AlphaGo: Mastering the Game of Go with Deep Neural Networks and Tree Search

AlphaGo: Mastering the game of Go
with deep neural networks and tree search
Karel Ha
article by Google DeepMind
Optimization Seminar, 20th April 2016

Applications of AI
spam ﬁlters
1

Applications of AI
spam ﬁlters
recommender systems (Netﬂix, YouTube)
1

Applications of AI
spam ﬁlters
predictive text (Swiftkey)
1

Applications of AI
spam ﬁlters
audio recognition (Shazam, SoundHound)
1

Applications of AI
spam ﬁlters
audio recognition (Shazam, SoundHound)
self-driving cars
1

Artistic-Style Painting (1/2)
[1] Gatys, Ecker, and Bethge 2015 [2] Li and Wand 2016 2

Artistic-Style Painting (2/2)
Champandard 2016 3

C Code Generated Character by Character
Karpathy 2015 4

Algebraic Geometry Generated Character by Character
Karpathy 2015 5

Game of Thrones Generated Character by Character
http://pjreddie.com/darknet/rnns-in-darknet/ 5

JON
He leaned close and onions, barefoot from
his shoulder. “I am not a purple girl,” he
said as he stood over him. “The sight of
you sell your father with you a little choice.”
“I say to swear up his sea or a boy of stone
and heart, down,” Lord Tywin said. “I love
your word or her to me.”
Darknet (on Linux)

JON
He leaned close and onions, barefoot from
his shoulder. “I am not a purple girl,” he
said as he stood over him. “The sight of
you sell your father with you a little choice.”
“I say to swear up his sea or a boy of stone
and heart, down,” Lord Tywin said. “I love
your word or her to me.”
Darknet (on Linux)
JON
Each in days and the woods followed his
king. “I understand.”
“I am not your sister Lord Robert?”
“The door was always some cellar to do his
being girls and the Magnar of Baratheon,
and there were thousands of every bite of
half the same as though he was not a great
knight should be seen, and not to look at
the Redwyne two thousand men.”
Darknet (on OS X)

DeepDrumpf: a Twitter bot / neural network which learned
the language of Donald Trump from his speeches
Hayes 2016 6

We’ve got nuclear weapons that are obsolete. I’m going to create jobs just by making the worst thing ever.
Hayes 2016 6

The biggest risk to the world, is me, believe it or not.
Hayes 2016 6

I am what ISIS doesn’t need.
Hayes 2016 6

I’d like to beat that @HillaryClinton. She is a horror. I told my supporter Putin to say that all the time. He
has been amazing.
Hayes 2016 6

I’d like to beat that @HillaryClinton. She is a horror. I told my supporter Putin to say that all the time. He
has been amazing.
I buy Hillary, it’s beautiful and I’m happy about it.
Hayes 2016 6

Atari Player by Google DeepMind
https://youtu.be/0X-NdPtFKq0?t=21m13s
Mnih et al. 2015 7

Heads-up Limit Holdem Poker Is Solved!
Bowling et al. 2015 8

Heads-up Limit Holdem Poker Is Solved!
Cepheus http://poker.srv.ualberta.ca/
0.000986 big blinds per game on expectation
Bowling et al. 2015 8

https://dataaspirant.com/2014/09/19/supervised-and-unsupervised-learning/ 8

Supervised Learning (SL)
http://www.nickgillian.com/ 9

1. data collection: Google Search, Facebook “Likes”, Siri, Netﬂix, YouTube views, LHC collisions, KGS Go
Server...

Server...
2. training on training set

Server...
3. testing on testing set

Server...
3. testing on testing set
4. deployment

Mathematical Regression
https://thermanuals.wordpress.com/descriptive-analysis/sampling-and-regression/
10

Classiﬁcation
https://kevinbinz.files.wordpress.com/2014/08/ml-svm-after-comparison.png 11

Underﬁtting and Overﬁtting
https://www.researchgate.net/post/How_to_Avoid_Overfitting 12

Beware of overﬁtting!

