BIG DATA ANALYTICS, MACHINE LEARNING COGNITIVE

ALGORITHMS, AND THE MIND

Prof. Leonid PerlovskyNortheastern University, lperl@rcn.com

Tutorial, INNS Big Data

8 Aug 2015

OUTLINE

• The fundamental principles of the mind-brain - The mind is more powerful than standard algorithms- Can we learn from the mind?

• Mathematical models and experiments- Big Data in “simple” perception, concepts, instincts, emotions- Big Data in learning situations, hierarchy

• Cognitive algorithms and engineering applications- Big Data in cybersecurity, gene-phenotype associations, medical

applications to disease diagnostics, financial predictions, data mining in distributed data bases

• Mind higher abilities, models and experiments- language, cognition, intuitions, conscious and unconscious,

abilities for symbols, functions of the beautiful and musical emotions

• Future research directions

MIND FUNDAMENTAL PRINCIPLES

• Mechanisms of - Instincts, emotions, concepts- Hierarchy

Bottom-up and Top-down signals

• Higher emotions and cognition- The knowledge instinct- Abstract concepts- Beautiful

• Language and cognition- Interaction between L & C- Emotions of prosody connect L & C- Music emotions

Overcome cognitive dissonance, enable accumulating knowledgeUnify psyche divided by L

• Few principles explain much about the mind

MATHEMATICAL MODEL OF CONCEPTS

•Concepts are neural representations (memories)

•Perception: match memories to sensor patterns

•Mathematics: dynamic logic (DL)- DL is a process-logic, “from vague to crisp”- Vague representations match visual perceptions

•Experimental proof- Imagine an object (with closed eyes), it is vague- Open eyes, crisp perception takes 0.6 sec- M. Bar et al, 2006, PNAS; fMRI experiments at Harvard Brain Imaging Center;

- vague ~ unconscious

DYNAMIC LOGIC (DL)

•Mathematical models of mind since the 1950s failed - Artificial intelligence, pattern recognition, neural networks…

•Reason: Combinatorial Complexity (CC) of matching memories and sensor patterns

- More computations than the size of the Universe

•CC is equivalent to Gödelian incompleteness in a finite system

- Logic is the reason for failures

•DL, vague-to-crisp processes, eliminates CC

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DYNAMIC LOGIC ILLUSTRATIONperception / detection of objects below noise

CC, unsolvable for decades, Big Data in “simple” perceptionS/N ratio improved by 100 times

S/N improvement x 70

0 1 kmCross-Range

Ra

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e1

km0

(a)TrueTracks

b

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Initial state of model 2 iterations

5 iterations 9 iterations 12 iterations Converged state

TRACKING OF MOVING OBJECTS BELOW NOISE

INTEGRATE SIGNALS FROM 3 SENSORS, #1 (of 3) (unsolvable since 1970s)

INTEGRATE SIGNALS FROM 3 SENSORSSensor #2 (of 3)

INTEGRATE SIGNALS FROM 3 SENSORSSensor #3 (of 3)

SITUATIONS (“real” Big Data)RANDOM ORDER

obje

cts

Situations (random)

each situation is a collection of objects only few are relevant

LEARNING SITUATIONS SORTED DATA

obje

cts

Situations (sorted)

the DL algorithm found situations and relevant objects

unsolvable since the 1970s

SITUATION LEARNING: ERRORS

convergence in 3 iterations

FINANCIAL MARKET PREDICITION

Recommended Portfolios vs. Marketsportfolio gains: rec-sp = 6.2%, rec-nq = 7.4% (vs. markets sp = 1.8%, nq = -4.2% loss)

risk measures: gain/st.dev = 3.6, 4.0 (vs mkts 0.35, -.45), average exosure = 14% (vs. mkt 100%)

94.00%

96.00%

98.00%

100.00%

102.00%

104.00%

106.00%

108.00%

110.00%

12/30/2005 1/29/2006 3/1/2006 3/31/2006 5/1/2006 5/31/2006 7/1/2006

date

cu

mu

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ain

% (

VA

MI)

SP weeklyVAMI

NQ weeklyVAMI

RecSP+T weeklyVAMI

RecNQ+T weeklyVAMI

COGNITIVE ALGORITHMS AND ENGINEERING APPLICATIONS

•Engineering problems have been solved, unsolvable for decades:

• Patterns under noise• Tracking moving objects under noise• Integrating signals from multiple sensors• “Real” Big data• Learning and recognition of situations• Financial predictions• Data mining in disparate data sources• NEXT (“real” Big data)• Correlation of genes and diseases beyond 1 gene• Adaptive cybersecurity• Evolution and languages and cultures

CORRELATING GENES AND DISEASES

•Whole genome data studies - hundreds of thousands SNPs- many diseases have been correlated to genes- Still, in most successful correlations only few percents are

explained, even when the disease is known to be genetic, why?

