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COGNITIVE COMPUTATIONAL INTELLIGENCE for data mining, financial prediction, tracking, fusion, language, cognition, and cultural evolution Leonid Perlovsky.

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Presentation on theme: "COGNITIVE COMPUTATIONAL INTELLIGENCE for data mining, financial prediction, tracking, fusion, language, cognition, and cultural evolution Leonid Perlovsky."— Presentation transcript:

1 COGNITIVE COMPUTATIONAL INTELLIGENCE for data mining, financial prediction, tracking, fusion, language, cognition, and cultural evolution Leonid Perlovsky Visiting Scholar, Harvard University Technical Advisor, AFRL IASTED CI 2009 Honolulu, HI 1:30 – 5:30 pm, Aug. 19

2 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

3 INTRODUCTION The mind

4 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]

5 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: ~ 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

6 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

7 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

8 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

9 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 –This number ~ the size of the Universe > all the events in the Universe during its entire life

10 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 COMBINATORIAL COMPLEXITY SINCE the 1950s

11 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 )

12 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

13 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

14 ARISTOTLE VS. G Ö DEL 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

15 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

16 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

17 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

18 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]

19 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

20 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) M m (S m,n), parameters S m, m = 1, …; –Models predict expected signals from objects Goal: learn object-models and match to signals (knowledge instinct)

21 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) | M m (S m,n)) –l (x(n) | M m (S m,n)) is a conditional similarity for x(n) given m {n} are not independent, M(n) may depend on n’ CC: L contains M N items: all associations of pixels and models (LOGIC)

22 SIMILARITY Similarity as likelihood –l (x(n) | M m (S m,n)) = pdf(x(n) | M m (S m,n)), –a conditional pdf for x(n) given m –e.g., Gaussian pdf(X(n)|m) = G(X(n)|M m,C m ) = 2  -d/2 detC m -1/2 exp(-D mn T C m -1 D mn /2); D mn = X(n) – M m (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) | M m (S m,n)) = abs(x(n))*pdf(x(n) | M m (S m,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)|M m,C m ) –Use for continuous data (signals, images)

23 DYNAMIC LOGIC (DL) non-combinatorial solution Start with a set of signals and unknown object-models –any parameter values S m –associate signals (n) and models (m) –(1)f(m|n) = r(m) l (n|m) / r(m') l (n|m') Improve parameter estimation –(2)S m = S m +  f(m|n) [  ln l (n|m)/  M m ]*[  M m /  S m ] Continue iterations (1)-(2). Theorem: NMF is a converging system - similarity increases on each iteration - aesthetic emotion is positive during learning

24 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

25 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

26 APPLICATION 1 – CLUSTERING (data mining) Find “natural” groups or clusters in data Use Gaussian pdf and simple models l (n|m) = 2  -d/2 detC m -1/2 exp(-D mn T C m -1 D mn /2); D mn = X(n) – M m (n) M m (n) = M m ; each model has just 1 parameter, S m = M m –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)/  M m =  (-D mn T C m -1 D mn ) /  M m = C m -1 D mn + D mn T C m -1 = 2 C m -1 D mn, (C is symmetric) M m = M m +  f(m|n) C m -1 D mn … In this case, even simpler equations can be derived samples in class m: N m = f(m|n); N = N m rates (priors): r m = N m / N means:M m = f(m|n) X(n) / N m covariances:C m = f(m|n) Dmn * Dmn T / N m - simple interpretation: N m, M m, C m 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

27 Example 2: GMTI Tracking and Detection Below Clutter 18 dB improvement 01 km Cross-Range Range 1 km 0 (a) True Tracks b Range 1 km 0 Initial state of model2 iterations 5 iterations9 iterations12 iterations Converged state DL starts with uncertain knowledge and converges rapidly on exact solution

28 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

29 TRACKING EXAMPLE complexity and improvement Technical difficulty -Signal/Clutter = - 3 dB, standard tracking requirements 15 dB -Computations, standard hypothesis testing ~ , unsolvable Solved by Dynamic Logic -Computations: 2x10 7 -Improvement 18 dB

