Download (2009). Cognitive computational intelligence

COGNITIVE COMPUTATIONAL INTELLIGENCE
for
data mining, financial prediction, tracking, fusion,
language, cognition, and cultural evolution
IASTED CI 2009
Honolulu, HI
1:30 – 5:30 pm, Aug. 19
Leonid Perlovsky
Visiting Scholar, Harvard University
Technical Advisor, AFRL
OUTLINE
1. Cognition and Logic
2. The Knowledge Instinct
-Dynamic Logic
3. Language
4. Integration of cognition and language
5. High Cognitive Functions
6. Evolution of cultures
7. Future directions
INTRODUCTION
The mind
PHYSICS AND MATHEMATICS OF THE MIND
RANGE OF CONCEPTS

Logic is sufficient to explain mind
– [Newell, “Artificial Intelligence”, 1980s]

No new specific mathematical concepts are needed
– Mind is a collection of ad-hoc principles, [Minsky, 1990s]

Specific mathematical constructs describe the
multiplicity of mind phenomena
– “first physical principles of mind”
– [Grossberg, Zadeh, Perlovsky,…]

Quantum computation
– [Hameroff, Penrose, Perlovsky,…]

New unknown yet physical phenomena
– [Josephson, Penrose]
GENETIC ARGUMENTS
FOR THE “FIRST PRINCIPLES”

Only 30,000 genes in human genome
– Only about 2% difference between human and apes
– Say, 1% difference between human and ape minds
– Only about 300 proteins

Therefore, the mind has to utilize few inborn
principles
– If we count “a protein per concept”
– If we count combinations: 300300 ~ unlimited => all concepts
and languages could have been genetically h/w-ed (!?!)

Languages and concepts are not genetically
hardwired
– Because they have to be flexible and adaptive
COGNITION
• Understanding
the world
– Perception
– Simple objects
– Complex situations
• Integration
of real-time signals and existing (a
priori) knowledge
– From signals to concepts
– From less knowledge to more knowledge
EXAMPLE

Example: “this is a chair, it is for sitting”

Identify objects
– signals -> concepts

What in the mind help us do this?
Representations, models, ontologies?
– What is the nature of representations in the
mind?
– Wooden chairs in the world, but no wood in the
brain
VISUAL PERCEPTION

Neural mechanisms are well studied
– Projection from retina to visual cortex (geometrically accurate)
– Projection of memories-models
• from memory to visual cortex
– Matching: sensory signals and models
– In visual nerve more feedback connections than feedforward
• matching involves complicated adaptation of models and signals

Difficulty
– Associate signals with models
– A lot of models (expected objects and scences)
– Many more combinations: models<->pixels

Association + adaptation
– To adapt, signals and models should be matched
– To match, they should be adapted
ALGORITHMIC DIFFICULTIES
A FUNDAMENTAL PROBLEM?

Cognition and language involve evaluating large
numbers of combinations
– Pixels -> objects -> scenes

Combinatorial Complexity (CC)
– A general problem (since the 1950s)
• Detection, recognition, tracking, fusion, situational awareness,
language…
• Pattern recognition, neural networks, rule systems…

Combinations of 100 elements are 100100
– This number ~ the size of the Universe
• > all the events in the Universe during its entire life
COMBINATORIAL COMPLEXITY
SINCE the 1950s

CC was encountered for over 50 years

Statistical pattern recognition and neural networks: CC of
learning requirements

Rule systems and AI, in the presence of variability : CC of rules
– Minsky 1960s: Artificial Intelligence
– Chomsky 1957: language mechanisms are rule systems

Model-based systems, with adaptive models: CC of
computations
– Chomsky 1981: language mechanisms are model-based (rules and parameters)

Current ontologies, “semantic web” are rule-systems
– Evolvable ontologies : present challenge
CC AND TYPES OF LOGIC
CC is related to formal logic
– Law of excluded middle (or excluded third)
• every logical statement is either true or false
– Gödel proved that logic is “illogical,” “inconsistent” (1930s)
– CC is Gödel's “incompleteness” in a finite system
Multivalued logic eliminated the
– Still, the math. of formal logic
– Excluded 3rd -> excluded (n+1)
“law of excluded third”
Fuzzy logic eliminated the “law of excluded third”
– How to select “the right” degree of fuzziness
– The mind fits fuzziness for every statement at every step => CC
Logic pervades all algorithms and neural networks
– rule systems, fuzzy systems (degree of fuzziness), pattern recognition,
neural networks (training uses logical statements)
LOGIC VS. GRADIENT ASCENT

Gradient ascent maximizes without CC
– Requires continuous parameters
– How to take gradients along “association”?
• Data Xn (or) to object m
• It is a logical statement, discrete, non-differentiable
– Models / ontologies require logic => CC

Multivalued logic does not lead to gradient ascent

Fuzzy logic uses continuous association variables, b
– A new principle is needed to specify gradient ascent along fuzzy
associations: dynamic logic
DYNAMIC LOGIC

Dynamic Logic unifies formal and fuzzy logic
– initial “vague or fuzzy concepts” dynamically evolve into
“formal-logic or crisp concepts”

Dynamic logic
– based on a similarity between models and signals

Overcomes CC
– fast algorithms

Proven in neuroimaging experiments (Bar, 2006)
– Initial representations-memories are vague
– “close-eyes” experiment
ARISTOTLE VS. GÖDEL
logic, forms, and language

Aristotle
– Logic: a supreme way of argument
– Forms: representations in the mind
 Form-as-potentiality evolves into form-as-actuality
 Logic is valid for actualities, not for potentialities (Dynamic Logic)
– Thought language and thinking are closely linked
 Language contains the necessary uncertainty

From Boole to Russell: formalization of logic
– Logicians eliminated from logic uncertainty of language
– Hilbert: formalize rules of mathematical proofs forever

Gödel (the 1930s)
– Logic is not consistent
 Any statement can be proved true and false

