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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.

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slide1
COGNITIVE COMPUTATIONAL INTELLIGENCEfordata 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
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
INTRODUCTION

The mind

physics and mathematics of the mind range of concepts
PHYSICS AND MATHEMATICS OF THE MINDRANGE 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
GENETIC ARGUMENTSFOR 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
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
  • 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
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
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
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 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 “law of excluded third”
    • Still, the math. of formal logic
    • Excluded 3rd -> excluded (n+1)
  • 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
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
  • 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 g del logic forms and language
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
outline1
OUTLINE
  • Cognition, complexity, and logic
    • Logic does not work, but the mind does
  • The Mind and Knowledge Instinct
    • Neural Modeling Fields and Dynamic Logic
  • Language
  • Integration of cognition and language
  • Higher Cognitive Functions
  • Future directions
structure of the mind
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
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
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
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
NEURAL MODELING FIELDSbasic 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 instinct1
THE KNOWLEDGE INSTINCT
  • The knowledge instinct = maximize similarity between signals and models
  • Similarity between signals and models, L
    • L = l ({x}) = l (x(n))
    • l (x(n)) = r(m) l (x(n) | Mm(Sm,n))
    • 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
  • 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
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\')
  • Improve parameter estimation
    • (2) Sm = Sm + a f(m|n) [ln l (n|m)/Mm]*[Mm/Sm]
  • Continue iterations (1)-(2). Theorem: NMF is a convergingsystem

- similarity increases on each iteration

- aesthetic emotion is positive during learning

outline2
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
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
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); Dmn = X(n) – Mm(n)

Mm(n) = Mm;each model has just 1 parameter, Sm = Mm

    • This is clustering with Gaussian Mixture Model
  • For complex l(n|m) derivatives can be taken numerically
  • For simple l(n|m) derivatives can be taken manually
    • 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 + DmnTCm-1 = 2 Cm-1 Dmn, (C is symmetric)

Mm = Mm + a f(m|n) Cm-1 Dmn

  • In this case, even simpler equations can be derived

samples in class m: Nm = f(m|n); N = Nm

rates (priors): rm = Nm / N

means: Mm = f(m|n) X(n) / Nm

covariances: Cm = f(m|n) Dmn * DmnT / Nm

- 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
slide27

1 km

(a)

True

Tracks

Range

0

Cross-Range

0

1 km

b

Initial state of model

2 iterations

1 km

Range

0

5 iterations

9 iterations

12 iterations

Converged state

Example 2: GMTI Tracking and Detection

Below Clutter

DL starts with uncertain knowledge and converges rapidly on exact solution

18 dB improvement

slide28

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

slide29

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
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
APPLICATION 3

FINDING PATTERNS IN IMAGES

slide32

IMAGE PATTERN BELOW NOISE

Object Image

Object Image + Clutter

y

y

x

x

slide33

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 ObjectsNumber of Computations

1 1010

2 1020

3 1030

nmf models
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… )

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)

slide36

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

y (m) Range

x (m) Cross-range

slide37

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

3 Object Image + Clutter

y

y

x

x

slide38

b

d

a

c

h

e

f

g

IMAGE PATTERNS BELOW CLUTTER

(dynamic logic iterations see note-text)

Logical complexity = MN = 105000, unsolvable; DL complexity = 107

S/C improvement ~ 16 dB

slide39

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

y

x

slide40

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

2

3

108 vs. 1010

2x108vs. 1020

3x108 vs. 1030

  • Previously un-computable (1030), can now be computed (3x108 )
  • This pertains to many complex information-finding problems
application 4
APPLICATION 4

SENSOR FUSION

Concurrent fusion, navigation, and detection

below clutter

sensor fusion
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 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)
  • Note: this solves the difficult problem of concurrent detection, tracking, and fusion
concurrent navigation fusion and detection
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
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
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:

signature position

where

classification features

Note: Also have a pdf for a single clutter component pdf(wnm| k=0) which is uniform in βnm, Gaussian in fnm.

data model and likelihood similarity

Compute parameters that maximize the log-likelihood

Data Model and Likelihood Similarity

Total pdf of data samples is the summation of conditional pdfs (summation over targets plus clutter)

(mixture model)

classification feature parameters

UAV parameters

target parameters

concurrent parameter estimation signature association nmf iterations
Concurrent Parameter Estimation / Signature Association (NMF iterations)

FIND SOLUTION FOR SET OF “BEST” PARAMETERS BY ITERATING BETWEEN…

Parameter Estimationand Association Probability Estimation (Bayes rule)

(probability that sample wnm was generated by target k)

Note1: bracket notation

Note2: proven to converge (e.g. EM algorithm)

Note 3: Minimum MSE solution incorporates GPS measurements

slide53

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
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
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

UAV position

(Note: Results are based upon Monte Carlo simulations with synthetic data)

Error falls off as ~ 1/√M, where M = # UAVs in the swarm

application 5
APPLICATION 5

DETECTION IN SEQUENCES OF IMAGES

detection in a sequence of images
DETECTION IN A SEQUENCE OF IMAGES

Signature + high noise level (SNR= -6dB)

Signature + low noise level (SNR= 25dB)

signature is present, but is obscured by noise

detection in image sequence ten rotation frames were used
DETECTION IN IMAGE SEQUENCETEN ROTATION FRAMESWERE USED

Iteration 10

Iteration 100

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.