It is like learning for a mathematical exam by memorizing proofs.

Reinforcement Learning (RL)
https://youtu.be/0X-NdPtFKq0?t=16m57s 13

Reinforcement Learning (RL)
Specially: games of self-play
https://youtu.be/0X-NdPtFKq0?t=16m57s 13

Tree Search
Optimal value v∗(s) determines the outcome of the game:
Silver et al. 2016 14

Tree Search
from every board position or state s

Tree Search
under perfect play by all players.

Tree Search
It is computed by recursively traversing a search tree containing
approximately bd possible sequences of moves, where

Tree Search
b is the games breadth (number of legal moves per position)

Tree Search
b is the games breadth (number of legal moves per position)
d is its depth (game length)

Game tree of Go
Sizes of trees for various games:
chess: b ≈ 35, d ≈ 80
Go: b ≈ 250, d ≈ 150
Allis et al. 1994 15

Game tree of Go
chess: b ≈ 35, d ≈ 80
Go: b ≈ 250, d ≈ 150 ⇒ more positions than atoms in the
universe!

Game tree of Go
chess: b ≈ 35, d ≈ 80
universe!
That makes Go a googol
[10100
] times more complex
than chess.
https://deepmind.com/alpha-go.html

Game tree of Go
chess: b ≈ 35, d ≈ 80
universe!
[10100
than chess.
How to handle the size of the game tree?

Game tree of Go
chess: b ≈ 35, d ≈ 80
universe!
[10100
than chess.
for the breadth: a neural network to select moves

Game tree of Go
chess: b ≈ 35, d ≈ 80
universe!
[10100
than chess.
for the depth: a neural network to evaluate the current
position

Game tree of Go
chess: b ≈ 35, d ≈ 80
universe!
[10100
than chess.
for the depth: a neural network to evaluate the current
position
for the tree traverse: Monte Carlo tree search (MCTS)

Neural Networks (NN): Inspiration
http://pages.cs.wisc.edu/~bolo/shipyard/neural/local.html 17

inspired by the neuronal structure of the mammalian cerebral
cortex

cortex
but on much smaller scales

cortex
suitable to model systems with a high tolerance to error

cortex
suitable to model systems with a high tolerance to error
e.g. audio or image recognition

Neural Networks: Modes
Dieterle 2003 18

Two modes
Dieterle 2003 18

Two modes
feedforward for making predictions
Dieterle 2003 18

Two modes
feedforward for making predictions
backpropagation for learning
Dieterle 2003 18

Neural Networks: an Example of Feedforward
http://stevenmiller888.github.io/mind-how-to-build-a-neural-network/ 19

Gradient Descent in Neural Networks

Motto: ”Learn by mistakes!”

Motto: ”Learn by mistakes!”
However, error functions are not necessarily convex or so “smooth”.

Convolutional Neural Networks (CNN or ConvNet)
http://code.flickr.net/2014/10/20/introducing-flickr-park-or-bird/ 21

(Deep) Convolutional Neural Networks
The hierarchy of concepts is captured in the number of layers: the deep in “Deep Learning”.

Backgammon: Man vs. Fate
Chess: Man vs. Man
22

Go: Man vs. Self
Robert ˇS´amal (White) versus Karel Kr´al (Black), Spring School of Combinatorics 2016 22

Rules of Go
Black versus White. Black starts the game.
23

Rules of Go
the rule of liberty
23

Rules of Go
the rule of liberty
the “ko” rule
23

Rules of Go
the rule of liberty
the “ko” rule
Handicap for diﬀerence in ranks: Black can place 1 or more stones
in advance (compensation for White’s greater strength). 23

Scoring Rules: Area Scoring
https://en.wikipedia.org/wiki/Go_(game) 24

A player’s score is:
the number of stones that the player has on the board

plus the number of empty intersections surrounded by that
player’s stones

plus the number of empty intersections surrounded by that
player’s stones
plus komi(dashi) points for the White player
which is a compensation for the ﬁrst move advantage of the Black player