Aristotle and Alexander the Great
OUTLINE
•
Cognition, complexity, and logic
- Logic does not work, but the mind does
•
The Mind and Knowledge Instinct
•
Language
•
Integration of cognition and language
•
Higher Cognitive Functions
•
Future directions
- Neural Modeling Fields and Dynamic Logic
STRUCTURE OF THE MIND

Concepts
– Models of objects, their relations, and situations
– Evolved to satisfy instincts

Instincts
– Internal sensors (e.g. sugar level in blood)

Emotions
– Neural signals connecting instincts and concepts
• e.g. a hungry person sees food all around

Behavior
– Models of goals (desires) and muscle-movement…

Hierarchy
– Concept-models and behavior-models are organized in a “loose”
hierarchy
THE KNOWLEDGE INSTINCT

Model-concepts always have to be adapted
– lighting, surrounding, new objects and situations
– even when there is no concrete “bodily” needs

Instinct for knowledge and understanding
– Increase similarity between models and the world

Emotions related to the knowledge instinct
– Satisfaction or dissatisfaction
• change in similarity between models and world
– Related not to bodily instincts
• harmony or disharmony (knowledge-world): aesthetic emotion
REASONS FOR PAST LIMITATIONS

Human intelligence combines conceptual
understanding with emotional evaluation

A long-standing cultural belief that emotions
are opposite to thinking and intellect
– “Stay cool to be smart”
– Socrates, Plato, Aristotle
– Reiterated by founders of Artificial Intelligence [Newell,
Minsky]
Neural Modeling Fields (NMF)

A mathematical construct modeling the mind
–
–
–
–
–
Neural synaptic fields
A loose hierarchy
bottom-up signals, top-down signals
At every level: concepts, emotions, models, behavior
Concepts become input signals to the next level
NEURAL MODELING FIELDS
basic two-layer mechanism: from signals to concepts

Bottom-up signals
– Pixels or samples (from sensor or retina)
x(n), n = 1,…,N

Top-down signals (concept-models)
Mm(Sm,n), parameters Sm, m = 1, …;
– Models predict expected signals from objects

Goal: learn object-models and match to
signals (knowledge instinct)
THE KNOWLEDGE INSTINCT

The knowledge instinct = maximize similarity
between signals and models

Similarity between signals and models, L
– L = l ({x}) = l (x(n))
n
– l (x(n)) =  r(m) l (x(n) | Mm(Sm,n))
m
– l (x(n) | Mm(Sm,n)) is a conditional similarity for x(n) given m
• {n} are not independent, M(n) may depend on n’

CC: L contains MN items: all associations of
pixels and models (LOGIC)
SIMILARITY

Similarity as likelihood
– l (x(n) | Mm(Sm,n)) = pdf(x(n) | Mm(Sm,n)),
– a conditional pdf for x(n) given m
– e.g., Gaussian pdf(X(n)|m) = G(X(n)|Mm,Cm)
= 2p-d/2 detCm-1/2 exp(-DmnTCm-1 Dmn/2); Dmn = X(n) – Mm(n)
– Note, this is NOT the usual “Gaussian assumption”
• deviations from models D are random, not the data X
• multiple models {m} can model any pdf, not one Gaussian model
– Use for sets of data points

Similarity as information
– l (x(n) | Mm(Sm,n)) = abs(x(n))*pdf(x(n) | Mm(Sm,n)),
– a mutual information in model m on data x(n)
– L is a mutual information in all model about all data
–
e.g., Gaussian pdf(X(n)|m) = G(X(n)|Mm,Cm)
– Use for continuous data (signals, images)
DYNAMIC LOGIC (DL)
non-combinatorial solution

Start with a set of signals and unknown object-models
– any parameter values Sm
– associate signals (n) and models (m)
– (1)

f(m|n) = r(m) l (n|m) /  r(m') l (n|m')
m'
Improve parameter estimation
– (2) Sm = Sm + a  f(m|n) [ln l (n|m)/Mm]*[Mm/Sm]
n

Continue iterations (1)-(2). Theorem: NMF is a
converging system
- similarity increases on each iteration
- aesthetic emotion is positive during learning
OUTLINE
•
Cognition, complexity, and logic
-
•
Logic does not work, but the mind does
The Mind and Knowledge Instinct
-
Neural Modeling Fields and Dynamic Logic
- Application examples
•
Language
•
Integration of cognition and language
•
Higher Cognitive Functions
•
Future directions
APPLICATIONS

Many applications have been developed
– Government
– Medical
– Commercial (about 25 companies use this technology)

Sensor signals processing and object recognition
– Variety of sensors

Financial market predictions
– Market crash on 9/11 predicted a week ahead

Internet search engines
– Based on text understanding

Evolving ontologies for Semantic Web

Every application needs models
– Future self-evolving models: integrated cognition and language
APPLICATION 1 – CLUSTERING
(data mining)


Find “natural” groups or clusters in data
Use Gaussian pdf and simple models
l (n|m) = 2p-d/2 detCm-1/2 exp(-DmnTCm-1 Dmn/2);
Mm(n) = Mm; each
–


This is clustering with Gaussian Mixture Model
Simplification, not essential
Simplify parameter estimation equation for Gaussian pdf and simple models
ln l (n|m)/Mm =  (-DmnTCm-1 Dmn) /Mm = Cm-1 Dmn + DmnT Cm-1 = 2 Cm-1 Dmn, (C is symmetric)
Mm = Mm + a  f(m|n) Cm-1 Dmn
…

model has just 1 parameter, Sm = Mm
For complex l(n|m) derivatives can be taken numerically
For simple l(n|m) derivatives can be taken manually
–

Dmn = X(n) – Mm(n)
n
In this case, even simpler equations can be derived
samples in class m:
Nm = 
f(m|n);
N=
n
rates (priors):
rm = Nm / N
means:
Mm =
covariances:
Cm =
 Nm
m
 f(m|n) X(n) / Nm
 f(m|n) Dmn * DmnT / Nm
n
n
- simple interpretation: Nm, Mm, Cm are weighted averages. The only difference from standard
mean and covariance estimation is weights f(m|n), probabilities of class m

