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Cognitive Science 101

Cognitive Science 101. Cognition is computation But what type? Fundamental question of research on the human cognitive architecture. Cognitive Architecture. Rules operating on symbols grammar logic Spreading activation in simple processors massively interconnected in a large network

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Cognitive Science 101

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  1. Cognitive Science 101 • Cognition is computation • But what type? • Fundamental question of research on the human cognitive architecture University of Amsterdam

  2. Cognitive Architecture • Rules operating on symbols • grammar • logic • Spreading activation in simple processors • massively interconnected in a large network • Symbolic vs. Connectionist architecture? • Integrated Connectionist/Symbolic (ICS) Architecture • Grammar: Phonology • Architecture: defined by four components University of Amsterdam

  3. ƒ G “dogs” σ σ σ k     k k æ t æ æ t t Processing (Learning) The ICS Architecture dog+s dgz A University of Amsterdam

  4. Processing I: Activation • Computational neuroscience • Key sources • Hopfield 1982, 1984 • Cohen and Grossberg 1983 • Hinton and Sejnowski 1983, 1986 • Smolensky 1983, 1986 • Geman and Geman 1984 • Golden 1986, 1988 University of Amsterdam

  5. –λ (–0.9) a1 a2 i1 (0.6) i2 (0.5) Processing I: Activation Processing — spreading activation — is optimization: Harmony maximization University of Amsterdam

  6. ƒ G σ σ σ k     k k æ t æ æ t t The ICS Architecture cat kæt A University of Amsterdam

  7. –λ (–0.9) a1 a2 i1 (0.6) i2 (0.5) Processing II: Optimization • Cognitive psychology • Key sources: • Hinton & Anderson 1981 • Rumelhart, McClelland, & the PDP Group 1986 Processing — spreading activation — is optimization: Harmony maximization University of Amsterdam

  8. a1 and a2must not be simultaneously active (strength: λ) Harmony maximization is satisfaction of parallel, violable well-formedness constraints –λ (–0.9) a1 a2 a1must be active (strength: 0.6) a2must be active (strength: 0.5) CONFLICT i1 (0.6) i2 (0.5) Optimal compromise: 0.79 –0.21 Processing II: Optimization Processing — spreading activation — is optimization: Harmony maximization University of Amsterdam

  9. Processing II: Optimization • The search for an optimal state can employ randomness • Equations for units’ activation values have random terms • pr(a) ∝eH(a)/T • T (‘temperature’) ~ randomness  0 during search • Boltzmann Machine (Hinton and Sejnowski 1983, 1986); Harmony Theory (Smolensky 1983, 1986) University of Amsterdam

  10. ƒ G σ σ σ k     k k æ t æ æ t t The ICS Architecture cat kæt A University of Amsterdam

  11. Two Fundamental Questions Harmony maximization is satisfaction of parallel, violable constraints 2. What are the constraints? Knowledge representation Prior question: 1. What are the activation patterns — data structures — mental representations — evaluated by these constraints? University of Amsterdam

  12. Representation • Symbolic theory • Complex symbol structures • Generative linguistics (Chomsky & Halle ’68 …) • Particular linguistic representations • Markedness Theory (Jakobson, Trubetzkoy, ’30s …) • Good (well-formed) linguistic representations • Connectionism(PDP) • Distributed activation patterns • ICS • realization of (higher-level) complex symbolic structures in distributed patterns of activation over (lower-level) units (‘tensor product representations’ etc.) • will employ ‘local representations’ as well University of Amsterdam

  13. σ σ k k æ t æ t σ/rε k/r0 æ/r01 t/r11 [σ k [æ t]] Representation University of Amsterdam

  14. ƒ G σ σ σ k     k k æ t æ æ t t The ICS Architecture cat kæt A University of Amsterdam

  15. σ k æ t *violation ‘cat’ W a[σk [æ t ]] * Constraints NOCODA: A syllable has no coda [Maori] * H(a[σk [æ t]) = –sNOCODA < 0 University of Amsterdam

  16. ƒ G σ σ σ k    k k æ t æ æ t t The ICS Architecture cat kæt A University of Amsterdam

  17. ƒ G Constraint Interaction ?? σ σ σ k   k k æ t æ æ t t The ICS Architecture cat kæt A University of Amsterdam

  18. Constraint Interaction I • Harmonic Grammar • Legendre, Miyata, Smolensky 1990 et seq. University of Amsterdam

  19. = H σ H k æ t = H(k ,σ) > 0 H(σ, t) < 0 NOCODA ONSET = Constraint Interaction I The grammar generates the representation that maximizes H: this best-satisfies the constraints, given their differential strengths Any formal language can be so generated. University of Amsterdam

  20. ƒ G Constraint Interaction I: HG σ σ σ k  k k æ t æ æ t t The ICS Architecture cat kæt A University of Amsterdam

  21. ƒ G σ σ σ k k k æ t æ æ t t The ICS Architecture cat kæt A ? University of Amsterdam

  22. ƒ G σ σ σ k k k æ t æ æ t t The ICS Architecture cat kæt A HG Powerful: French syntax (Legendre, et al. 1990 et seq.) Prince & Smolensky(1991 et seq.) Too powerful? University of Amsterdam

  23. ƒ G Constraint InteractionII σ σ σ σ σ k k k k k æ t æ æ æ æ t t t t The ICS Architecture cat kæt A University of Amsterdam

  24. ƒ G Constraint Interaction II: OT σ σ σ k k k æ t æ æ t t The ICS Architecture cat kæt A University of Amsterdam

  25. Constraint Interaction II: OT • Strict domination • “Grammars can’t count” • Stress is on the initial heavy syllable iff the number of light syllables n obeys No way University of Amsterdam

  26. Intro to OT University of Amsterdam

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