Ranks of Players
Kyu and Dan ranks

Ranks of Players
Kyu and Dan ranks
or alternatively, Elo ratings

Policy and Value Networks

Training the (Deep Convolutional) Neural Networks

SL Policy Network (1/2)
13-layer deep convolutional neural network

goal: to predict expert human moves

task of classiﬁcation

trained from 30 millions positions from the KGS Go Server

stochastic gradient ascent:
∆σ ∝
∂ log pσ(a|s)
∂σ
(to maximize the likelihood of the human move a selected in state s)

∆σ ∝
∂ log pσ(a|s)
∂σ
Results:

∆σ ∝
∂ log pσ(a|s)
∂σ
Results:
44.4% accuracy (the state-of-the-art from other groups)

∆σ ∝
∂ log pσ(a|s)
∂σ
Results:
55.7% accuracy (raw board position + move history as input)

∆σ ∝
∂ log pσ(a|s)
∂σ
Results:
55.7% accuracy (raw board position + move history as input)
57.0% accuracy (all input features)

Small improvements in accuracy led to large improvements
in playing strength

Rollout Policy
Rollout policy pπ(a|s) is faster but less accurate than SL
policy network.

Rollout Policy
policy network.
accuracy of 24.2%

Rollout Policy
policy network.
accuracy of 24.2%
It takes 2µs to select an action, compared to 3 ms in case
of SL policy network.

RL Policy Network (1/2)
identical in structure to the SL policy network

goal: to win in the games of self-play

weights ρ initialized to the same values, ρ := σ

games of self-play

games of self-play
between the current RL policy network and a randomly
selected previous iteration

games of self-play
to prevent overﬁtting to the current policy

games of self-play
to prevent overﬁtting to the current policy
∆ρ ∝
∂ log pρ(at|st)
∂ρ
zt
at time step t, where reward function zt is +1 for winning and −1 for losing.

Results (by sampling each move at ∼ pρ(·|st)):

80% of win rate against the SL policy network

85% of win rate against the strongest open-source Go
program, Pachi (Baudiˇs and Gailly 2011)

85% of win rate against the strongest open-source Go
program, Pachi (Baudiˇs and Gailly 2011)
The previous state-of-the-art, based only on SL of CNN:
11% of “win” rate against Pachi

Value Network (1/2)
similar architecture to the policy network, but outputs a single
prediction instead of a probability distribution

Value Network (1/2)
goal: to estimate a value function
vp
(s) = E[zt|st = s, at...T ∼ p]
that predicts the outcome from position s (of games played
by using policy p)

Value Network (1/2)
vp
(s) = E[zt|st = s, at...T ∼ p]
by using policy p)
Double approximation: vθ(s) ≈ vpρ (s) ≈ v∗(s).

Value Network (1/2)
vp
(s) = E[zt|st = s, at...T ∼ p]
by using policy p)
task of regression

Value Network (1/2)
vp
(s) = E[zt|st = s, at...T ∼ p]
by using policy p)
task of regression
stochastic gradient descent:
∆θ ∝
∂vθ(s)
∂θ
(z − vθ(s))
(to minimize the mean squared error (MSE) between the predicted vθ(s) and the true z)

Value Network (2/2)

Value Network (2/2)
Consecutive positions are strongly correlated.

Value Network (2/2)
Value network memorized the game outcomes, rather than
generalizing to new positions.

Value Network (2/2)
Solution: generate 30 million (new) positions, each sampled
from a seperate game

Value Network (2/2)
Solution: generate 30 million (new) positions, each sampled
from a seperate game
almost the accuracy of Monte Carlo rollouts (using pρ), but
15000 times less computation!

Evaluation Accuracy in Various Stages of a Game
Move number is the number of moves that had been played in the given position.