Compare with Measured Image (w/o noise)

Iteration 600

target signature

Extracted from low noise image

Extracted from high noise image

TARGET SIGNATURE
slide60

APPLICATION 6

  • Radar Imaging through walls

- Inverse scattering problem

- Standard radar imaging algorithms (SAR) do not work because of multi-paths, refractions, clutter

radar imaging through walls
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
DYNAMIC LOGIC / NMF

INTEGRATED INFORMATION:

objects; relations;

situations; behavior

Dynamic

Logic

combining

conceptual analysis

with

emotional evaluation

MODELS

- objects

- relations

- situations

- behavioral

Data and

Signals

classical methodolgy no closure
CLASSICAL METHODOLGYno closure

Result: Conceptual objects

MODELS/templates

  • objects, sensors
  • physical models

Recognition

Input: World/scene

signals

Sensors /

Effectors

nmf closure basic two layer hierarchy signals and concepts
NMF: closurebasic two-layer hierarchy: signals and concepts

Result: Conceptual objects

Attention / Action

Correspondence /

Similarity measures

signals Sim.signals

MODELS

  • objects, sensors
  • physical models

signals

Sensors /

Effectors

Input: World/scene

slide66

APPLICATION 7

  • Prediction

- Financial prediction

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
NMF/DL PREDICTION
  • General non-linear regression (GNLR)
    • y(x) = f(m|n) ym(x) = f(m|n) (Amx+bm)
    • Amand bm are estimated similar to A,b in linear regression with the

following change: all (…) are changed into f(m|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
FINANCIAL PREDICTIONEfficient 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
FINANCIAL PREDICTIONBASICS 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)
bioinformatics
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
NMF/DL FOR COGNITIONSUMMARY
  • 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…
outline3
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
LANGUAGE ACQUISITIONAND 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
APPLICATION: SEARCH ENGINEBASED 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
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)) )
  • 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
example1
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%)
slide79

DATA

data samples (horizontal axis) are sorted by situations hence the horizontal lines for repeated objects

slide80

DATA

data samples (horizontal axis) are random as in real life

slide83

ASSOCIATIONS

f(m|n)* f(m’|n),

f(m|n) f(m’|n), m=true, m’=computed

outline4
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
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
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
INTEGRATEDLANGUAGE 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
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
outline5
OUTLINE
  • Cognition, complexity, and logic
  • The Mind and Knowledge Instinct
  • Language
  • Integration of cognition and language
  • Higher Cognitive Functions
  • Future directions
higher cognitive functions

Action/Adaptation

Similarity measures

Models

Action/Adaptation

meanings

Similarity measures

Models

situations

objects

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
beauty
BEAUTY
  • Harmony is an elementary aesthetic emotion
  • The highest forms of aesthetic emotion, beautiful
    • 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
  • Beautiful “reminds” us of our purposiveness
    • 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
  • Beauty is separate from sex, but sex makes use of all our abilities, including beauty
intuition
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
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
outline6
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
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
GOD, SNAKE, and fMRI
  • Majority often make irrational, heuristic choices (CEM-type)
  • Stable 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
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 AND SYMBOLSmathematical 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
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

Action

Action

Similarity

Similarity

grounded in language

Action

Action

Similarity

Similarity

grounded in language

grounded in real-world objects

SYMBOLIC ABILITY
  • Integrated hierarchies of Cognition and Language
    • High level cognition is only possible due to language
    • Much of cognition if vague and unconscious

language

cognition

M

M

M

M

outline7
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
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

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evolution of cultures
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

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dynamics of differentiation and synthesis
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

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cultural states can be measured
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
MODELING “spiritual aspects” ofCULTURAL EVOLUTION
  • Differentiation, synthesis, hierarchy

dD/dt = a D G(S); G(S) = (S - S0) exp(-(S-S0) / S1)

dS/dt = -bD + dH

H = H0 + e*t

knowledge acquiring culture
KNOWLEDGE-ACQUIRING CULTURE

Average synthesis, high differentiation; oscillating solution

Knowledge accumulates; no stability

traditional culture
TRADITIONAL CULTURE

High synthesis, low differentiation; stable solution

Stagnation, stability increases

terrorist s consciousness
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
INTERACTING CULTURES
  • Early: Dynamic culture affects traditional culture, no reciprocity
  • Later: 2 dynamic cultures stabilize each other

Knowledge accumulation + stability

future simulations of evolution
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
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
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
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
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
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

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language emotions and concepts
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)

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synthesis
SYNTHESIS
  • People cannot live without synthesis
    • Feel of wholeness
    • Meaning and purpose of life
  • 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
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
DIFFERENTIATION OF EMOTIONS
  • Historical evolution of human consciousness
    • Animal calls are undifferentiated
      • concept-emotion-communication-action
    • Ancient languages are highly emotional (Humboldt, Levy-Brule)
  • 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
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
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

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dl nmf theory of the mind confirmed in experiments
DL/NMF THEORY OF THE MIND CONFIRMED IN EXPERIMENTS
  • Neural mechanisms of perception and cognition
    • 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
future directions research predictions and testing of nmf dl
FUTURE DIRECTIONSresearch, 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

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the end
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
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
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
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