1. Schema Theorem in Language Acquisition A Rags to Riches Story BOOT-LA, Indiana University, April 23, 2003

2. Schema Theorem in Language Acquisition

3. 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(1996:86)

4. Schema Theorem in Language Acquisition 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

5. Schema Theorem in Language Acquisition Poverty of the Stimulus Rational Steps for Inclusion in UG/LAD A. A native speaker of a particular language knows a particular aspect of syntax. Ex. structure- dependency, Binding Principles, etc. B. This aspect of syntax could not have been acquired from the language input available to children. C. This aspect of syntax is not learnt from outside. D. This aspect of syntax is built-in to the mind. Cook & Newson(1996:86)

6. Schema Theorem in Language Acquisition Poverty of the Stimulus A Problem: A. A native speaker of a particular language knows a particular aspect of syntax. Ex. structure- dependency, Binding Principles, etc. B. This aspect of syntax could not have been acquired from the language input available to children. C. This aspect of syntax is not learnt from outside. D. This aspect of syntax is built-in to the mind.

7. Schema Theorem in Language Acquisition 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)

8. Schema Theorem in Language Acquisition Poverty of the Stimulus Faulty Step B Reasoning: a) Helen said that Jane i voted for herself i. b)*Helen i said that Jane voted for herself i. Cook & Newson (1996:84) 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 Jane i voted for her i.

9. Schema Theorem in Language Acquisition 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 (1997:246) 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)

10. Schema Theorem in Language Acquisition 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

11. Schema Theorem in Language Acquisition 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: 1. a population of chromosomes (bit string) 2. a fitness function (judges goodness) 3. mating and procreation (Holland, 1975; Mitchell, 1996)

12. Schema Theorem in Language Acquisition Genetic Algorithms from purely random beginnings a solution emerges very quickly – even for optimizations that cant be performed by traditional serial computational methods

13. Schema Theorem in Language Acquisition Genetic Algorithms Schema Theorem: explanation of how GAs work 101 is an instantiation of the categories (schemata): {***, 1**, *0*, **1, 10*, 1*1, *01, 101} (of a possible 27) 1** is a category representation of {100, 101, 110, 111, (1*1, 1*0, 11*, 10*)}

14. Schema Theorem in Language Acquisition Genetic Algorithms If 101 is judged as being 75% fit, it simultaneously guestimates {***, 1**, *0*, **1, 10*, 1*1, *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

15. Schema Theorem in Language Acquisition 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

16. Schema Theorem in Language Acquisition 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

17. Schema Theorem in Language Acquisition Wealth of the Stimulus Schema Theorem in Language Acquisition Schema Theorem tokens evaluation outcome GAs chromosomes fitness function optimal solution Acquisition experience learning grammar

18. Schema Theorem in Language Acquisition 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

19. Schema Theorem in Language Acquisition 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

20. Schema Theorem in Language Acquisition 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

21. Schema Theorem in Language Acquisition Wealth of the Stimulus Traditional Progression 1. infants attend to phonetic features 2. phonetic features allow access to phonological system 3. access to phonology allows access to words and short phrases 4. 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)

22. Schema Theorem in Language Acquisition Wealth of the Stimulus Schema Theorem Based Progression 1. 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

23. Schema Theorem in Language Acquisition 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