These are iterative equations, f(m|n) depends on parameters; theorem: iterations converge
Example 2: GMTI Tracking and Detection
Below Clutter
1 km
DL starts with uncertain knowledge and converges rapidly on exact solution
0
Range
(a)
True
Tracks
Cross-Range
1 km
b
Initial state of model
2 iterations
0
Range
1 km
0
5 iterations
9 iterations
12 iterations
18 dB improvement
Converged state
TRACKING AND DETECTION
BELOW CLUTTER (movie, same as above)
DL starts with uncertain knowledge, and similar to human mind does not sort through
all possibilities, but converges rapidly on exact solution
3 targets, 6 scans, signal-to-clutter, S/C ~ -3.0dB
TRACKING EXAMPLE
complexity and improvement
• Technical difficulty
- Signal/Clutter = - 3 dB, standard tracking requirements 15 dB
- Computations, standard hypothesis testing ~ 101700, unsolvable
• Solved by Dynamic Logic
- Computations: 2x107
- Improvement 18 dB
CRAMER-RAO BOUND (CRB)

Can a particular set of models be estimated from a particular
(limited) set of data?
– The question is not trivial
• A simple rule-of-thumb: N(data points) > 10*S(parameters)
• In addition: use your mind: is there enough information in the data?

CRB: minimal estimation error (best possible estimation) for
any algorithm or neural neworks, or…
– When there are many data points, CRB is a good measure
(=ML=NMF)
– When there are few data points (e.g. financial prediction) it might be
difficult to access performance
• Actual errors >> CRB

Simple well-known CRB for averaging several measurements
st.dev(n) = st.dev(1)/√n

Complex CRB for tracking:
–
Perlovsky, L.I. (1997a). Cramer-Rao Bound for Tracking in Clutter and Tracking Multiple
Objects. Pattern Recognition Letters, 18(3), pp.283-288.
APPLICATION 3
FINDING PATTERNS IN IMAGES
IMAGE PATTERN BELOW NOISE
Object Image + Clutter
y
y
Object Image
x
x
PRIOR STATE-OF-THE-ART
Computational complexity
Multiple Hypothesis Testing (MHT) approach:
try all possible ways of fitting model to the data
For a 100 x 100 pixel image:
Number of Objects
Number of Computations
1
1010
2
1020
3
1030
NMF MODELS

Information similarity measure
lnl (x(n) | Mm(Sm,n)) = abs(x(n))*ln pdf(x(n) | Mm(Sm, n))
n = (nx,ny)

Clutter concept-model (m=1)
pdf(X(n)|1) = r1

Object concept-model (m=2… )
k  K / 2
pdf(x(n) | Mm(Sm, n)) = r2  G(X(n)|Mm (n,k),Cm)
Mm (n,k) = n0 + a*(k2,k); (note: k, K require no estimation)
k  K / 2
Y
ONE PATTERN BELOW CLUTTER
X
SNR = -2.0 dB
DYNAMIC LOGIC WORKING
DL starts with uncertain knowledge, and similar to human mind converges rapidly on
exact solution
• Object invisible to
human eye
• By integrating
data with the
knowledge-model
DL finds an object
below noise
x (m) Cross-range
MULTIPLE PATTERNS
BELOW CLUTTER
Three objects in noise
object 1
object 2 object 3
SCR
- 0.70 dB -1.98 dB -0.73 dB
3 Object Image + Clutter
y
y
3 Object Image
x
x
IMAGE PATTERNS BELOW CLUTTER
(dynamic logic iterations see note-text)
a
b
c
d
e
f
g
h
Logical complexity = MN = 105000, unsolvable; DL complexity = 107
S/C improvement ~ 16 dB
MULTIPLE TARGET DETECTION
DL WORKING EXAMPLE
DL starts with uncertain knowledge, and similar to human mind does not sort through
all possibilities like an MHT, but converges rapidly on exact solution
x
COMPUTATIONAL REQUIREMENTS
COMPARED
Dynamic Logic (DL) vs. Classical State-of-the-art Multiple
Hypothesis Testing (MHT)
Based on 100 x 100 pixel image
Number of Objects
Number of Computations
DL
vs.
MHT
1
108
vs.
1010
2
2x108
vs.
1020
3
3x108
vs.
1030
• Previously un-computable (1030), can now be computed (3x108 )
• This pertains to many complex information-finding problems
APPLICATION 4
SENSOR FUSION
Concurrent fusion, navigation, and detection
below clutter
SENSOR FUSION

The difficult part of sensor fusion is association of data
among sensors
– Which sample in one sensor corresponds to which sample in
another sensor?

If objects can be detected in each sensor individually
– Still the problem of data association remains
– Sometimes it is solved through coordinate estimation
• If 3-d coordinates can be estimated reliably in each sensor
– Sometimes it is solved through tracking
• If objects could be reliably tracked in each sensor, => 3-d
coordinates

If objects cannot be detected in each sensor individually
– We have to find the best possible association among multiple
samples
– This is most difficult: concurrent detection, tacking, and fusion
NMF/DL SENSOR FUSION

NMF/DL for sensor fusion requires no new
conceptual development

Multiple sensor data require multiple sensor
models
– Data: n -> (s,n); X(n) -> X(s,n)
– Models Mm(n) -> Mm(s,n)

PDF(n|m) is a product over sensors
– This is a standard probabilistic procedure, another
sensor is like another dimension
– pdf(m|n) ->  pdf(m|s,n)
s

