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Attendee questionnaire • Name • Affiliation/status Area of study/research For each of these subjects: Linguistics (Optimality Theory) Computation (connectionism/neural networks) Philosophy (symbolic/connectionist debate) Psychology (infant phonology) please indicate your relative level of interest (for these lectures) [1 = least, 5 = most] background [1 = none, 5 = expert] Thank you

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  • Attendee questionnaireNameAffiliation/statusArea of study/researchFor each of these subjects:Linguistics (Optimality Theory)Computation (connectionism/neural networks)Philosophy (symbolic/connectionist debate)Psychology (infant phonology)please indicate your relative level ofinterest (for these lectures) [1 = least, 5 = most]background [1 = none, 5 = expert]Thank you

  • Optimality in Cognition and GrammarPaul SmolenskyCognitive Science DepartmentJohns Hopkins University

  • Optimality in Cognition and GrammarPaul Smolensky Cognitive Science Department, Johns Hopkins University

    Plan of lecturesCognitive architectureSymbols and neuronsSymbols in neural networksOptimization in neural networksOptimization in grammar I: HG OTOptimization in grammar II: OTOT in neural networks

  • Cognitive architectureCentral dogma of cognitive science:Cognition is computationBut what type of computation?What exactly is computation, and what work must it do in cognitive science?

  • ComputationFunctions, cognitivePixels objects locations [low- to high-level vision]Sound stream word string [phonetics + ]Word string parse tree [syntax]Underlying form surface form [phonology]petit copain: /ptit + kop/ [p.ti.ko.p]petit ami: /ptit + ami/ [p.ti.ta.mi]Reduction of complex procedures for evaluating functions to combinations of primitive operationsComputational architecture: Operations: primitives + combinatorsData

  • Symbolic ComputationComputational architecture: Operations: primitives + combinatorsData The Pure Symbolic Architecture (PSA)Data: strings, (binary) trees, graphs, OperationsPrimitivesConcatenate (string, tree) = consFirst-member(string); left-subtree(tree) = ex0 CombinatorsComposition: f(x) =def g(h(x)))IF(x = A) THEN ELSE

  • PassiveFew leaders are admired by George admire(George, few leaders)(s) = cons(ex1(ex0(ex1(s))), cons(ex1(ex1(ex1(s))), ex0(s))) But for cognition, need a reduction to a very different computational architecture

  • The cognitive architecture: The connectionist hypothesisRepresentations: Distributed activation patternsPrimitive operations (e.g.)Multiplication of activations by synaptic weightsSummation of weighted activation valuesNon-linear transfer functions Combination: Massive parallelism PDP ComputationAt the lowest computational level of the mind/brain

  • Criticism of PDP (e.g., neuroscientists)

    Much too simple Misguided. Relevant complaint: Much too complex Target of computational reduction must be within the scope of neural computation. Confusion between two questions

  • The cognitive questionfor neuroscienceWhat is the function of each component of the nervous system? Our question is quite different.

  • The neural question for cognitive science

    How are complex cognitive functions computed by a mass of numerical processors like neuronseach very simple, slow, and imprecise relative to the components that have traditionally been used to construct powerful, general-purpose computational systems? How does the structure arise that enables such a medium to achieve cognitive computation?

  • The ICS HypothesisThe Integrated Connectionist/Symbolic Cognitive Architecture (ICS)In higher cognitive domains, representations and fuctions are well approximated by symbolic computationThe Connectionist Hypothesis is correctThus, cognitive theory must supply a computational reduction of symbolic functions to PDP computation

  • PassiveNet

  • The ICS IsomorphismTensor product representationsTensorial networks

  • Within-level compositionalityW =Wcons0[Wex1Wex0Wex1] + Wcons1[Wcons0(Wex1Wex1Wex1)+Wcons1(Wex0)](s) = cons(ex1(ex0(ex1(s))), cons(ex1(ex1(ex1(s))), ex0(s))) Between-level reduction

  • Levels

  • The ICS Architecturedog+sAdgz

    RepresentationGrammar G Function Algorithm AConstraints: NOCODAoptimal: optimal:Activation PatternConnection WeightsHarmony OptimizationSpreading Activation

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  • Processing I: ActivationComputational neuroscience

