Observing Trends in Novel Metrics of Neural Networks

foulchilianAI and Robotics

Oct 20, 2013 (3 years and 9 months ago)

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1

Observing Trends in Novel Metrics of Neural Networks
Created Through Artificial Evolution and Natural Selection



Jordan Perr


10/2/09


Version 3
.x

(Siemen’s Submission)








Table of Contents

1. Abstract

2

2. Introduction

3

2.1. A Brief History of Cognitive Science

3

2.2. Research

4

2.3. Relevance

6

3. Polyworld

7

4. Metrics and Results

9

4.1 Causal Density

9

4.2 Integrated Information

9

4.3 Synergy

11

5. Conclusion and Future Plans

13

6. Bibliography

14












2

1. Abstract

Researchers

of artificial intelligence
recognize that understanding consciousness is a
major component of understanding intelligence
. Since the early sixties, computer
scientists such as Lawrence J. Fogel were beginning to apply concepts
such as

evolution
and natural selection to the pursuit of more intelligent

and possibly conscious artificial
machines [8].
Today, researchers such as
Vir
gil Griffith, Anil K. Seth, and
Larry Yaeger

are continuing that research
by reviving
and revamping
techniques such as
simulated

evolution using modern personal computers.
This paper

extends
the works

of
those
researchers and others

by
applying

new

metr
ics such as Integrated Information, Causal
Density, and
my own metric,
Synergy
,

to networks generated by

Polyworld
. This work

attempt
s

to correlate any one of those metrics to observed intelligence

and evolutionary
fitness
.

It is an in
-
depth look at curren
t research being done on such measurements of
artificial neural networks, a critical look at the history of Cognitive Science, and the
introduction of a new type of metric to the scientific community.











3

2
.
Introduction

2
.1.
A Brief History of
Cognitive Science

What is life and consciousness? Such a question, until recently, belonged to the
domain of existential philosophers and white
-
haire
d mad scientists. Traditional “bottom
up”

scientific inquiry of the 19th century saw little room for
theore
tical

inquiries into

consciousness

and mind
,
favoring

much more quantitative
studies

such as
a
natomy

and
p
hysics

[11].
In fact, the earliest pioneering thoughts

of evolutionary artificial
intelligence
can be traced

back to the likes of Charles Darwin and Fyodor Dostoevsky
. In
their time,

the power of natural deterministic forces over biological creatures

was
minimized

by the scientific community

(not to mention the C
hurch and general public
.
)

Early p
sychologists suc
h as Sigmund Freud began to apply the scientific method to
studying observed behavior in human subjects, combining rigorous properties of
scientific inquiry with formerly philosophic ideas concerning behavior.

In the middle of the 20th century,

the tools a
vailable to the scientific community
became more robust and
accurate.

S
cientists such as James Watson and Francis
Crick

were able to uncover
an

underlying mechanism (DNA) of seemingly magical properties
of biological
entities
.
Such
a discovery

only helped
to further the notion that intelligence
and consciousness might well be explainable by scientific inquiry
: thus

the

field of
c
ybernetics was born

[6].

For the first time, scientists felt that they had a clear path
to
studying and understanding

the underlyi
ng physical mechanisms that are manifested as
consciousness and life.

Towards the later part of the 20th century, better microscopes and the invention of the
modern computer change
d

c
ybernetics so drastically that the field
came

to the verge of
4

collapse. M
odern scientists were looking

to combine the disciplines of neuroscience,
anatomy, p
sych
ology, computer science, and even p
hilosophy into

one new discipline.
Cognitive s
cience was born.

Currently, leading researchers are exploring how neural networks evolve
in
simulation
. Many different calculable metrics about these neural networks are being
explored.
This paper attempts

to explain the state of this area of research, introduce the
reader

to some of these metrics, and
showcase new data concerning
them.



2
.2.
Research

My research started with

Lawrence J. Fogel's
book on his early experiments in
simulated evolution

[8].

These experiments were conducted to prove that iterative
evolution alon
e could produce mechanisms
that

perform a given task better than
randomly constructed machines. His
work

showed the world that evolutionary algorithms
could, in fact, produce very accurate re
sults to very complex problems.

I
set out to
c
reate

a

finite stat
e machine

(FSM)

evolver using the modern Java Virtual
Machi
ne. With it, I

was able to replicate his astounding results.
The speed at which my
Java FSM Evolver was able to
evolve fit machines

le
d me to believe that applying the
concept of iterative evolutio
n

would be a fruitful approach

to

more

complex problems

such as generating artificial intelligence
.


