Graded Generability in OT

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? Graded Generability in OT

• Problem identified by Matt Goldrick
• Aphasic errors predominantly k ? t but also t ? k
  occurs, rarely
• Exceptional behavior w.r.t. markedness
• How is this possible if dor cor in UG? Under
  no possible ranking can t ? k
• Must we allow violations of dor cor ?
• Alternative approach via processing theory
• Crucial global vs. local optimization

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? OT ? prI?O via Connectionism

• Candidate A realized as an activation pattern a
  (distributed or local to a unit)
• Harmony of A H(a), numerical measure of
  consistency between a and the connection weights
  W
• Grammar W
• Discrete symbolic candidate space embedded in a
  continuous state space
• Search Probability of A prT(a) ? eH(a)/T
• During search, T ? 0

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? Harmony Maxima

• Patterns realizing optimal symbolic structures
  are global Harmony maxima
• Patterns realizing suboptimal symbolic structures
  are local Harmony maxima
• Search should find the global optimum
• Search will find a local optimum
• Example Simple local network for doing ITBerber
  syllabification

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BrbrNet
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BrbrNets Global Harmony Maxima

• Contrasts with Goldsmiths Dynamic Linear Models
  (Goldsmith Larson 90 Prince 93)
• For a given input string, a state of BrbrNet is
  a global Harmony maximum if and only if it
  realizes the syllabification produced by the
  serial Dell-Elmedlaoui algorithm
• (assuming no sonority plateaux)

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BrbrNets Search Dynamics

• Greedy local optimization
• at each moment, make a small change of state so
  as to maximally increase Harmony
• (gradient ascent)

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/txznt/ ? tx.znt yousing stored
H
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The Hardest Case 12378/t.bs.ya
hypothetical, but compare tbx.lakkw she
even behaved as a miser
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Parsing sonority profile 8 1 2 1 3 4 5 7 8 7
a.tb.kf.zn.yay
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BrbrNets Local Harmony Maxima

• An output pattern in BrbrNet is a local Harmony
  maximum if and only if it realizes a sequence of
  legal Berber syllables (i.e., an output of Gen)
• That is, every activation value is 0 or 1, and
  the sequence of values is that realizing a
  sequence of substrings taken from the inventory
  CV, CVC, V, VC,
• where C denotes 0, V denotes 1 and denotes a
  word edge

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? Competence, Performance

• So how can t ? k ?
• t a global max, k a local max
• now we can get k when should get t
• Distinguish Search Dynamics (performance) from
  Harmony Landscape (competence)
• the universals in the Harmony Landscape require
  that, absent performance errors, we must have k ?
  t
• an imperfect Search Dynamics allows t ? k
• The huge general case/exception contrast
• ts output derives from UG
• ks output derives from performance error

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? Summary

• Exceptions to markedness universals may
  potentially be modeled as performance errors the
  unmarked (optimal) elements are global Harmony
  maxima, but local search can end up with marked
  elements which are local maxima
• Applicable potentially to sporadic, unsystematic
  exceptions in I ? O mapping
• Extensible to systematic exceptions in I ? O or
  to exceptional grammars???