    Key sourcesHopfield 1982, 1984Cohen and Grossberg 1983Hinton and Sejnowski 1983, 1986Smolensky 1983, 1986Geman and Geman 1984 Golden 1986, 1988

  • Processing I: ActivationProcessing spreading activation is optimization: Harmony maximization

    Chart4

    000

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    a1

    a2

    H

    A1-exact

    A2-exact

    H

    Time

    Competitive Net

    Sheet1

    TimeInput 1Input 2Inhibdelta-tA1A1-exactA2A2-exactH

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    0.7680476208-0.1891002524

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    0.7700865803-0.1911392119

    0.7710321005-0.1920847321

    0.7719315072-0.1929841387

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    0.775811823-0.1968644546

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    0.7777148113-0.1987674429

    0.7782882983-0.1993409299

    0.778833816-0.1998864476

    0.7793527285-0.2004053601

    0.7798463333-0.2008989649

    0.7803158648-0.2013684963

    0.7807624969-0.2018151285

    0.7811873465-0.2022399781

    0.781591476-0.2026441075

    0.7819758958-0.2030285274

    0.7823415673-0.2033941988

    0.7826894047-0.2037420363

    0.7830202779-0.2040729095

    0.7833350143-0.2043876458

    0.7836344007-0.2046870323

    0.7839191859-0.2049718175

    0.784190082-0.2052427136

    0.7844477663-0.2055003979

    0.7846928832-0.2057455148

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    a1

    a2

    A1-exact

    A2-exact

    Time

    Competitive Net

    Sheet1

    TimeInput 1Input 2Inhibdelta-tA1A1-exactA2A2-exactH

    00.60.50.90.500000

    10.60.50.90.50.30.20190762310.250.15313704760.16125

    20.60.50.90.50.33750.29375879590.240.1985962140.163846875

    30.60.50.90.50.360750.34237528730.2181250.20308326370.1658332266

    40.60.50.90.50.382218750.37363255790.1967250.1923633110.1676250155

    50.60.50.90.50.4025831250.39756885460.17636406250.17636963770.1692421028

    60.60.50.90.50.42192773440.41809600490.1570196250.15891422560.1707015241

    70.60.50.90.50.44030503590.4367550540.1386423320.14144314370.1720186518

    80.60.50.90.50.45776346860.45416879370.12118389980.12448883970.1732073596

    90.60.50.90.50.47434897930.47060358220.10459838910.10823173380.1742801684

    100.60.50.90.50.49010521460.48618668670.08884215380.09271734640.1752483783

    110.60.50.90.50.50507363810.50099039930.07387373030.07794020960.1761221877

    120.60.50.90.50.51929364040.51506462540.0596537280.06387626150.1769108007

    130.60.50.90.50.53280264260.52844954250.04614472590.05049531920.177622524

    140.60.50.90.50.54563619470.54118054760.03331117380.03776585140.1782648542

    150.60.50.90.50.55782806910.55329022040.02111929930.02565677310.1788445572

    160.60.50.90.50.56941034990.56480912970.00953701850.01413809380.1793677392

    170.60.50.90.50.58041351660.5757661902-0.00146614820.00318112210.1798399109

    180.60.50.90.50.5908665250.5861888435-0.0119191566-0.00724149680.1802660459

    190.60.50.90.50.60079688290.5961031683-0.0218495145-0.01715580830.1806506328

    200.60.50.90.50.6102307230.605533962-0.0312833546-0.02658659680.1809977224

    210.60.50.90.50.61919287110.614504809-0.0402455026-0.03555744190.1813109708

    220.60.50.90.50.62770691170.6230381421-0.0487595433-0.04409077420.1815936774

    230.60.50.90.50.63579525030.6311552994-0.0568478819-0.05220793120.1818488202

    240.60.50.90.50.6434791720.6388765782-0.0645318036-0.05992920990.1820790866

    250.60.50.90.50.65077889760.6462212858-0.0718315292-0.06727391740.1822869019

    260.60.50.90.50.6577136370.6532077877-0.0787662686-0.07426041930.1824744553