Note: this solves the difficult problem of
concurrent detection, tracking, and fusion
Source: UAS
Roadmap 20052030
UNCLASSIFIED
CONCURRENT NAVIGATION,
FUSION, AND DETECTION
 multiple
target detection and localization based on data from
multiple micro-UAVs
A
complex case
–detection requires fusion (cannot be done with one sensor)
–fusion requires exact target position estimation in 3-D
–target position can be estimated by triangulation from multiple views
–this requires exact UAV position
• GPS is not sufficient
• UAV position - by triangulation relative to known targets
–therefore target detection and localization is performed concurrently
with UAV navigation and localization, and fusion of information from
multiple UAVs
 Unsolvable
using standard methods. Dynamic logic can solve
because computational complexity scales linearly with number
of sensors and targets
GEOMETRY: MULTIPLE
TARGETS, MULTIPLE UAVS
UAV m
Xm = X0m + Vmt
UAV 1
Xm=(Xm,Ym,Zm)
X1=(X1,Y1,Z1)
X1 = X01 + V1t
CONDITIONAL SIMILARITIES (pdf) FOR
TARGET k
Data from UAV m, sample number n, where βnm = signature position
and fnm = classification feature vector:
Similarity for the data, given target k:
where
signature position
classification
features
Note: Also have a pdf for a single clutter component pdf(w nm| k=0) which is uniform
in βnm, Gaussian in fnm.
Data Model and Likelihood Similarity
Total pdf of data samples is the summation of conditional pdfs
(summation over targets plus clutter)
(mixture model)
UAV parameters
Compute parameters
maximize the log-likelihood
target parameters
classification feature
parameters
that
Concurrent Parameter Estimation / Signature
Association (NMF iterations)
FIND SOLUTION FOR SET OF “BEST” PARAMETERS BY ITERATING
BETWEEN…
Parameter Estimation
and
Association Probability
Estimation (Bayes rule)
(probability that sample w nm
was generated by target k)
Note1: bracket notation
Note2: proven to converge (e.g. EM algorithm)
Note 3: Minimum MSE solution incorporates GPS measurements
Sensor 1 (of 3): Models Evolve to Locate
Target Tracks in Image Data
Sensor 2 (of 3): Models Evolve to Locate
Target Tracks in Image Data
Sensor 3 (of 3): Models Evolve to Locate
Target Tracks in Image Data
NAVIGATION, FUSION, TRACKING, AND DETECTION
(this is the basis for the previous 3 figures, all fused in x,y,z, coordinates;
double-click on the blob to play movie)
Model Parameters Iteratively Adapt to
Locate the Targets
Estimated Target Position
vs. iteration# (4 targets)
Error vs. iteration#
(4 targets)
Parameter Estimation Errors Decrease with
Increasing Number of UAVs in the Swarm
Error in Parameter Estimates vs. clutter level and # of UAVs in
the swarm
Target position
(Note: Results are
based upon Monte
Carlo simulations with
synthetic data)
Error falls off as ~ 1/√M, where
M = # UAVs in the swarm
UAV position
APPLICATION 5
DETECTION IN
SEQUENCES OF IMAGES
DETECTION IN
A SEQUENCE OF IMAGES
Signature + low noise
level (SNR= 25dB)
Signature + high noise
level (SNR= -6dB)
signature is present,
but is obscured by
noise
DETECTION IN IMAGE SEQUENCE
TEN ROTATION FRAMES WERE USED
Iteration 10
Iteration 100
Iteration 600
Compare with
Measured Image (w/o
noise)
Iteration 400

Upon convergence of the
model, important parameters
are estimated, including center
of rotation, which will next be
used for spectrum estimation.

Four model components were
used, including a uniform
background component. Only
one component became
associated with point source.
TARGET SIGNATURE
Extracted from low noise image
Extracted from high noise image
APPLICATION 6
• Radar Imaging through walls
- Inverse scattering problem
- Standard radar imaging algorithms (SAR) do not work because of multipaths, refractions, clutter
SCENARIO
RADAR IMAGING THROUGH WALLS
Standard SAR imaging does not work
Because of refraction, multi-paths and clutter
Estimated model, work in progress
Remains:
-increase convergence area
-increase complexity of scenario
-adaptive control of sensors
DYNAMIC LOGIC / NMF
INTEGRATED INFORMATION:
objects; relations;
situations; behavior
Data and
Signals
Dynamic
Logic
combining
conceptual analysis
with
emotional evaluation
MODELS
- objects
- relations
- situations
- behavioral
CLASSICAL METHODOLGY
no closure
Result: Conceptual objects
Recognition
signals
MODELS/templates
•objects, sensors
•physical models
Sensors /
Effectors
Input: World/scene
NMF: closure
basic two-layer hierarchy: signals and concepts
Result: Conceptual objects
Correspondence /
Similarity measures
signals
Attention / Action
Sim.signals
MODELS
•objects, sensors
•physical models
Sensors /
Effectors
signals
Input: World/scene
APPLICATION 7
• Prediction
- Financial prediction
PREDICTION

Simple: linear regression
– y(x) = Ax+b
– Multi-dimensional regression: y,x,b are vectors, A is a m-x
– Problem: given {y,x}, estimate A,b

Solution to linear regression (well known)
– Estimate means <y>, <x>, and x-y covariance matrix C
– A = Cyx Cxx-1; b = <y> - A<x>

Difficulties
– Non-linear y(x), unknown shape
– y(x) changes regime (from up to down)
• and this is the most important event (financial prediction)
– No sufficient data to estimate C
• required ~10*dx+y3 data points, or more
NMF/DL PREDICTION

General non-linear regression (GNLR)
– y(x) =  f(m|n) ym(x) =  f(m|n) (Amx+bm)
m
m
– Amand bm are estimated similar to A,b in linear regression with the
following change: all  (…) are changed into  f(m|n)(…)
n
n

For prediction, we remember that f(m|n) = f(m|x)

Interpretation
– m are “regimes” or “processes”, f(m|x) determines influence of
regime m at point x (probability of process m being active)

Applications
– Non-linear y(x), unknown shape
– Detection of y(x) regime change (e.g. financial prediction or control)
• Minimal number of parameters: 2 linear regressions; f(m|n) are functions of the
same parameters
• Efficient estimation (ML)
• Potential for the fastest possible detection of a regime change
FINANCIAL PREDICTION
Efficient Market Hypothesis

Efficient market hypothesis, strong:
– no method for data processing or market analysis will bring
advantage over average market performance (only illegal
trading on nonpublic material information will get one
ahead of the market)
• Reasoning: too many market participants will try the same
tricks