•Several genes might be responsible - How to find which genes relate to which disease? - Sorting combinations => CC- Find “situations” of genes using DL algorithm

sorted messagesby types of malware

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s1

411 119,610

ADAPTIVE CYBERSECURITY

MATHEMATICAL MODELS OF THE MIND AND COGNITIVE ALGORITHMS

MATHEMATICAL MODELS OF INSTINCTS AND EMOTIONS

• Instincts- Sensors measuring vital parameters- Indicating safe range- E.g. sugar level in blood

•Emotions - When unsafe, neural signals are sent to decision regions- These neural signals are felt as emotions - Low sugar level in blood is felt as emotion of hunger

•Grossberg and Levine, 1987

KNOWLEDGE INSTINCT (KI)

•Adequate representations are necessary for survival

•KI drives to improve representations (knowledge)

•KI mathematical model - Maximize similarity between concepts and percepts- Cannot be solved w/o DL

•KI satisfaction – aesthetic emotions- related to knowledge not to bodily needs (“spiritual”) - not only in museum, but in every act of perception

•Experimental proof: these emotions exist and different from other emotions (Cabanac et al, 2010)

HIERARCHY OF THE MIND

situations

objects

abstract ideas

sensory-motor signals

…

Interacting top-down and bottom-up signals

• Concepts at every level unify lower-level concepts

The “highest model”

HIERARCHY OF THE MIND

situations

objects

abstract ideas

sensory-motor signals

…

• Higher level abstract concepts are - vague and unconscious- only understood due to language

• Concepts at every level unify lower-level concepts

The “highest model”

HIERARCHY OF THE MIND

situations

objects

abstract ideas

sensory-motor signals

…

• Concepts at the top unify entire life experience-meaning of life-understanding - satisfaction of KI -emotion of the beautiful

• Concepts of behavior- emotion of the sublime

• Higher level abstract concepts are - vague and unconscious- only understood due to language

• Concepts at every level unify lower-level concepts

The “highest model”

LANGUAGE AND COGNITION DUAL HIERARCHY

situations

objects

abstract ideas

COGNITION

phrases

words

abstract words/phrases

LANGUAGE

sensory-motor signals

…

SURROUNDINGLANGUAGE

words for objects

phrases for situations

language sounds

language descriptions of abstract thoughts

… …

sensory-motor language models

• Language is crisp and

conscious w/o life experience, because it exists around ready-made

• Cognition cannot be learned w/o language

(1) abstract concepts do not exist in the world

(2) cognition is only grounded in experience at the very bottom

•Experimental proof (Binder 2006): concrete words -> language & cognition, abstract words -> only language brain

•We also need emotional motivation

EMOTIONS OF THE BEAUTIFUL

• The highest aesthetic emotion, beautiful - improvement of the highest concepts (at the top of

the hierarchy)- feel emotion of beautiful

• Beautiful “reminds” us of our purposiveness- the “top” concepts unify all our experience- vague and unconscious- perceived as our purpose (“aimless purposiveness”)- scientific beauty – valid and general theory (or

experiment)

• Beauty is separate from sex (different instincts)- sex uses all our abilities, including beauty

• Spiritually sublime emotions- similar to the beautiful, but related to behavior - how to make beauty a part of your life, how to make life meaningful

MUSICAL EMOTIONS(C. Darwin: “the greatest mystery”)

• Knowledge contradict to instincts and other knowledge- Contradictions are unpleasant and usually discarded- Ancient Greeks new this 2600 years ago, Aesop: The Fox and the Grape- Fox cannot get the Grape, so – “the grape is sour”- People discard contradictions

• Cognitive dissonance, CD - Discomfort due to holding contradictory knowledge- Contradictions are unpleasant and discarded- Every new word would be discarded before proved useful- For language to evolve, every word need a “sweetener”

• Emotions of speech prosody (melody of intonation)- A motivation to overcome CD- Originally language was like songs- Connects language and cognition

MUSICAL EMOTIONS(C. Darwin: “the greatest mystery”)

• Musical emotions help to- Overcome CD, and create unity of mind- Hold contradictory knowledge- E.g. CD between trust, love, betrayal are addressed by many

songs

• Why musical emotions are so powerful?- Knowledge contradicts instincts and other knowledge- We live in these contradictions- Music enables human evolution

• Experimental proof (Masataka et al 2012; Cabanac et al 2013)- Students at exams devote less time to difficult questions- To avoid stress, grades go down- With music in the background – more time to difficult questions- Grades go up

FUTURE DIRECTIONS• Mathematical development and simulation tests

–DL in Hierarchy, Unifying mechanisms (synthesis)–Add prosody emotions to computer models of language & cognition evolution –Evolution of music–Joint evolution of language, cognition, music, and cultures

• Psycholinguistic and cognitive experiments–Measure emotionality of various languages–Measure musical emotions

• Cultural evolution – study effects of languages and music

• 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

• Human-computer interaction, robotics–Acquire cultural knowledge–Enable culturally-sensitive communication–Help us understand ourselves–Help us understand each other