    270.60.50.90.50.66430163930.6598535539-0.0853542709-0.08090618550.1826437222

    280.60.50.90.50.67056024160.6661752022-0.0916128732-0.08722783380.1827964856

    290.60.50.90.50.67650591370.6721885402-0.0975585453-0.09324117170.1829343546

    300.60.50.90.50.68215430220.6779086041-0.1032069338-0.09896123570.1830587813

    310.60.50.90.50.68752027130.6833496973-0.1085729029-0.10440232890.1831710765

    320.60.50.90.50.6926179420.6885254252-0.1136705736-0.10957805680.1832724228

    330.60.50.90.50.69746072910.6934487299-0.1185133607-0.11450136150.1833638879

    340.60.50.90.50.70206137680.6981319222-0.1231140084-0.11918455380.1834464352

    350.60.50.90.50.70643199220.7025867125-0.1274846238-0.12363934410.1835209341

    360.60.50.90.50.71058407680.7068242401-0.1316367084-0.12787687170.1835881693

    370.60.50.90.50.71452855720.7108551011-0.1355811888-0.13190773260.1836488491

    380.60.50.90.50.71827581350.7146893746-0.1393284451-0.13574200620.1837036126

    390.60.50.90.50.72183570710.7183366484-0.1428883386-0.139389280.1837530367

    400.60.50.90.50.72521760590.7218060426-0.1462702375-0.14285867420.183797642

    410.60.50.90.50.72843040980.7251062324-0.1494830414-0.1461588640.1838378982

    420.60.50.90.50.73148257360.7282454701-0.1525352051-0.14929810170.1838742294

    430.60.50.90.50.73438212910.7312316053-0.1554347607-0.15228423690.1839070184

    440.60.50.90.50.73713670680.734072105-0.1581893384-0.15512473660.1839366104

    450.60.50.90.50.73975355570.7367740719-0.1608061873-0.15782670350.1839633172

    460.60.50.90.50.74223956210.7393442623-0.1632921937-0.16039689390.1839874201

    470.60.50.90.50.74460126820.7417891031-0.1656538998-0.16284173470.1840091729

    480.60.50.90.50.7468448890.7441147076-0.1678975206-0.16516733910.1840288049

    490.60.50.90.50.74897632880.746326891-0.1700289604-0.16737952250.1840465227

    500.60.50.90.50.75100119660.7484311849-0.1720538282-0.16948381650.1840625131

    510.60.50.90.50.7529248210.7504328512-0.1739774525-0.17148548280.1840769444

    520.60.50.90.50.75475226410.7523368951-0.1758048957-0.17338952670.1840899686

    530.60.50.90.50.75648833510.7541480777-0.1775409667-0.17520070930.184101723

    540.60.50.90.50.75813760260.7558709278-0.1791902342-0.17692355940.1841123313

    550.60.50.90.50.75970440670.7575097536-0.1807570382-0.17856238520.1841219053

    560.60.50.90.50.76119287050.7590686529-0.1822455021-0.18012128450.1841305459

    570.60.50.90.50.76260691120.7605515238-0.1836595428-0.18160415540.184138344

    580.60.50.90.50.76395024990.7619620742-0.1850028814-0.18301470580.1841453817

    590.60.50.90.50.76522642160.7633038312-0.1862790532-0.18435646280.1841517333

    600.60.50.90.50.76643878470.76458015-0.1874914163-0.18563278160.1841574657

    610.60.50.90.50.76759052970.765794222-0.1886431613-0.18684685360.1841626391

    620.60.50.90.50.76868468740.766949083-0.189737319-0.18800171460.1841673081

    630.60.50.90.50.76972413730.7680476208-0.1907767688-0.18910025240.1841715219

    640.60.50.90.50.77071161460.7690925822-0.1917642462-0.19014521380.1841753248

    650.60.50.90.50.77164971810.7700865803-0.1927023497-0.19113921190.1841787569

    660.60.50.90.50.77254091640.7710321005-0.193593548-0.19208473210.1841818545

    670.60.50.90.50.77338755480.7719315072-0.1944401864-0.19298413870.18418465

    680.60.50.90.50.77419186130.7727870492-0.1952444928-0.19383968080.1841871729

    690.60.50.90.50.77495595240.773600866-0.196008584-0.19465349760.1841894499

    700.60.50.90.50.7756818390.7743749925-0.1967344706-0.19542762410.1841915048

    710.60.50.90.50.77637143130.7751113644-0.1974240628-0.1961639960.1841933594

    720.60.50.90.50.77702654390.775811823-0.1980791755-0.19686445460.1841950332