Efficient market hypothesis, week:
– to get ahead of average market performance one has to do
something better than the rest of the world: better math.
methods, or better analysis, or something else (it is
possible to get ahead of the market legally)
FINANCIAL PREDICTION
BASICS OF MATH. PREDICTION
 Basic idea: train from t1 to t2, predict and trade on t2+1;
increment: t1->t1+1, t2->t2+1; …
– Number of data points between t1 to t2 should be >> number
of parameters
 Decide
on frequency of trading, it should correspond
to your psychological makeup and practical situation
– E.g. day-trading has more potential for making (or losing) a
lot of money fast, but requires full time commitment
 Get
past data, split into 3 sets: (1)developing,
(2)testing, (3)final test (best, in real time, paper
trades)
 After
much effort on (1), try on (2), if work, try on (3)
FINANCIAL MARKET PREDICITION
Recommended Portfolios vs. Markets
portfolio gains: rec-sp = 6.2%, rec-nq = 7.4% (vs. markets sp = 1.8%, nq = -4.2% loss)
risk measures: gain/st.dev = 3.6, 4.0 (vs mkts 0.35, -.45), average exosure = 14% (vs. mkt 100%)
110.00%
108.00%
cumulative gain % (VAMI)
106.00%
104.00%
102.00%
100.00%
98.00%
SP weeklyVAMI
NQ weeklyVAMI
RecSP+T weeklyVAMI
96.00%
94.00%
12/30/2005
RecNQ+T weeklyVAMI
1/29/2006
3/1/2006
3/31/2006
date
5/1/2006
5/31/2006
7/1/2006
BIOINFORMATICS
 Many potential applications
– combinatorial complexity of existing algorithms
 Drug
design
– Diagnostics: which gene / protein is responsible
• Pattern recognition
• Identify a pattern of genes responsible for the condition
– Relate sequence to function
• Protein folding (shape)
• Relate shape to conditions
 Many
basic problems are solved sub-optimally
(combinatorial complexity)
– Alignment
– Dynamic system of interacting genes / proteins
• Characterize
• Relate to conditions
NMF/DL FOR COGNITION
SUMMARY

Cognition
– Integrating knowledge and data / signals

Knowledge = concepts = models

Knowledge instinct = similarity(models, data)

Aesthetic emotion = change in similarity

Emotional intelligence
– combination of conceptual knowledge and emotional
evaluation

Applications
– Recognition, tracking, fusion, prediction…
OUTLINE
•
Cognition, complexity, and logic
•
The Mind and Knowledge Instinct
•
Higher models and Language
•
Integration of cognition and language
•
Higher Cognitive Functions
•
Future directions
LANGUAGE ACQUISITION
AND COMPLEXITY

Chomsky: linguistics should study the
mind mechanisms of language (1957)

Chomsky’s language mechanisms
– 1957: rule-based
– 1981: model-based (rules and parameters)

Combinatorial complexity
– For the same reason as all rule-based and
model-based methods
APPLICATION: SEARCH ENGINE
BASED ON UNDERSTANDING
 Goal-instinct:
– Find conceptual similarity between a query and text
 Analyze
query and text in terms of concepts
 “Simple”
non-adaptive techniques
– By keywords
– By key-sentences = set of words
• Define a sequence of words (“bag of words”)
• Compute coincidences between the bag and the document
• Instead of the document use chunks of 7 or 10 words
 How
to learn useful sentences?
NMF OF SET-MODELS

Next level in the hierarchy above patterns

Situations are sets of objects (and relations)

Language - sets of words (and relations-grammar)
– Say, we know how to find objects and words oi, wi
– model-set: Mm({oi}) = (Leonid, chair, sit) – how to take derivatives?

Models of sets
– l (x(n) | Mm(Sm,n)) =


 pmix(ni) (1 -pmi(1-x(ni)) )
i
Data { x(n,i) }, 0 or 1 for absent or present objects
Parameters { p(m,i) } between 0 and 1, to be estimated
– Probabilities of object i present in situation m
– Vague models, p = 0.5; exact p = 0 or 1

Learning difficulty:
– most of objects are irrelevant
EXAMPLE

Total number of objects = 1000

Total number of situations = 10

Number of objects in a situation = 50

Number of relevant objects in a situation = 10

Number of examples of each situation = 800

Number of examples of random sets = 8,000 (50%)
DATA
data samples (horizontal axis) are sorted by situations hence the horizontal lines for
repeated objects
DATA
data samples (horizontal axis) are random as in real life
DL LEARNING (in 3 iterations)
ERRORS
N

n 1
f(m|n)* f(m’|n),
ASSOCIATIONS
 f(m|n) f(m’|n), m=true, m’=computed
m
OUTLINE
•
Cognition, complexity, and logic
•
The Mind and Knowledge Instinct
•
Language
•
Integration of cognition and language
•
Higher Cognitive Functions
•
Future directions
WHAT WAS FIRST
COGNITION OR LANGUAGE?

How language and thoughts come together?

Language seems completely conscious
– A child at 5 knows about “good” and “bad” guys
– Philosophers and theologists discussed good and evil for millennia
– What are neural mechanisms?

How do we learn correct associations between words and objects?
– Among zillions of incorrect ones

Logic:
– Same mechanisms for L. & C.
– Does not work

DL: sub-conceptual, sub-conscious integration
LANGUAGE vs. COGNITION
• “Nativists”, - since the 1950s
- Language is a separate mind mechanism (Chomsky)
- Pinker: language instinct
• “Cognitivists”, - since the 1970s
- Language depends on cognition
- Talmy, Elman, Tomasello…
• “Evolutionists”, - since the 1980s
- Hurford, Kirby, Cangelosi…
- Language transmission between generations
• Co-evolution of language and cognition
INTEGRATED
LANGUAGE AND COGNITION

Language and cognition: the dual model
– Every model m has linguistic and cognitive-sensory parts
• Mm = { Mmcognitive,Mmlanguage };
– Language and cognition are fused at vague pre-conceptual level
• before concepts are learned

Joint evolution of language and cognition
– Newborn mind: initial models are vague placeholders
– Language is acquired ready-made from culture
– Language guides cognition