30 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

31 APPLICATION 3 FINDING PATTERNS IN IMAGES

32 IMAGE PATTERN BELOW NOISE Object Image y Object Image + Clutter y x x

33 Multiple Hypothesis Testing (MHT) approach: try all possible ways of fitting model to the data PRIOR STATE-OF-THE-ART Computational complexity For a 100 x 100 pixel image: Number of Objects Number of Computations

34 NMF MODELS Information similarity measure ln l (x(n) | M m (S m,n)) = abs(x(n))*ln pdf(x(n) | M m (S m, n)) n = (n x,n y ) Clutter concept-model (m=1) pdf(X(n)|1) = r 1 Object concept-model (m=2… ) pdf(x(n) | M m (S m, n)) = r 2 G(X(n)|M m (n,k),C m ) M m (n,k) = n 0 + a*(k 2,k); (note: k, K require no estimation)

35 ONE PATTERN BELOW CLUTTER Y X SNR = -2.0 dB

36 DYNAMIC LOGIC WORKING y (m) Range x (m) Cross-range 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

37 Three objects in noise object 1 object 2 object 3 SCR dB dB dB MULTIPLE PATTERNS BELOW CLUTTER y y x x 3 Object Image + Clutter3 Object Image

38 a b c d fe h g IMAGE PATTERNS BELOW CLUTTER (dynamic logic iterations see note-text) Logical complexity = M N = , unsolvable; DL complexity = 10 7 S/C improvement ~ 16 dB

39 MULTIPLE TARGET DETECTION DL WORKING EXAMPLE x y 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

40 COMPUTATIONAL REQUIREMENTS COMPARED Dynamic Logic (DL) vs. Classical State-of-the-art Multiple Hypothesis Testing (MHT) Based on 100 x 100 pixel image 10 8 vs x10 8 vs x10 8 vs Number of Objects Number of Computations DL vs. MHT Previously un-computable ( ), can now be computed ( 3x10 8 ) This pertains to many complex information-finding problems

41 APPLICATION 4 SENSOR FUSION Concurrent fusion, navigation, and detection below clutter

42 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

43 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 M m (n) -> M m (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

44 Source: UAS Roadmap UNCLASSIFIED

45 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

46 GEOMETRY: MULTIPLE TARGETS, MULTIPLE UAVS UAV 1 X 1 = X 01 + V 1 t X 1 =(X 1,Y 1,Z 1 ) UAV m X m =(X m,Y m,Z m ) X m = X 0m + V m t

47 CONDITIONAL SIMILARITIES (pdf) FOR TARGET k Data from UAV m, sample number n, where β nm = signature position and f nm = 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 β nm, Gaussian in f nm.

48 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) UAV parameterstarget parameters classification feature parameters

49 Concurrent Parameter Estimation / Signature Association (NMF iterations) Note1: bracket notation Note2: proven to converge (e.g. EM algorithm) Note 3: Minimum MSE solution incorporates GPS measurements 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)

50 Sensor 1 (of 3): Models Evolve to Locate Target Tracks in Image Data

51 Sensor 2 (of 3): Models Evolve to Locate Target Tracks in Image Data

52 Sensor 3 (of 3): Models Evolve to Locate Target Tracks in Image Data

53 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)

54 Model Parameters Iteratively Adapt to Locate the Targets Error vs. iteration# (4 targets) Estimated Target Position vs. iteration# (4 targets)

55 Parameter Estimation Errors Decrease with Increasing Number of UAVs in the Swarm Error falls off as ~ 1/√M, where M = # UAVs in the swarm (Note: Results are based upon Monte Carlo simulations with synthetic data) Error in Parameter Estimates vs. clutter level and # of UAVs in the swarm Target position UAV position

56 APPLICATION 5 DETECTION IN SEQUENCES OF IMAGES

57 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

58 DETECTION IN IMAGE SEQUENCE TEN ROTATION FRAMES WERE USED Iteration 10Iteration 100Iteration 400 Iteration 600 Compare with Measured Image (w/o noise) 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.