5


Results from my Java finite state machine evolver
.

Similar

results to Fogel Et Al. 1966.


After creating
the

finite state machine evolution environment

described above
, I
wanted to create a program
in
which a virtual
“creature”

would evolve
both physically
and behaviorally in an attempt to create an
agent that resembled early carbon

based life.
My research

le
d me to a Google Tech Talk given by Virgil Gri
ffith at the AlifeX
conference
from

2007

[9].

In this talk, Griffith demonstrated how a program called
Polyworld
was

being used to observe behavioral trends in virtual agents evolving within
a virtual environment. The similarities between my idea and Polyw
orld were striking. I
was able to
contribute

modifications to the source code of Polyworld
that

are

be
ing

integrated into the main distribution and

will

be used by
a number

of scientists around the
world.

I felt comfortable working within Polyworld and dec
ided to use the program in my
future research.


6

2
.3.
Relevance


From a scientific perspective,
this research

will prove to be of
major

significance when
discussing the implications and usefulness of these metrics

in determining behavioral
properties of a n
eural network
. Integrated Information and Causal Density are
not
merely
mathematical measurements of a network'
s topology
, but are theoretically indicative of
consciousness and intelligence
. Previous efforts have been made to correlate metrics such
as netw
ork complexity to evolutionary time spent in Polyworld
.
The results of one such
experiment

(concerning complexity)

are shown below:


Complexity over Evolutionary Time:

Yaeger Et Al.
[4]

Notice the steep increase and plateau

at step 5000.



The scientific
community wants to observe such trends so that we may understand
exactly what parts of a neural network must be strengthened to encourage intelligence.

If
one can determine a certain set of metrics that are plausibly linked to intelligence, they
7

can use he
uristics built upon those metrics to guide the evolution of new agents in
simulation.
My work extend
s

the efforts of those
before me and add
s

to the world’s
knowledge of

how other such metrics change

as

neural networks

evolve
.

I also hope to
introduce a ne
w metric, Synergy, which can be used for many of the same analytical
reasons as Integrated Information, Complexity, and Causal Density.


Evolutionary computation has real world, every day uses.

Experiments have been done
to show how evolutionary algorithms

can be used to train robot
s

to navigate a physical
maze
, among other things

[12].

Many flight control systems used by major airlines and
the Air Force were
aided in their creation

by evolutionary computation. Another example
is
Automated Mathematician
,

a
project

in the late
1970s
that

aimed
to create a machine
capable of “discovering” mathematical formulas using evolutionary algorithms. The
Automated Mathematician was able to rediscover Goldbach’s
C
onjecture and the Unique
Prime Factorization Theorem
without human intervention

[8]
.

3
.
Polyworld

Polyworld is the de
s
ce
n
d
a
nt of Lawrence J. Fogel's
FSM

evolution environment.
Utilizing the power of modern day personal computers, Polyworld accurately simulate
s

the evolution and learning processes of
multipl
e complex

haploid agents in a virtual
(
yet
realistic
)

environment. Polyworld's agents (Polyworldians) are under continuous control
of an Artificial Neural Network (ANN
) that

is encoded in
each agent’s

genome. The
ANN of a Polyworldian takes visual input fr
om the rendered virtual environment (pixels),
and cause
s

the creature to physically interact with that environment.

In this way,
Polyworld
ians are completely immersed in
this virtual playing field and end up evolving
to meet the needs of that environment.
This system

allows scientists to observe how
8

ANNs evolve through interaction

with each
other

and the
ir

environment.

Experiments
have already shown
that
behaviors such as cannibalism, tribalism, and mating ritual
s

are
exhibited by Polyworldians without the

intervention of a human

[9].



A simulation running in Polyworld.

Each rectangular block on the field is a representation of one Polyworldian.


Full anatomical

and functional

matrices of each Polyworldian’s ANN

and
genealogy logs are
automatically
recorded along with a whole host of other
data during a
Polyworld simulation
. This recorded data is critical for the analysis of trends in
Polyworldian neural networks. To analyze the trends in different mathematical metrics, I
wrote scripts to parse the d
ata recorded by Polyworld and feed
said data to
different

algorithms

for metric calculation
.


9

4
. Metrics

and Results

4
.1

Causal Density


Causal Density is a measurement of how centralized a given neural network is.
More precisely,
casual density reflects t
he number of interactions among nodes in a
neural network that are causally significant

[13].
This metric is calculated by taking the
number of links that are deemed to be causally significant and dividing that number by a
value directly proportional to th
e size of the neural network.


