Cognitive Science 101

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Cognitive Science 101

• Cognition is computation
• But what type?
• Fundamental question of research on the human
  cognitive architecture

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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

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The ICS Architecture
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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

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Processing I Activation
Processing spreading activation is
optimization Harmony maximization
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The ICS Architecture
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Processing II Optimization

• Cognitive psychology
• Key sources
• Hinton Anderson 1981
• Rumelhart, McClelland, the PDP Group 1986

Processing spreading activation is
optimization Harmony maximization
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Processing II Optimization
Processing spreading activation is
optimization Harmony maximization
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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)

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The ICS Architecture
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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?

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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

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Representation
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The ICS Architecture
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Constraints
NOCODA A syllable has no coda Maori
H(as k æ t) sNOCODA 16
The ICS Architecture
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The ICS Architecture
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Constraint Interaction I

• Harmonic Grammar
• Legendre, Miyata, Smolensky 1990 et seq.

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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.
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?
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HG Powerful French syntax (Legendre, et al. 1990
et seq.)
Prince Smolensky (1991 et seq.)
Too powerful?
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The ICS Architecture
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Constraint Interaction II OT

• Strict domination
• Grammars cant count

• Stress is on the initial heavy syllable iff the
  number of light syllables n obeys

No way
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Intro to OT
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The ICS Architecture
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