    730.60.50.90.50.77764890090.7764781198-0.1987015325-0.19753075140.1841965438

    740.60.50.90.50.77824014010.777111921-0.1992927717-0.19816455260.1841979071

    750.60.50.90.50.77880181730.7777148113-0.1998544489-0.19876744290.1841991374

    760.60.50.90.50.77933541060.7782882983-0.2003880422-0.19934092990.1842002479

    770.60.50.90.50.77984232430.778833816-0.2008949559-0.19988644760.18420125

    780.60.50.90.50.78032389230.7793527285-0.2013765239-0.20040536010.1842021544

    790.60.50.90.50.78078138190.7798463333-0.2018340135-0.20089896490.1842029707

    800.60.50.90.50.7812159970.7803158648-0.2022686286-0.20136849630.1842037074

    810.60.50.90.50.78162888140.7807624969-0.202681513-0.20181512850.1842043722

    820.60.50.90.50.78202112150.7811873465-0.2030737531-0.20223997810.1842049722

    830.60.50.90.50.78239374970.781591476-0.2034463812-0.20264410750.1842055138

    840.60.50.90.50.78274774640.7819758958-0.203800378-0.20302852740.1842060025

    850.60.50.90.50.78308404330.7823415673-0.2041366749-0.20339419880.1842064436

    860.60.50.90.50.78340352530.7826894047-0.2044561569-0.20374203630.1842068416

    870.60.50.90.50.78370703330.7830202779-0.2047596648-0.20407290950.1842072009

    880.60.50.90.50.78399536580.7833350143-0.2050479974-0.20438764580.1842075251

    890.60.50.90.50.78426928170.7836344007-0.2053219133-0.20468703230.1842078177

    900.60.50.90.50.78452950190.7839191859-0.2055821334-0.20497181750.1842080818

    910.60.50.90.50.7847767110.784190082-0.2058293426-0.20524271360.1842083202

    920.60.50.90.50.78501155960.7844477663-0.2060641912-0.20550039790.1842085353

    930.60.50.90.50.78523466590.7846928832-0.2062872974-0.20574551480.1842087294

    940.60.50.90.50.78544661680.7849260457-0.2064992484-0.20597867720.1842089046

    950.60.50.90.50.78564797020.7851478366-0.2067006017-0.20620046820.1842090627

    960.60.50.90.50.78583925590.7853588107-0.2068918874-0.20641144230.1842092054

    970.60.50.90.50.78602097730.7855594954-0.2070736089-0.2066121270.1842093342

    980.60.50.90.50.78619361260.7857503927-0.2072462442-0.20680302430.1842094504

    990.60.50.90.50.78635761620.7859319797-0.2074102478-0.20698461130.1842095553

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    A1

    A2

    H

    A1-exact

    A2-exact

    Time

    Sheet2

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

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    A2-exact

    a1 (i1 = 0.6)

    a2 (i2 = 0.5)

    Competitive Net

    Sheet3

    000

    000

    000

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    a1

    a2

    H

    A1-exact

    A2-exact

    H

    Time

    Competitive Net

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    2425282132202292402532682852104

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    A1A2I1I2Inhib-0.5A1A2I1I2Inhib-0.4A1A2I1I2Inhib-0.3A1A2I1I2Inhib-0.2A1A2I1I2Inhib-0.1A1A2I1I2Inhib0A1A2I1I2Inhib0.1A1A2I1I2Inhib0.2A1A2I1I2Inhib0.3A1A2I1I2Inhib0.4A1A2I1I2Inhib0.5A1A2I1I2Inhib0.6A1A2I1I2Inhib0.7A1A2I1I2Inhib0.8A1A2I1I2Inhib0.9A1A2I1I2Inhib1

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    -0.5

    -0.4

    -0.3

    -0.2

    -0.1

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    0.6

    0.7

    0.8

    0.9

    1

    a2

    Harmony

    a1

    Competitive Net

    MBD00079BEA.unknown

    Chart5

    00

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    a1

    a2

    A1-exact

    A2-exact

    Time

    Competitive Net

    Sheet1

    TimeInput 1Input 2Inhibdelta-tA1A1-exactA2A2-exactH

    00.60.50.90.500000

    10.60.50.90.50.30.20190762310.250.15313704760.16125

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