4
.2

Integrated Information


Integrated Information

(

)

is the measure of how much information
is contained
by a neural network

and
,

at the same time, how synchronized the network is.

The actual
algorithm by which scientists c
alculate


is beyond the scope of this paper (see
[16]
.)

Information, for the sake of this measurement, is defined as the reduction in possible
states a given network experiences by the choosing of one particular future state. This
sounds like a mouthful,
but is pretty intuitive in reality. Picture an unabridged dictionary
with millions of definitions to choose from. By picking a particular definition to study,
one has eliminated the millions of other definitions from their interest. With a smaller and
more

concise dictionary, the
number

of possible definitions

excluded from consideration

is much smaller when one definition in particular is chosen.


The second component to


is how synergized the network is. To understand
synergy,
consider

the following thought experiment: A human and an array of
photosensitive diodes

(a camera)

are placed in front of a projector screen. The human is
10

told to push a button whenever the screen is white, and to release the button when the
screen turns black. T
he
camera
is connected to a similar sort of device. When the screen
turns from bright to dark (and vice versa), both subjects will indicate the change

properly.
Most would agree that the human subject
consciously

chose to press their button while
the camer
a did it without being conscious. Why is the human conscious and the camera
not? What makes the human unique?


One answer to those questions is that the human mind
contains

more integrated
information than the camera’s sensor. When the human

subject

sees t
he screen chang
e
from light to dark, their

mind explores

a virtually limitless number of
new possible states
.
They might question whether the screen
will

flash green, whe
ther the ex
periment
will

be
over soon,

or

whether

he or she
had
parked in an illegal p
arking space. The human mind
has a vast amount of information and is incredibly skilled at connecting and organizing
it
.
In other words
, the human mind contains a relatively large amount of synergized
information, or

.


The camera, on the other hand, is s
imply allowing photo
n
s emitted by the
projector to cause electrons locked within
its

photo
resistors to be freed. Each phot
odiode
can experience an unlimited number of states (off, on, or somewhere in between) so we
can assume that each photodiode contains
some amount of information. The camera’s


remains low, however, due to the fact that each photodiode is on its own circuit and one
photodiode can
not really affect the state of another.

This isolation of nodes drives the
camera’s integrated information ver
y low and shows how

synchronicity

conceptually

affects

.


What, then, is the trend in


for a neural network being evolved in Polyworld? To
calculate this trend, I used the open source Consciousness project developed by Virgil
11

Griffith. This piece of soft
ware uses the fastest known
, though still incredibly inefficient
,

algorithm for calculating

.
Consciousness performs the calculation in a Big
-
Oh time

that
is

worse than exponential.
Calculating



for a network of 11

nodes takes about
5

seconds
on a modern laptop
, calculating


for 12 nodes takes 30 seconds, and

calculating


for

13
nodes
takes longer than 10 minutes
.

To observe trends in Polyworld’s neural networks
(which generally have over 150 nodes) I had to manually prune out un
-
nee
ded nodes to
reduce the size of said networks.
Due to the error introduced in this pruning process and
the sheer
amount of time the process consumed
, I was unable to observe any noticeable
trend in


over evolutionary time.

R
esearchers

are currently
workin
g to reduce the run
time of Integrated Information calculation, though a better algorithm may still be years
away.


4
.3

Synergy


During

this

study of Integrated Info
rmation, I was curious as to whe
ther or not the
“Synchronicity” factor alone could be an in
teresting metric for analysis.
I therefore
developed an algorithm to
quantify how closely packed a given neural network is. This
algorithm works recursively by summing

the strength

of

every connection from a given
neuron and
that of
any connections thereaf
ter (proportionately scaled). The algorithm
does this for each node in the network and returns the mean value considering every
node.

Refer to the pseudocode below for clarification of this novel algorithm.


12


In effect, Synergy
tells us how easily an action potential emitted by the average
neuron can
affect

the entire network. This measurement can be useful and interesting in a
number of ways. One use for such a metric might be
to discover

how vital a single
employee is to a larg
e corporation, how well connected a given person might be to the
world as a whole, or even how well a computer system is functioning on the internet. The
uses for this type of standardized metric are limitless.