59 TARGET SIGNATURE Extracted from low noise image Extracted from high noise image

60 APPLICATION 6 Radar Imaging through walls - Inverse scattering problem - Standard radar imaging algorithms (SAR) do not work because of multi- paths, refractions, clutter

61 SCENARIO

62 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

63 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

64 CLASSICAL METHODOLGY no closure Result: Conceptual objects signals Input: World/scene Sensors / Effectors MODELS/templates objects, sensors physical models Recognition

65 NMF: closure basic two-layer hierarchy: signals and concepts Result: Conceptual objects signals Input: World/scene Sensors / Effectors Correspondence / Similarity measures MODELS objects, sensors physical models Attention / Action signals Sim.signals

66 APPLICATION 7 Prediction - Financial prediction

67 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,, and x-y covariance matrix C –A = C yx C xx -1 ; b = - A 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*d x+y 3 data points, or more

68 NMF/DL PREDICTION General non-linear regression (GNLR) –y(x) = f(m|n) y m (x) = f(m|n) ( A m x+b m ) –A m and b m 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

69 FINANCIAL PREDICTION Efficient Market Hypothesis Efficient market hypothesis, s trong: –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)

70 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)

71 FINANCIAL MARKET PREDICITION

72 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

73 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…

74 OUTLINE Cognition, complexity, and logic The Mind and Knowledge Instinct Higher models and Language Integration of cognition and language Higher Cognitive Functions Future directions

75 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

76 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?

77 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 o i, w i –model-set: M m ({o i }) = (Leonid, chair, sit) – how to take derivatives? Models of sets –l (x(n) | M m (S m,n)) = p mi x(ni) (1 -p mi (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

78 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%)

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

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

81 DL LEARNING (in 3 iterations)

82 ERRORS

83 ASSOCIATIONS f(m|n)* f(m’|n), f(m|n) f(m’|n), m=true, m’=computed

84 OUTLINE Cognition, complexity, and logic The Mind and Knowledge Instinct Language Integration of cognition and language Higher Cognitive Functions Future directions

85 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

86 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

87 INTEGRATED LANGUAGE AND COGNITION Language and cognition: the dual model –Every model m has linguistic and cognitive-sensory parts M m = { M m cognitive,M m language }; –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)

88 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

89 OUTLINE Cognition, complexity, and logic The Mind and Knowledge Instinct Language Integration of cognition and language Higher Cognitive Functions Future directions

90 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 Similarity measures Models Action/Adaptation Models Action/Adaptation Similarity measures objects situations meanings

91 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

92 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

93 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

94 OUTLINE Cognition, complexity, and logic The Mind and Knowledge Instinct Language Integration of cognition and language Higher Cognitive Functions Future directions

95 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, 12 th 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

96 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

97 SYMBOL “A most misused word in our culture” (T. Deacon) Cultural and religious symbols –Provoke wars and make piece Traffic Signs

98 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

99 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”

100 SYMBOLIC ABILITY Integrated hierarchies of Cognition and Language –High level cognition is only possible due to language –Much of cognition if vague and unconscious Similarity Action Similarity Action Similarity cognition language M M M M grounded in real-world objects grounded in language

101 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

102 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

103 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

104 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

105 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

106 MODELING “spiritual aspects” of CULTURAL 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

107 KNOWLEDGE-ACQUIRING CULTURE Average synthesis, high differentiation; oscillating solution Knowledge accumulates; no stability

108 TRADITIONAL CULTURE High synthesis, low differentiation; stable solution Stagnation, stability increases

109 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 19 th century –Fascists and communists in the 20 th century –Current Moslem terrorists

110 INTERACTING CULTURES Knowledge accumulation + stability 1) Early: Dynamic culture affects traditional culture, no reciprocity 2) Later: 2 dynamic cultures stabilize each other

111 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

112 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 {M C, M L } 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.

113 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

114 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

115 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 ”

116 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

117 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

118 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”

119 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

120 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

121 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 (14 th to 19 th 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

122 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

123 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

124 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

125 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?

126 PUBLICATIONS 330publications OXFORD UNIVERSITY PRESS (2000; 3 rd printing) 2007 Neurodynamics of High Cognitive Functions with Prof. Kozma, Springer Sapient Systems with Prof. Mayorga, Springer 2010: Dynamic Logic With Dr. Deming, Springer

127 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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