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Transcript of Attendee questionnaire Name Affiliation/status Area of study/research For each of these subjects:...
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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
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Optimality in Cognition and GrammarPaul SmolenskyCognitive Science DepartmentJohns Hopkins University
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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
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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?
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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
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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
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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
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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
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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
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The cognitive questionfor neuroscienceWhat is the function of each component of the nervous system? Our question is quite different.
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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?
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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
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PassiveNet
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The ICS IsomorphismTensor product representationsTensorial networks
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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
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Levels
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The ICS Architecturedog+sAdgz
RepresentationGrammar G Function Algorithm AConstraints: NOCODAoptimal: optimal:Activation PatternConnection WeightsHarmony OptimizationSpreading Activation
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Units
Representations
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dtepsilon
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H
a
Time
X
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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
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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
00.60.50.90.500000
10.60.50.90.50.30.20190762310.250.15313704760.16125
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a1
a2
H
A1-exact
A2-exact
H
Time
Competitive Net
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