Mental Navigation: Global Measures of Complex Netwroks

erminerebelIA et Robotique

15 nov. 2013 (il y a 3 années et 10 mois)

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Mental Navigation: Global Measures
of Complex Netwroks

Guillermo Cecchi


IBM Research, T.J. Watson Center

Overview


General motivation


The lexicon network


Brain imaging networks

Global Measures of Biological
Networks



Characterization of global states



Functional mechanisms

Motivation: Approaches to
Quantify Meaning

Reductionist
: meaning is molecular, piece
-
wise, and verificationist. Each
linguistic item corresponds to an object in the world. There are

statements, and they can only be true or false. Ex.,
the moon is blue
.

Natural language is "corrupt", fraught with inconsistency and ambiguity.

Ref.: Aristotle, logical positivism.


Holistic
: meaning arises as a collective phenomenon within a sentence,

with the whole language and the external world. Ex.,
in a blue moon
.

Natural language is "embodied" and intertwined with the context, ambiguity

is part of the message. Ref.: Quine, Kuhn.

Good

Bad

Knife

Fork

Mother

Father

Lion






Stripes

Lion


Feline

Tiger


Stripes

Lion


Feline

Tiger


Stripes

Predator Prey
Zebra

Diffusion in the Semantic
Network


Psychophysical evidence of “priming” of related
meanings (Quillian, Burguess, Posner)


Imaging evidence for spread of activation to the
neural representation of related meanings
(Damasio, Ungerleider).


Fast and unconscious spread of activation
(Dehaene).


Mental and neural navigation (Spitzer).

Wordnet: Building Sets of Meanings


Wordnet attempts to characterize the set of linguistic meanings, the words that
represent their relationships. Those include hypernimy, hyponimy, synonimy,
antonimy, among others. A typical entry in wordnet reads:

%zahir> wn dog
-
hholn

Holonyms of noun dog

2 of 6 senses of dog

Sense 1

dog, domestic dog, Canis familiaris


MEMBER OF: Canis, genus Canis


MEMBER OF: Canidae, family Canidae


MEMBER OF: Carnivora, order Carnivora


MEMBER OF: Eutheria, subclass Eutheria


MEMBER OF: Mammalia, class Mammalia


MEMBER OF: Vertebrata, subphylum Vertebrata, Craniata, subphylum Craniata


MEMBER OF: Chordata, phylum Chordata


MEMBER OF: Animalia, kingdom Animalia, animal kingdom


MEMBER OF: pack

Sense 5

pawl, detent, click, dog


PART OF: ratchet, rachet, ratch

Organization of the Semantic Network


Does a Canary Sing?



Does a Canary Fly?



Does a Canary Breathe?


Meanings

are not in one to one correspondence with
words

Committee

Piece of wood

Friend

Pal

Comrade

Board

Meanings

are hierarchical (Quillian)

Semantic Relationships


Antonymy
: opposite meanings


good is antonym of evil
.


Hypernymy


Hyponymy
: generic or universal,
specific or particular


tree is hypernym of oak
.


Meronymy


Holonymy
: part of


branch is meronym of tree
.


Polysemy
: meanings share a common word


board as official body of persons, and as slab of wood.

What to Measure


Wordnet

can be embedded in a graph of ~70,000
nodes and ~200,000 edges. What are the collective
properties of the graph?



Scaling


Evidence for self
-
organization


Navigation
:


Small
-
world
-
ness


Navigation

Distribution of Links

Small
-
world: Low Clustering,
Short Diameter

c =
cn
/(nn*(nn
-
1))

d = <
D
min
>
all pairs

Regular to Small
-
World

Watts & Strogatz, 1998

Clustering and Average Minimal Distance

See also Ferrer i Cancho & Sole, 2001

Impact of Polysemous Links

Dissolution of Tree Structure with Polysemy

Blind Navigation

Measuring Network Navigation

C

connectivity matrix,
P

exponentiation:

P

=
C
N

e


P
ij

= number of paths between
i

and
j
of length
N

P
j

k
1
N

[
e
1

e
1
T

+ (
k
2
/
k
1
)
N

e
2
e
2
T

+ …]

Where
k
1

is the first eigenvalue and
e
1

the first eigenvector

e
{
e
i
} provide a limiting behavior of a blind, non
-
detailed

balanced navigation of the graph, or “traffic”.

Traffic

head

point

line

Conclusions


Evidence for self
-
organization and small
-
world
-
ness


Polysemy organizes and shortens the
network


Ubiquity across languages


May reflect preeminence of metaphoric
thinking


The global perspective reveals possible
mechanisms

Brain Activity as a Network


Brain activity revealed by imaging:


Need for non
-
stimulus driven analysis


How to characterize such a structure?


1

if
Corr[
v
i
(
t
)
v
j
(
t
)]
t

m

P
0


0

otherwise


C
ij

=

P
0
|
{
C
ij

}
connected


Define a connectivity matrix as:

Traffic in the Brain: Chronic Pain

regular graph


Pain

1.
Thalamus (1/3)

2.
S1 (hand)

3.
Cerebellum (1/3)

4.
Posterior Parietal (1/4)

5.
Prefrontal (1/6)

6.
Prefrontal (2/6)

7.
S1 (foot)



Pain Surrogate


Prefrontal (2/6)



Visual Surrogate


Prefrontal (3/6)

Connections Dendogram

Group I

pf1, pf2, pf4, pf5, pf6, s1 (foot),
pparietal3, pparietal4


Group II

thal1, thal2, thal3, venst2, psins,
ancing1, ancing2


Group III

amygd1, amygd2, amygd3, nacc1,
nacc2, pf3, venst1, venteg1, venteg2


Group IV

s2_1, s2_1, anins, pscing, PM,
cereb1, cereb2, cereb3, s1
-
hand,
motor, pparietal1, pparietal3


I

II

III

IV

Preliminary Conclusions


The network analysis exposes a coherent
functional organization



It provides novel functional hypotheses for
further experimentation


General Conclusions


The global/network approach unveils
emergent states of biological networks



Provides tools for functional dissection



Guides the search for mechanisms

Credits


Mariano Sigman, Rockefeller


INEBA, Paris


Vania Apkarian, Northwestern University


Dante Chialvo, UCLA


Victor Martinez, Univ. Baleares, Spain