Each position evaluated by:
forward pass of the value network vθ

Each position evaluated by:
forward pass of the value network vθ
100 rollouts, played out using the corresponding policy

Elo Ratings for Various Combinations of Networks

The Main Algorithm

MCTS Algorithm
The next action is selected by lookahead search, using simulation:

MCTS Algorithm
1. selection phase

MCTS Algorithm
1. selection phase
2. expansion phase

MCTS Algorithm
1. selection phase
2. expansion phase
3. evaluation phase

MCTS Algorithm
1. selection phase
2. expansion phase
3. evaluation phase
4. backup phase (at end of all simulations)

MCTS Algorithm
1. selection phase
2. expansion phase
3. evaluation phase
Each edge (s, a) keeps:
action value Q(s, a)

MCTS Algorithm
1. selection phase
2. expansion phase
3. evaluation phase
visit count N(s, a)

MCTS Algorithm
1. selection phase
2. expansion phase
3. evaluation phase
visit count N(s, a)
prior probability P(s, a) (from SL policy network pσ)

MCTS Algorithm
1. selection phase
2. expansion phase
3. evaluation phase
visit count N(s, a)
prior probability P(s, a) (from SL policy network pσ)
The tree is traversed by simulation (descending the tree) from the
root state.

MCTS Algorithm: Selection

At each time step t, an action at is selected from state st
at = arg max
a
(Q(st , a) + u(st , a))

At each time step t, an action at is selected from state st
at = arg max
a
(Q(st , a) + u(st , a))
where bonus
u(st , a) ∝
P(s, a)
1 + N(s, a)

MCTS Algorithm: Expansion

A leaf position may be expanded (just once) by the SL policy network pσ.

A leaf position may be expanded (just once) by the SL policy network pσ.
The output probabilities are stored as priors P(s, a) := pσ(a|s).

MCTS: Evaluation

MCTS: Evaluation
evaluation from the value network vθ(s)

MCTS: Evaluation
evaluation by the outcome z using the fast rollout policy pπ until the end of game

MCTS: Evaluation
evaluation by the outcome z using the fast rollout policy pπ until the end of game
Using a mixing parameter λ, the ﬁnal leaf evaluation V (s) is
V (s) = (1 − λ)vθ(s) + λz

MCTS: Backup
At the end of simulation, each traversed edge is updated by accumulating:
the action values Q

MCTS: Backup
At the end of simulation, each traversed edge is updated by accumulating:
the action values Q
visit counts N

Once the search is complete, the algorithm
chooses the most visited move from the root
position.

Percentage of Simulations
percentage frequency with which actions were selected from the root during simulations

Principal Variation (Path with Maximum Visit Count)
The moves are presented in a numbered sequence.

AlphaGo selected the move indicated by the red circle;

Fan Hui responded with the move indicated by the white square;

Fan Hui responded with the move indicated by the white square;
in his post-game commentary, he preferred the move (labelled 1) predicted by AlphaGo.

Scalability
asynchronous multi-threaded search

Scalability
simulations on CPUs

Scalability
simulations on CPUs
computation of neural networks on GPUs

Scalability
simulations on CPUs
AlphaGo:
40 search threads

Scalability
simulations on CPUs
AlphaGo:
40 search threads
40 CPUs

Scalability
simulations on CPUs
AlphaGo:
40 search threads
40 CPUs
8 GPUs

Scalability
simulations on CPUs
AlphaGo:
40 search threads
40 CPUs
8 GPUs
Distributed version of AlphaGo (on multiple machines):

Scalability
simulations on CPUs
AlphaGo:
40 search threads
40 CPUs
8 GPUs
40 search threads

Scalability
simulations on CPUs
AlphaGo:
40 search threads
40 CPUs
8 GPUs
40 search threads
1202 CPUs

Scalability
simulations on CPUs
AlphaGo:
40 search threads
40 CPUs
8 GPUs
40 search threads
1202 CPUs
176 GPUs