Language hides from us how vague are our thoughts
– With opened eyes it is difficult to recollect vague imaginations
– Language is like eyes for abstract concepts
– Usually we talk without full understanding (like kids)
INNER LINGUISTIC FORM
HUMBOLDT, the 1830s

In the 1830s Humboldt discussed two types of
linguistic forms
– words’ outer linguistic form (dictionary) – a formal designation
– and inner linguistic form (???) – creative, full of potential

This remained a mystery for rule-based AI,
structural linguistics, Chomskyan linguistics
– rule-based approaches using the mathematics of logic make
no difference between formal and creative

In NMF / DL there is a difference
– static form of learned (converged) concept-models
– dynamic form of vague-fuzzy concepts, with creative learning
potential, emotional content, and unconscious content
OUTLINE
•
Cognition, complexity, and logic
•
The Mind and Knowledge Instinct
•
Language
•
Integration of cognition and language
•
Higher Cognitive Functions
•
Future directions
HIGHER COGNITIVE FUNCTIONS

Abstract models are at higher levels of hierarchy
– create higher meaning and purpose from lower models
– vague-fuzzy, less conscious

Emotion of the beautiful
– when improve knowledge of the highest model = purpose of life
meanings
Action/Adaptation
Similarity measures
Models
situations
Similarity measures
Action/Adaptation
Models
objects
BEAUTY

Harmony is an elementary aesthetic emotion

The highest forms of aesthetic emotion, beautiful

Beautiful “reminds” us of our purposiveness

Beauty is separate from sex, but sex makes use of all our abilities,
including beauty
– related to the most general and most important models
– models of the meaning of our existence, of our purposiveness
– beautiful object stimulates improvement of the highest models of meaning
– Kant called beauty “aimless purposiveness”: not related to bodily purposes
– he was dissatisfied by not being able to give a positive definition: knowledge
instinct
– absence of positive definition remained a major source of confusion in
philosophical aesthetics till this very day
INTUITION

Complex states of perception-feeling of unconscious
fuzzy processes
– involves fuzzy unconscious concept-models
– in process of being learned and adapted
• toward crisp and conscious models, a theory
– conceptual and emotional content is undifferentiated
– such models satisfy or dissatisfy the knowledge instinct before
they are accessible to consciousness, hence the complex
emotional feel of an intuition

Artistic intuition
– composer: sounds and their relationships to psyche
– painter: colors, shapes and their relationships to psyche
– writer: words and their relationships to psyche
INTUITION: Physics vs. Math.

Mathematical intuition is about
– Structure and consistency within the theory
– Relationships to a priori content of psyche

Physical intuition is about
– The real world, first principles of its organization, and
mathematics describing it

Beauty of a physical theory discussed by physicists
– Related to satisfying knowledge instinct
• the feeling of purpose in the world
OUTLINE
•
Cognition, complexity, and logic
•
The Mind and Knowledge Instinct
•
Language
•
Integration of cognition and language
•
Higher Cognitive Functions
•
Future directions
WHY ADAM WAS EXPELLED FROM
PARADISE?

God gave Adam the mind, but forbade to eat from the Tree of
Knowledge
– All great philosophers and theologists from time immemorial
pondered this
– Maimonides, 12th century
• God wants people to think for themselves (true or false)
• Adam wanted ready-made knowledge (good or bad)
• Thinking for oneself is difficult (this is our predicament)

Today we can approach this scientifically
–
–
–
–

Rarely we use the KI
Often we use ready-made heuristics, rules-of-thumb
Both are evolutionary adaptations
Cognitive effort minimization (CEM) is opposite to the KI
2002 Nobel Prize in Economics (work of Kahneman and Tversky)
– People’s choices are often irrational
– Like Adam we use rules = cultural wisdom, not our own
GOD, SNAKE, and fMRI
 Majority
often make
choices (CEM-type)
 Stable
irrational,
heuristic
minority is rational (KI-type)
 fMRI
– KI-type think with cortex (uniquely human)
– CEM-type think with amygdala (animals)
 God
demands us being humans
 “Snake’s
apple” pulled Adam back to animals
SYMBOL

“A most misused word in our culture”
(T. Deacon)

Cultural and religious symbols
– Provoke wars and make piece

Traffic Signs
SIGNS AND SYMBOLS
mathematical semiotics

Signs: stand for something else
– non-adaptive entities (mathematics, AI)
– brain signals insensitive to context (Pribram)

Symbols
– Symbols=signs (mathematics, AI: mix up)
– general culture: deeply affect psyche
– psychological processes connecting conscious
and unconscious (Jung)
– brain signals sensitive to context (Pribram)
– processes of sign interpretation

DL: mathematics of symbol-processes
– Vague-unconscious -> crisp-conscious
SYMBOLS and “SYMBOLIC AI”

Founders of “symbolic AI” believed that by using
“symbolic” mathematical notations they would
penetrate into the mystery of mind
– But mathematical symbols are just notations (signs)
– Not psychic processes

This explains why “symbolic AI” was not successful

This also illustrates the power of language over
thinking
– Wittgenstein called it
• “bewitchment (of thinking) by language”
SYMBOLIC ABILITY

