Schema%20Theorem%20in%20Language%20Acquisition

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Schema Theorem in Language Acquisition

• A Rags to Riches Story
• BOOT-LA, Indiana University, April 23, 2003

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(No Transcript)
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Poverty of the Stimulus

• The poverty-of-the-stimulus argument, otherwise
  known as Platos Problem, claims that the nature
  of language knowledge is such that it could not
  have been acquired from the actual samples of
  language available to the human child. Cook
  Newson(199686)

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Poverty of the Stimulus

• What counts as evidence?
• positive evidence requirement no correction,
  explanation etc.
• occurrence requirement must occur in normal
  language situations
• uniformity requirement must be available to all
  children regardless of culture, class, language
• take-up requirement must be used by children

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Poverty of the Stimulus

• Rational Steps for Inclusion in UG/LAD
• A native speaker of a particular language knows a
  particular aspect of syntax. Ex.
  structure-dependency, Binding Principles, etc.
• This aspect of syntax could not have been
  acquired from the language input available to
  children.
• This aspect of syntax is not learnt from outside.
• This aspect of syntax is built-in to the mind.
• Cook Newson(199686)

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Poverty of the Stimulus

• A Problem
• A native speaker of a particular language knows a
  particular aspect of syntax. Ex.
  structure-dependency, Binding Principles, etc.
• This aspect of syntax could not have been
  acquired from the language input available to
  children.
• This aspect of syntax is not learnt from outside.
• This aspect of syntax is built-in to the mind.

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Poverty of the Stimulus

• Step B is in practice assumed, and rarely
  rigorously demonstrated
• increasingly we find existence proofs of
  acquisition tasks previously believed impossible
  via statistical, data-driven methods (ex.
  Chalmers, 1990 Elman, 1995)

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Poverty of the Stimulus

• Faulty Step B Reasoning
• a) Helen said that Janei voted for herselfi.
• b)Heleni said that Jane voted for herselfi.
• Cook Newson (199684)
• no context could let them unerringly distinguish
  the binding of anaphors and of pronominals.
• implicitly assumes that at this point, the only
  utterances / experience the child has access to
  are these two possible interpretations
• in fact, by the time children produce /
  understand sentences of this level of complexity,
  theyve had extensive experience producing and
  interpreting anaphors and pronominals (OGrady,
  1997)
• moreover, from the outset children show a bias
  towards binding to the nearest antecedent they
  have the most trouble with sentences like
• Helen said that Janei voted for heri.

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Poverty of the Stimulus

• Faulty Step B Reasoning
• a) It is likely that John will be delayed.
• b) It is probable that John will be delayed.
• c) John is likely to be delayed.
• d)John is probable to be delayed.
• OGrady (1997246)
• common argument against analogy as a learning
  method
• denies analogy based on anything but these
  specific cases by the time a child produces /
  understands sentences such as these, they already
  have extensive linguistic knowledge that would
  preclude such naive analogies
• Other studies have shown analogy can be a useful
  technique for the acquisition of categories and
  grammatical structure (McLennan, ms. Tomasello,
  2000 for example)

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What to do?

• Simply denying UG doesnt solve our problem since
  traditional linguists intuitions about the input
  remain unchanged and lead us back to the same
  conclusions
• Genetic Algorithms seem to have a similar problem
  they look more efficient than they possibly
  could be similar sense of getting something
  for nothing

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Genetic Algorithms

• problem solving technique which is capable of
  assessing an extremely large and complicated
  problem space on the basis of a restricted
  impoverished input set
• Three primary elements
• a population of chromosomes (bit string)
• a fitness function (judges goodness)
• mating and procreation
• (Holland, 1975 Mitchell, 1996)

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Genetic Algorithms

• from purely random beginnings a solution emerges
  very quickly even for optimizations that cant
  be performed by traditional serial computational
  methods

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Genetic Algorithms

• Schema Theorem explanation of how GAs work
• 101
• is an instantiation of the categories (schemata)
• , 1, 0, 1, 10, 11, 01, 101
• (of a possible 27)
• 1
• is a category representation of
• 100, 101, 110, 111, (11, 10, 11, 10)

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Genetic Algorithms

• If 101 is judged as being 75 fit, it
  simultaneously guestimates , 1, 0, 1,
  10, 11, 01, 101 as being 75 fit
• Given a population with multiple instantiations,
  implicit calculation of category fitness becomes
  more accurate
• Fuzzy judgments are still useful
• Selection, biased by fitness, selects not for
  highly fit individuals but (implicitly) highly
  fit categories by targeting highly fit individuals

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Genetic Algorithms

• the profound insight
• GAs make use of category information without
  explicit category definitions, explicit biases,
  or explicit reference to category information.
  It implicitly acts on categories through category
  instantiations

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Genetic Algorithms

• taken in this light it is easier to see how GAs
  skip a great deal of the computational load
  through implicit parallelism
• Critical characteristics
• use a population of tokens (parallelism)
• a selection process that targets / discovers
  salient / relevant dimensions of substructure
  within those tokens

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Wealth of the Stimulus

• Schema Theorem in Language Acquisition

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Wealth of the Stimulus

• Experiences
• entire sensory experiences that include
  linguistic stimuli
• importantly, all sensory information impacts
  memory and is available to be correlated
• infants are exquisitely sensitive to detailed and
  correlated sensory information at least until
  they learn what to ignore (Rovee-Collier, 1991)
• population because stored distributed within
  the same neural structures continuous, not
  digital

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Wealth of the Stimulus

• Learning
• in most basic neural sense continuous,
  correlative, passive
• reduces sensory noise reinforces correlated
  multimodal sensory experience
• a type of selection process because salient
  dimensions emerge through the process

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Wealth of the Stimulus

• Grammar
• Schematic / analogical (following Tomasello,
  2000 Hofstadter and usage based models)
• More subtle correlations, or higher level
  correlations will take more time to be
  distinguished from noise results in a course
  of development
• Acquisitional prerequisites may exist, but its a
  mistake to believe that relevant information
  isnt being collected long before certain
  phenomena appear all input has a physiological
  impact

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Wealth of the Stimulus

• Traditional Progression
• infants attend to phonetic features
• phonetic features allow access to phonological
  system
• access to phonology allows access to words and
  short phrases
• access to words gives access to syntax

• matches the observed developmental increase in
  grammatical complexity
• input is only informative to the linguistic
  module acquired at each stage
• linguistic evidence sets innate parameters
• serial, computationally expensive (thus UG)

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Wealth of the Stimulus

• Schema Theorem Based Progression
• Every utterance an infant hears provides a tiny
  bit of information about the phonetics,
  phonotactics, phonology, morphology, word
  categories, syntax, tense and aspect system,
  pragmatics, semantic categories, diexis,
  references every aspect of their language

• will also match the observed developmental
  increase in grammatical complexity
• input is informative to every aspect of language
  even though its contribution may not clearly
  surface or be attended to immediately
• parallel, computationally efficient, flexible,
  adaptable
• in line with whats going on in other fields

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Conclusion

• A population of tokens implicitly carries
  exponentially more information about the set than
  the tokens themselves represent. Parallel
  systems (of which GAs and the brain are examples)
  that act on that population can make use of
  category information that is not explicitly
  stated. Formal systems cannot.
• Without changing our observations of the input,
  development, or the outcome, by taking a more
  biologically plausible perspective on the
  information processing going on, we can see that
  the linguistic environment is far richer than
  impoverished