Elo Ratings for Various Combinations of Threads

Results: the strength of AlphaGo

Tournament with Other Go Programs

Fan Hui
https://en.wikipedia.org/wiki/Fan_Hui 50

Fan Hui
professional 2 dan

Fan Hui
professional 2 dan
European Go Champion in 2013, 2014 and 2015

Fan Hui
professional 2 dan
European Professional Go Champion in 2016

Fan Hui
professional 2 dan
biological neural network:

Fan Hui
professional 2 dan
100 billion neurons

Fan Hui
professional 2 dan
100 billion neurons
100 up to 1,000 trillion neuronal connections

AlphaGo versus Fan Hui
AlphaGo won 5:0 in a formal match on October 2015.
51

AlphaGo versus Fan Hui
AlphaGo won 5:0 in a formal match on October 2015.
[AlphaGo] is very strong and stable, it seems
like a wall. ... I know AlphaGo is a computer,
but if no one told me, maybe I would think
the player was a little strange, but a very
strong player, a real person.
Fan Hui 51

Lee Sedol “The Strong Stone”
https://en.wikipedia.org/wiki/Lee_Sedol 52

professional 9 dan

professional 9 dan
the 2nd in international titles

professional 9 dan
the 5th youngest (12 years 4 months) to become
a professional Go player in South Korean history

professional 9 dan
Lee Sedol would win 97 out of 100 games against Fan Hui.

professional 9 dan
Lee Sedol would win 97 out of 100 games against Fan Hui.
biological neural network comparable to Fan Hui’s (in number
of neurons and connections)

I heard Google DeepMind’s AI is surprisingly
strong and getting stronger, but I am
conﬁdent that I can win, at least this time.
Lee Sedol
52

I heard Google DeepMind’s AI is surprisingly
strong and getting stronger, but I am
conﬁdent that I can win, at least this time.
Lee Sedol
...even beating AlphaGo by 4:1 may allow
the Google DeepMind team to claim its de
facto victory and the defeat of him
[Lee Sedol], or even humankind.
interview in JTBC
Newsroom
52

AlphaGo versus Lee Sedol
https://en.wikipedia.org/wiki/AlphaGo_versus_Lee_Sedol 53

In March 2016 AlphaGo won 4:1 against the legendary Lee Sedol.

AlphaGo won all but the 4th game; all games were won
by resignation.

by resignation.
The winner of the match was slated to win $1 million.

by resignation.
Since AlphaGo won, Google DeepMind stated that the prize will be
donated to charities, including UNICEF, and Go organisations.

by resignation.
Since AlphaGo won, Google DeepMind stated that the prize will be
donated to charities, including UNICEF, and Go organisations.
Lee received $170,000 ($150,000 for participating in all the ﬁve
games, and an additional $20,000 for each game won).

http://www.goratings.org/ (18th April 2016) 53

AlphaGo versus Ke Jie?
https://en.wikipedia.org/wiki/Ke_Jie 54

professional 9 dan

professional 9 dan
the 1st in (unoﬃcial) world ranking list

professional 9 dan
the youngest player to win 3 major international tournaments

professional 9 dan
head-to-head record against Lee Sedol 8:2

professional 9 dan
head-to-head record against Lee Sedol 8:2
biological neural network comparable to Fan Hui’s, and thus
by transitivity, also comparable to Lee Sedol’s

I believe I can beat it. Machines can be very
strong in many aspects but still have
loopholes in certain calculations.
Ke Jie
54

Ke Jie
Now facing AlphaGo, I do not feel the same
strong instinct of victory when I play a
human player, but I still believe I have the
advantage against it. It’s 60 percent in
favor of me.
Ke Jie
54

Ke Jie
Now facing AlphaGo, I do not feel the same
strong instinct of victory when I play a
human player, but I still believe I have the
advantage against it. It’s 60 percent in
favor of me.
Ke Jie
Even though AlphaGo may have defeated
Lee Sedol, it won’t beat me.
Ke Jie
54

Diﬃculties of Go
challenging decision-making

Diﬃculties of Go
intractable search space

Diﬃculties of Go
intractable search space
complex optimal solution
It appears infeasible to directly approximate using a policy or value function!