Integrated hierarchies of Cognition and Language
– High level cognition is only possible due to language
– Much of cognition if vague and unconscious
cognition
language
grounded in language
Action
Similarity
Action
Similarity
M
M
grounded in language
Similarity
Action
M
grounded in real-world objects
Similarity
Action
M
OUTLINE
•
Cognition, complexity, and logic
•
The Mind and Knowledge Instinct
•
Language
•
Integration of cognition and language
•
Higher Cognitive Functions
•
Future directions
- Evolution of languages and cultures
CULTURE AND LANGUAGE
• Animal consciousness
– Undifferentiated, few vague concepts
– No mental “space” between thought, emotion, and action
• Evolution of human consciousness and culture
– More differentiated concepts
– More mental “space” between thoughts, emotions, and actions
– Created by evolution of language
• Language, concepts, emotions
– Language creates concepts
– Still, colored by emotions
16-Sep-05
102
EVOLUTION OF CULTURES
• The knowledge instinct
– Two mechanisms: differentiation and synthesis
• Differentiation
– At every level of the hierarchy: more detailed concepts
– Separates concepts from emotions
• Synthesis
– Knowledge has to make meaning, otherwise it is useless
– Diverse knowledge is unified at the higher level in the hierarchy
– Connects concepts and emotions
 Connect language and cognition
 Connect high and low: concepts acquire meaning at the next level
16-Sep-05
103
DYNAMICS OF DIFFERENTIATION
AND SYNTHESIS
• Differentiation, D
– New knowledge comes from differentiating old knowledge,
 Speed of change of D ~ D
– Differentiation continues if knowledge is useful (emotional)
 Speed of change of D ~ - S
– Differentiation stops if knowledge is “too” emotional
 Speed of change of D ~ 0, if S id “too large”
• Synthesis, S
– Emotional value of knowledge
– Emotions per concept diminish with more concepts
 Speed of change of S ~ -D
– Synthesis grows in the hierarchy (H)
 Speed of change of S ~ H
16-Sep-05
104
CULTURAL STATES
CAN BE MEASURED

Differentiation
– Number of words

Synthesis
– Emotions per word

Hierarchy
– Social, political, cultural, language

“Material” measures
– Demographics, geopolitics, natural resources…
– Ignore for a moment
MODELING “spiritual aspects” of
CULTURAL EVOLUTION
 Differentiation,
synthesis,
hierarchy
dD/dt = a D G(S);
dS/dt = -bD + dH
H
= H0 + e*t
G(S) = (S - S0) exp(-(S-S0) / S1)
KNOWLEDGE-ACQUIRING
CULTURE
Average synthesis, high differentiation; oscillating solution
Knowledge accumulates; no stability
TRADITIONAL CULTURE
High synthesis, low differentiation; stable solution
Stagnation, stability increases
TERRORIST’S CONSCIOUSNESS

Ancient consciousness was “fused”
– Concepts, emotions, and actions were one
• Undifferentiated, fuzzy psychic structures
– Psychic conflicts were unconscious and projected outside
• Gods, other tribes, other people

Complexity of today’s world is “too much” for many
– Evolution of culture and differentiation
• Internalization of conflicts: too difficult
– Reaction: relapse into fused consciousness
• Undifferentiated, fuzzy, but simple and synthetic

The recent terrorist’s consciousness is “fused”
– European terrorists in the 19th century
– Fascists and communists in the 20th century
– Current Moslem terrorists
INTERACTING CULTURES
Early: Dynamic culture affects traditional culture, no reciprocity
2) Later: 2 dynamic cultures stabilize each other
1)
Knowledge accumulation + stability
FUTURE SIMULATIONS OF
EVOLUTION

Genetic evolution simulations (1980s - )
– Used basic genetic mechanisms
– Artificial Life, evolution models: Bak and Sneppen, Tierra, Avida

Evolution of cultural concepts
– Genes vs. memes (cultural concepts)
– Evolution of concepts vs. evolution of genes
• Culture evolves much faster than genetic evolution
• Human culture is <10,000 years, likely, no genetic evolution (?)
–
–
–
–
Evolution of languages
Concepts evolve from fuzzy to crisp and specific
Concepts evolve into a hierarchy
Concepts are propagated through language
MECHANISMS OF
CONCEPT EVOLUTION

Differentiation, synthesis, and language transmission

Differentiation
– Fuzzy contents become detail and clear
– A priori models, archetypes are closely connected to unconscious needs, to emotions,
to behavior
• Concepts have meanings

Cultural and generational propagation of concepts through language
– Integration of language and cognition is not perfect
• Language instinct is separate from knowledge instinct

Propagation of concepts through language
– A newborn child encounters highly-developed language
– Synthesis: cognitive and language models {MC, ML} are connected individually
– No guarantee that language model-concepts are properly integrated with the adequate
cognitive model-concepts in every individual
• And we know this imperfection occurs in real life
• Meanings might be lost
• Some people speak well, but do not quite understand and v.v.
SPLIT BETWEEN
CONCEPTUAL AND EMOTIONAL

Dissociation between language and cognition
– Might prevail for the entire culture

Words maintain their “formal” meanings
– Relationships to other words

Words loose their “real” meanings
– Connection to cognition, to unconscious and emotions

Conceptual and emotional dissociate
– Concepts are sophisticated but “un-emotional”
– Language is easy to use to say “smart” things
• but they are meaningless, unrelated to instinctual life
CREATIVITY

At the border of conscious and unconscious

Archetypes should be connected to consciousness
– To be useful for cognition

Collective concepts–language should be connected to
– The wealth of conceptual knowledge (other concepts)
– Unconscious and emotions

