talks/RBM_Seattle.pdfRecommender Systems Learn preferences Recommendations Restricted Boltzmann Machine E (x, h)= XN](https://reader035.vdocument.in/reader035/viewer/2022062920/5f0243a37e708231d40365aa/html5/thumbnails/41.jpg)
E(s,h) = �X
`
(Wsi`sj` + b)h`
si` sj`
h` = 0h 2 {0, 1}|Edge|
s 2 {�1,+1}|Vertex|
• Encompass general cluster algorithm frameworks
• In generalNiedermeyer,1988 Kandel and Domany,1991 Kawashima and Gubernatis,1995
“feature” E(s,h) = E(s)�
X
↵
[W↵F↵(s) + b↵]h↵
• Rejection free Monte Carlo updates when 1 + eb+W
1 + eb�W= e2�J
Boltzmann Machine for cluster update
![Page 42: A Video from Google DeepMind - GitHub Pageswangleiphy.github.io/talks/RBM_Seattle.pdfRecommender Systems Learn preferences Recommendations Restricted Boltzmann Machine E (x, h)= XN](https://reader035.vdocument.in/reader035/viewer/2022062920/5f0243a37e708231d40365aa/html5/thumbnails/42.jpg)
• Boltzmann Machines are learnable so they can adapt to various physical problems
• Boltzmann Machines parametrize Monte Carlo policies which can be optimized for efficiency
• The hidden units learn to play smart roles: Fortuin-Kasteleyn and Hubbard-Stratonovich transformations
Generate
Learn
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Plaquette Ising model
K —1610.03137“However, for K≠0, NO simple and efficient global update method is known.”
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Plaquette Ising model
K e�Ks1s2s3s4 !X
h
eW (s1s2+s3s4)h
![Page 45: A Video from Google DeepMind - GitHub Pageswangleiphy.github.io/talks/RBM_Seattle.pdfRecommender Systems Learn preferences Recommendations Restricted Boltzmann Machine E (x, h)= XN](https://reader035.vdocument.in/reader035/viewer/2022062920/5f0243a37e708231d40365aa/html5/thumbnails/45.jpg)
Plaquette Ising model
K
• Given s, sample h on each plaquette independently
• Given h, the Boltzmann Machine is an ordinary Ising model with modulated interactions, which can be sampled efficiently
• Rejection free cluster update!
e�Ks1s2s3s4 !X
h
eW (s1s2+s3s4)h
![Page 46: A Video from Google DeepMind - GitHub Pageswangleiphy.github.io/talks/RBM_Seattle.pdfRecommender Systems Learn preferences Recommendations Restricted Boltzmann Machine E (x, h)= XN](https://reader035.vdocument.in/reader035/viewer/2022062920/5f0243a37e708231d40365aa/html5/thumbnails/46.jpg)
Plaquette Ising model
K
LW, 1702.08586
e�Ks1s2s3s4 !X
h
eW (s1s2+s3s4)h
![Page 47: A Video from Google DeepMind - GitHub Pageswangleiphy.github.io/talks/RBM_Seattle.pdfRecommender Systems Learn preferences Recommendations Restricted Boltzmann Machine E (x, h)= XN](https://reader035.vdocument.in/reader035/viewer/2022062920/5f0243a37e708231d40365aa/html5/thumbnails/47.jpg)
• New tools for (quantum) many-body problems
• Moreover, it offers a new way of thinking
• Can we make new scientific discovery with it ?
• Can one design better algorithms with it ?
Machine learning for many-body physics
LW, 1606.00318 Li Huang and LW, 1610.02746
Li Huang, Yi-feng Yang and LW, 1612.01871LW, 1702.08586
![Page 48: A Video from Google DeepMind - GitHub Pageswangleiphy.github.io/talks/RBM_Seattle.pdfRecommender Systems Learn preferences Recommendations Restricted Boltzmann Machine E (x, h)= XN](https://reader035.vdocument.in/reader035/viewer/2022062920/5f0243a37e708231d40365aa/html5/thumbnails/48.jpg)
• New tools for (quantum) many-body problems
• Moreover, it offers a new way of thinking
• Can we make new scientific discovery with it ?
• Can one design better algorithms with it ?
Machine learning for many-body physics
LW, 1606.00318 Li Huang and LW, 1610.02746
Li Huang, Yi-feng Yang and LW, 1612.01871LW, 1702.08586 The fun just starts!
![Page 49: A Video from Google DeepMind - GitHub Pageswangleiphy.github.io/talks/RBM_Seattle.pdfRecommender Systems Learn preferences Recommendations Restricted Boltzmann Machine E (x, h)= XN](https://reader035.vdocument.in/reader035/viewer/2022062920/5f0243a37e708231d40365aa/html5/thumbnails/49.jpg)
Quantum many-body physics for ML
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MNIST database random imagesfrom the “Deep Learning” book by Goodfellow, Bengio, Courville https://www.deeplearningbook.org/
Quantum entanglement perspective on deep learningJing Chen, Song Cheng, Haidong Xie, LW, and Tao Xiang, 1701.04831
Dong-Ling Deng, Xiaopeng Li and S. Das Sarma, 1701.04844
Xun Gao, L.-M. Duan, 1701.05039 Y. Huang and J. E. Moore, 1701.06246
![Page 50: A Video from Google DeepMind - GitHub Pageswangleiphy.github.io/talks/RBM_Seattle.pdfRecommender Systems Learn preferences Recommendations Restricted Boltzmann Machine E (x, h)= XN](https://reader035.vdocument.in/reader035/viewer/2022062920/5f0243a37e708231d40365aa/html5/thumbnails/50.jpg)
A(x ! x
0) = min
1,
p(x)
p(x0)· ⇡(x
0)
⇡(x)
�
RBM Physical model
e.g. Falikov-Kimball (classical field + fermions) model
while for the RBM
ln[p(x)] =NX
i=1
a
i
x
i
+MX
j=1
ln⇣1 + e
bj+PN
i=1 xiWij
⌘
Hij = Kij + �ijU (xi � 1/2)
x1 x2 . . .
xN
h1 h2 h3 . . .
hM
ln[⇡(x)] =�U
2
NX
i=1
xi + ln deth1 + e
��H(x)i
x 2 {0, 1}N
h 2 {0, 1}M
![Page 51: A Video from Google DeepMind - GitHub Pageswangleiphy.github.io/talks/RBM_Seattle.pdfRecommender Systems Learn preferences Recommendations Restricted Boltzmann Machine E (x, h)= XN](https://reader035.vdocument.in/reader035/viewer/2022062920/5f0243a37e708231d40365aa/html5/thumbnails/51.jpg)
Train the RBM
NX
i=1
a
i
x
i
+MX
j=1
ln⇣1 + e
bj+PN
i=1 xiWij
⌘
=�U
2
NX
i=1
xi + ln det�1 + e
��H�
Supervised learning of the RBM
... ...
F (x)
x1
x2
xN
p(x) ⇠ ⇡(x)