AlphaGo: summary
Monte Carlo tree search

AlphaGo: summary
eﬀective move selection and position evaluation

AlphaGo: summary
through deep convolutional neural networks

AlphaGo: summary
trained by novel combination of supervised and reinforcement
learning

AlphaGo: summary
learning
new search algorithm combining

AlphaGo: summary
learning
neural network evaluation

AlphaGo: summary
learning
Monte Carlo rollouts

AlphaGo: summary
learning
scalable implementation

AlphaGo: summary
learning
multi-threaded simulations on CPUs

AlphaGo: summary
learning
parallel GPU computations

AlphaGo: summary
learning
parallel GPU computations
distributed version over multiple machines

Novel approach

Novel approach
During the match against Fan Hui, AlphaGo evaluated thousands
of times fewer positions than Deep Blue against Kasparov.

Novel approach
It compensated this by:
selecting those positions more intelligently (policy network)

Novel approach
evaluating them more precisely (value network)

Novel approach
Deep Blue relied on a handcrafted evaluation function.

Novel approach
AlphaGo was trained directly and automatically from gameplay.
It used general-purpose learning.

Novel approach
AlphaGo was trained directly and automatically from gameplay.
It used general-purpose learning.
This approach is not speciﬁc to the game of Go. The algorithm
can be used for much wider class of (so far seemingly)
intractable problems in AI!

Input features for rollout and tree policy
Silver et al. 2016

Selection of Moves by the SL Policy Network
move probabilities taken directly from the SL policy network pσ (reported as a percentage if above 0.1%).
Silver et al. 2016

Selection of Moves by the Value Network
evaluation of all successors s of the root position s, using vθ(s)
Silver et al. 2016

Tree Evaluation from Value Network
action values Q(s, a) for each tree-edge (s, a) from root position s (averaged over value network evaluations only)
Silver et al. 2016

Tree Evaluation from Rollouts
action values Q(s, a), averaged over rollout evaluations only
Silver et al. 2016

Results of a tournament between diﬀerent Go programs
Silver et al. 2016

Results of a tournament between AlphaGo and distributed Al-
phaGo, testing scalability with hardware
Silver et al. 2016

AlphaGo versus Fan Hui: Game 1
Silver et al. 2016

Silver et al. 2016

AlphaGo versus Lee Sedol: Game 1
https://youtu.be/vFr3K2DORc8
https://en.wikipedia.org/wiki/AlphaGo_versus_Lee_Sedol

AlphaGo versus Lee Sedol: Game 2 (1/2)
https://youtu.be/l-GsfyVCBu0

https://youtu.be/qUAmTYHEyM8

https://youtu.be/yCALyQRN3hw

https://youtu.be/mzpW10DPHeQ

Further Reading I
AlphaGo:
Google Research Blog
http://googleresearch.blogspot.cz/2016/01/alphago-mastering-ancient-game-of-go.html
an article in Nature
http://www.nature.com/news/google-ai-algorithm-masters-ancient-game-of-go-1.19234
a reddit article claiming that AlphaGo is even stronger than it appears to be:
“AlphaGo would rather win by less points, but with higher probability.”
https://www.reddit.com/r/baduk/comments/49y17z/the_true_strength_of_alphago/
a video of how AlphaGo works (put in layman’s terms) https://youtu.be/qWcfiPi9gUU
Articles by Google DeepMind:
Atari player: a DeepRL system which combines Deep Neural Networks with Reinforcement Learning (Mnih
et al. 2015)
Neural Turing Machines (Graves, Wayne, and Danihelka 2014)
Artiﬁcial Intelligence:
Artiﬁcial Intelligence course at MIT
http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/
6-034-artificial-intelligence-fall-2010/index.htm