Creativity in everyday life and in high art
– Connects conscious and unconscious

Conscious-Unconcious ≠ Emotional-Conceptual
– Different slicing of the psyche
DISINTEGRATION OF CULTURES
 Split
between conceptual and emotional
– When important concepts are severed from emotions
– There is nothing to sacrifice one’s life for
 Split
may dominate the entire culture
– Occurs periodically throughout history
– Was a mechanism of decay of old civilizations
– Old cultures grew sophisticated and refined but got severed from
instinctual sources of life
• Ancient Acadians, Babylonians, Egyptians, Greeks, Romans…
– New cultures (“barbarians”) were not refined, but vigorous
• Their simple concepts were strongly linked to instincts, “fused”
EMOTIONS IN LANGUAGE
• Animal vocal tract
– controlled by old (limbic) emotional system
– involuntary
• Human vocal tract
– controlled by two emotional centers: limbic and cortex
– Involuntary and voluntary
• Human voice determines emotional content of cultures
– Emotionality of language is in its sound: melody of speech
16-Sep-05
116
LANGUAGE:
EMOTIONS AND CONCEPTS
• Conceptual content of culture: words, phrases
–Easily borrowed among cultures
• Emotional content of culture
–In voice sound (melody of speech)
–Determined by grammar
–Cannot be borrowed among cultures
• English language (Diff. > Synthesis)
–Weak connection between conceptual and emotional (since 15 c)
–Pragmatic, high culture, but may lead to identity crisis
• Arabic language (Synthesis > Diff.)
–Strong connection between conceptual and emotional
–Cultural immobility, but strong feel of identity (synthesis)
16-Sep-05
117
SYNTHESIS
 People cannot live without
– Feel of wholeness
– Meaning and purpose of life
synthesis
 Creativity, life, and vigor requires synthesis
– Emotional and conceptual, conscious and unconscious
– In every individual
• Lost synthesis and meaning leads to drugs and personal disintegration
– In the entire culture
• Lost synthesis and meaning leads to cultural disintegration
 Historical evolution of consciousness
– From primitive, fuzzy, and fused to differentiated and refined
– Interrupted when synthesis is lost
– Differentiation and synthesis are in opposition, still both are required
– Example: religion vs. science
• Religious synthesis empowered human mind (15 c) and created conditions for development of
science (17 c)
• Scientific differentiation destroyed religious synthesis
• Evolution of our culture requires overcoming this split, and it is up to us, scientists and engineers
 Individual consciousness
– Combining differentiation and synthesis
– Jung called individuation, “the highest purpose in every life”
MECHANISM OF SYNTHESIS
 Integrating the entire wealth of knowledge
– Undifferentiated knowledge instinct “likelihood maximization”
• Global similarity
– Differentiated knowledge instinct
• Highly-valued concepts
• Local similarity among concepts
 Highly valued concepts acquire properties of instincts
– Affect adaptation, differentiation, and cognition of other concepts
– Generate emotions, which relate concepts to each other
 Differentiated knowledge instinct
– An emergent hierarchy of concept-values
– Differentiated emotions connect diverse concepts
– We need huge diversity of emotions to integrate conceptual
knowledge => synthesis
DIFFERENTIATION OF EMOTIONS

Historical evolution of human consciousness
– Animal calls are undifferentiated
• concept-emotion-communication-action
– Ancient languages are highly emotional (Humboldt, LevyBrule)

Language evolved toward unemotional differentiation
– Nevertheless, most conversations have little conceptual
content
• From villages to corporate board-rooms, people talk to
establish emotional contact
• Human speech affects recent and ancient emotional centers
– Inflections and prosody of human voice appeals directly to
ancient undifferentiated emotional mechanisms
– Accelerates differentiation, but endangers synthesis

Music evolved toward differentiation of emotions
– At once: creates tensions and wholeness in human soul
ROLE OF MUSIC IN EVOLUTION
OF THE MIND

Melody of human voice contains vital information
– About people’s world views and mutual compatibility
– Exploits mechanical properties of human inner ear
• Consonances and dissonances

Tonal system evolved (14th to 19th c.) for
– Differentiation of emotions
– Synthesis of conceptual and emotional
– Bach integrates personal concerns with “the highest”

Pop-song is a mechanism of synthesis
–
–
–
–

Integrates conceptual (lyric) and emotional (melody)
Also, differentiates emotions
Bach concerns are too complex for many everyday needs
Human consciousness requires synthesis immediately
Rap is a simplified, but powerful mechanism of synthesis
– Exactly like ancient Greek dithyrambs of Dionysian cult
EVOLUTION vs.
INTELLIGENT DESIGN
• Science
causal mechanisms
• Religion
teleology (purpose)
• Wrong!
– In basic physics causality and teleology are equivalent
– The principle of minimal energy is teleological
– More general, min. action (min. Lagrangian)
• The knowledge instinct
– Teleological principle in evolution of the mind and culture
– Dynamic logic is a causal law equivalent to the KI
– Causality and teleology are equivalent
16-Sep-05
122
DL/NMF THEORY OF THE MIND
CONFIRMED IN EXPERIMENTS

Neural mechanisms
cognition
of
perception
– bottom-up and top-down signals
– matching

Adaptive mechanisms
– synaptic connections

Dynamics of vagueness-fuzziness
– From vague to crisp

Unconscious - Conscious
– Corresponds to vague-crisp
and
FUTURE DIRECTIONS
research, predictions and testing of NMF/DL
• Mathematical development
– DL in Hierarchy, mechanisms of Synthesis
– Add emotions to computer models of language evolution
• Neuro-imaging and psycholinguistic experiments
–
–
–
–
Similarity-KI mechanisms, models
Higher cognitive functions: beautiful, sublime
Language-cognition interaction
Emotionality of various languages
• Multi-agent simulations
– Joint evolution of language and cognition
• Historical linguistics and anthropology
– Concurrent evolution of languages, consciousness, and cultures
• Music
– Direct effect on emotions, mechanism of synthesis
– Concurrent evolution of music, consciousness, and cultures
• Improve human condition around the globe
– Diagnose cultural states (up, down, stagnation), measure D, S, H
– Develop predictive cultural models, integrate spiritual and material causes
– Identify language and music effects that can advance consciousness and reduce tensions
• Robotic systems, Semantic Web, Cyberspace, and Interactive environment
–
–
–
–
–
Adaptive ontologies
Learn from human users
Acquire cultural knowledge and enable culturally-sensitive communication
Help us understand ourselves
Help us understand each other
124
THE END

Can we describe mathematically and
build a simulation model for evolution
of all of these abilities?

Can we build robotic systems
understanding us, collaborating with
us?
PUBLICATIONS
330publications
OXFORD UNIVERSITY PRESS
(2000; 3rd printing)
2007
Neurodynamics of High
Cognitive Functions
with Prof. Kozma, Springer
Sapient Systems
with Prof. Mayorga, Springer
2010:
Dynamic Logic
With Dr. Deming, Springer
BACK UP
Why
the mind and emotions?
NMF
vs. inverse problems
NMF
vs. biology of eye
Cognition
and understanding
Intelligent
agents
The
mind: Plato, Antisthenes, Aristotle, Occam, Locke, Kant, Jung, Chomsky,
Grossberg
DL,
KI, and Buddhism
Consciousness,
aesthetic emotions