I was curious to see the trend in Synergy as

a neural network is evolved through a
system like Polyworld. If the theories about relationships between Integrated Information
and consciousness prove to be true, Synergy might also have a valid claim to such
importance. I present to you the trend of

Syn
ergy over evolutionary time:



Graph of synergy value for every hundred
th

death.



This trend in particular was calculated by observing every hundred
th

time step in
a single Polyworld simulation of
approximately

30,000 steps. The resulting data is, as
you can see, quite noisy. The trend, however, is still clearly visible and strangely enough
13

seems to echo the trend in Complexity observed by Yaeger Et Al.
[4].

The synergy value
of the Polyworldian neural networks
seems to increase noisily, but steadily, for the first
5,000 time steps. After this point, the synergy value seems to plateau, or even decline for
the remainder of the simulation.


One possible
source of error

in the above trend graph may be the lackluster

number of trials tested. This was due, in part, to the
amount

of
time that

this calculation
took. To calculate synergy to a depth of 3 for every 100 steps of a 30,000 step Polyworld
run (like above), the computation time was about 36 hours. Future effort
s

should

be made
in optimizing the synergy calculation and running it with more raw data.

5
. Conclusion and Future Plans


In conclusion, evolutionary artificial intelligence seems to be a promising field for
future advancement. More effort must be made to o
ptimize the calculation of metrics
such as Integrated Information

and Synergy

so that more detailed trends may be
analyzed. Using these types of metrics to aid in the guided evolution of artificial neural
networks will undoubtedly yield new and exciting sy
stems. I plan to continue studying
and modifying Polyworld with the hope of
surpassing current expectations and limits
given to artificial machines
. As computers
become

more power
ful
,

as

quantum
computation becomes reality, and
as the
tools

mentioned in th
is paper

are given more
time to mature and grow, evolutionary computation is sure to
be a fruitful
and beneficial
field.

14


6
. Bibliography




1. G
iulio Tononi Et al.,
Measuring Information Integration,

BMC Neuroscience (2003).


2. Joseph T.

Lizier Et al
.,
Functional and Structural T
opologies in Evolved


Neural Networks,

(2009).


3. La
rry Yaeger Et al.,
Passive and Driven Trends in the Evolution of Complexity,



Journal of

Artificial Life (2008).


4.
Yaeger, L. S., Griffith, V., and Sporns, O. (2008).
Passive and Driven Trends in the




Evolution of Complexity.

In Bullock, S., Noble, J., Watson, R., and Bedau, M. A.,


editors,
Artificial Life XI: Proceedings of the Tenth International
Conference on the



Simulation and Synthesis of Living Systems,

p
.

725-732. MIT Press, Cambridge, MA.


5.
Gyorgy Buzsaki,
Rhythms of the Brain,

Oxford University Press, USA, 2006.


6. Jean
-
Pierre Dupuy (Translat
ed by M. B. DeBevoise),
On the Origins o
f Cognitive




Science: The Mechanization of the Mind,
The MIT Press, 2009.


7. Peter Dayan

and L. F. Abbott,
Theoretical Neuroscience: Computational and




Mathematical Modeling of Neural Systems,

The MIT Press, 2005.


8. L
awrence J. Fogel,
Inte
lligence Through Simulated Evolution: Forty Years of




Evolutionary Programming (Wiley Series on Intelligent Systems),

Wiley
-



Interscience, 1999.


9. Googl
e Tech Talks,
Polyworld: Using Evolution to Design Artificial Intelligence,




Nove
mber

2007.


10.

Christian Jacob,
Illustrating Evolutionary Computation with Mathematica


Morgan Kaufmann

Publishers
, 2001.


11. Eric R. Kandel,
In Search of Memory: The Emergence of a New Science of Mind,



Norton

Paperback, 2006.


12.
Stefano Nolfi and Dario Floreano
, Evolutionary Robotics: The Biology, Intelligence,




and Technology of Self
-
organizing Machines (Intelligent Robotics and Autonomous



Agents),

The MIT

Press, 2000.


15

13. Anil K. Seth,
Causal Connectivity of Evo
lved Neural Networks During Behavior,


Johns Hopkins University

(2009).


14. Murray Shanahan,
On the Dynamical Complexity of Small
-
world Networks of



Spiking Neurons,

to a
ppear in Physical Review E (2009).


15.

Gordon M. Shepherd (ed.),
The
Synaptic Organization of the Brain,


Oxford University Press.
USA, 2003.


16. Virgil Griffith Et Al.,
An Information
-
Based Measuer of Synergistic
Complexity


Based On Phi
, unpublished, 2009