Further Reading II
Introduction to Artiﬁcial Intelligence at Udacity
https://www.udacity.com/course/intro-to-artificial-intelligence--cs271
General Game Playing course https://www.coursera.org/course/ggp
Singularity http://waitbutwhy.com/2015/01/artificial-intelligence-revolution-1.html + Part 2
The Singularity Is Near (Kurzweil 2005)
Combinatorial Game Theory (founded by John H. Conway to study endgames in Go):
Combinatorial Game Theory course https://www.coursera.org/learn/combinatorial-game-theory
On Numbers and Games (Conway 1976)
Computer Go as a sum of local games: an application of combinatorial game theory (M¨uller 1995)
Chess:
Deep Blue beats G. Kasparov in 1997 https://youtu.be/NJarxpYyoFI
Machine Learning:
Machine Learning course
https://youtu.be/hPKJBXkyTK://www.coursera.org/learn/machine-learning/
Reinforcement Learning http://reinforcementlearning.ai-depot.com/
Deep Learning (LeCun, Bengio, and Hinton 2015)

Further Reading III
Deep Learning course https://www.udacity.com/course/deep-learning--ud730
Two Minute Papers https://www.youtube.com/user/keeroyz
Applications of Deep Learning https://youtu.be/hPKJBXkyTKM
Neuroscience:
http://www.brainfacts.org/

References I
Allis, Louis Victor et al. (1994). Searching for solutions in games and artificial intelligence. Ponsen & Looijen.
Baudiˇs, Petr and Jean-loup Gailly (2011). “Pachi: State of the art open source Go program”. In: Advances in
Computer Games. Springer, pp. 24–38.
Bowling, Michael et al. (2015). “Heads-up limit holdem poker is solved”. In: Science 347.6218, pp. 145–149. url:
http://poker.cs.ualberta.ca/15science.html.
Champandard, Alex J (2016). “Semantic Style Transfer and Turning Two-Bit Doodles into Fine Artworks”. In:
arXiv preprint arXiv:1603.01768.
Conway, John Horton (1976). “On Numbers and Games”. In: London Mathematical Society Monographs 6.
Dieterle, Frank Jochen (2003). “Multianalyte quantifications by means of integration of artificial neural networks,
genetic algorithms and chemometrics for time-resolved analytical data”. PhD thesis. Universität Tübingen.
Gatys, Leon A., Alexander S. Ecker, and Matthias Bethge (2015). “A Neural Algorithm of Artistic Style”. In:
CoRR abs/1508.06576. url: http://arxiv.org/abs/1508.06576.
Graves, Alex, Greg Wayne, and Ivo Danihelka (2014). “Neural turing machines”. In: arXiv preprint
arXiv:1410.5401.
Hayes, Bradley (2016). url: https://twitter.com/deepdrumpf.
Karpathy, Andrej (2015). The Unreasonable Effectiveness of Recurrent Neural Networks. url:
http://karpathy.github.io/2015/05/21/rnn-effectiveness/ (visited on 04/01/2016).

References II
Kurzweil, Ray (2005). The singularity is near: When humans transcend biology. Penguin.
LeCun, Yann, Yoshua Bengio, and Geoﬀrey Hinton (2015). “Deep learning”. In: Nature 521.7553, pp. 436–444.
Li, Chuan and Michael Wand (2016). “Combining Markov Random Fields and Convolutional Neural Networks for
Image Synthesis”. In: CoRR abs/1601.04589. url: http://arxiv.org/abs/1601.04589.
Mnih, Volodymyr et al. (2015). “Human-level control through deep reinforcement learning”. In: Nature 518.7540,
pp. 529–533. url:
https://storage.googleapis.com/deepmind-data/assets/papers/DeepMindNature14236Paper.pdf.
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PhD thesis. TU Graz.
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