MATHEMATICAL DETAILS AND OTHER TOPICS

• Math. Model of the Mind (3)

• Aristotle, Gödel, & Alexander the Great (1)

• Intuition (2)

• Evolution of Music and Consciousness (2)

• Evolution of Culture (6)

• Why Adam was expelled from paradise? (1)

• Terrorist’s consciousness (1)

• Future Directions (1)

MATH. MODEL OF TWO LAYERS

• The knowledge instinct = maximize similarity between signals and concepts (BU & TD)

• Similarity between signals and concepts, 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 signals and concepts (LOGIC)

n

m

DYNAMIC LOGIC (DL) non-combinatorial solution

• Start with a set of signals and unknown concepts- any parameter values Sm

- associate concepts with their contents (signals)

- (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]

(a determines speed of convergence)

- learn signal-contents of concepts

• Continue iterations (1)-(2). Theorem: DL converges- similarity increases on each iteration- aesthetic emotions are positive during learning

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n

MATH. MODEL OF LANGUAGE, COGNITION, & HIERARCHY

• How language and cognition interact- A concept m has vague cognitive and crisp language parts

Mm = { Mmcognitive, Mm

language };

- This model requires DL

• Ontogenetic development- Before 1-3 y.a. both representations are vague- After 5 y.a. language is crisp, cognitive rep. are learned from

vague to crisp guided by language

• Hierarchy, a product of similarity over layers, h

- L = l hh

ARISTOTLE VS. GÖDEL logic, forms, and DL

• 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)

• From Boole to Russell: formalization of logic• Logicians eliminated from logic uncertainty of language• Hilbert (1900s): formalize rules of mathematical proofs

• Gödel (the 1930s) • Logic is not consistent

• Any statement can be proven true and false

• Aristotle and Alexander the Great• “Nobody will understand”

INTUITION

• Vague states of incomplete thinking-feelings • vague partly-conscious representations• conceptual and emotional contents are

undifferentiated

• Artistic intuition • composer: sounds and their relations to psyche• painter: colors, shapes and relations to psyche• writer: words and their relations to psyche

INTUITION: Physics vs. Math.

• Mathematical intuition is about- Structure and consistency within the theory

• 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 the knowledge

instinctthe feeling of purpose in the world

DIFFERENTIATION AND SYNTHESIS

• The knowledge instinct in the mental hierarchy–Two mechanisms: differentiation and synthesis

• Differentiation –Down the hierarchy: more detailed concepts–Separate concepts from emotions

• Synthesis –Up the hierarchy, more unity, concepts closer to emotions–Connect knowledge to life–Connect concepts and emotions

Connect language and cognitionMeaning: concepts acquire meaning at the next level

EVOLUTION OF MUSIC AND CONSCIOUSNESS

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– Style and content like ancient Greek dithyrambs of Dionysian cult

EMOTIONALITY OF LANGUAGEAND CULTURE

•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 loss of values and identity crisis

•Arabic language (Synthesis > Diff.)–Strong connection between conceptual and emotional–Cultural immobility, but strong feel of identity (synthesis)

CULTURAL EVOLUTION HOW TO STUDY?

• Large-scale simulations of systems of autonomous agents, each agent with cognition and language- It is a significant effort, several Ph.D. dissertations

• “Mean-field theory”- A simplified mathematical solution- Following physics many-body problems

MEAN FIELD THEORY OF CULTURAL EVOLUTION

• Differentiation, D, synthesis, S, hierarchy, H

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

• dS/dt = -bD + dH

• H = H0 + e*t,

• Only few solutions

DYNAMIC CULTURE

Average synthesis, high differentiation; oscillating solutionKnowledge accumulates; no stability

TRADITIONAL CULTURE

High synthesis, low differentiation; stable solutionStagnation, stability increases

INTERACTING CULTURES

• Two cultures– dynamic and traditional– slow exchange by D and S

dDk/dt = ak Dk G(Sk) + xkDk

dSk/dt = -bkDk + dkHk + ykSk

Hk = H0k + ek*t

INTERACTING CULTURES

Knowledge accumulation + stability

1) Early: Dynamic culture affects traditional culture, no reciprocity2) Later: 2 dynamic cultures stabilize each other

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 themselvesAdam wanted ready-made knowledge Thinking for oneself is difficult (this is our predicament)

• Today we can approach this scientifically – Rarely we use the KI (at higher levels of the hierarchy)– 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

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 in the 20th century• Current terrorists

FUTURE DIRECTIONS• Mathematical development, and simulation tests

–DL in Hierarchy, mechanisms of Synthesis –Add prosody emotions to computer models of language & cognition evolution –Evolution of music–Joint evolution of language, cognition, music, and cultures

• Psycholinguistic and cognitive tests–Measure emotionality of various languages in labs –Measure musical emotions

• Cultural evolution – study effects of languages and music

• 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

• Human-computer interaction, robotics–Acquire cultural knowledge–Enable culturally-sensitive communication–Help us understand ourselves–Help us understand each other