Poverty of the Stimulus? A Rational ApproachAmy Perfors1([email protected]), Joshua B. Tenenbaum1([email protected]),and Terry Regier2([email protected])1Department of Brain and Cognitive Sciences, MIT;2Department of Psychology, University of ChicagoAbstractThe Poverty of the Stimulus (PoS) argument holds thatchildren do not receive enough evidence to infer the exis-tence of core aspects of language, such as the dependenceof linguistic rules on hierarchical phrase structure. Wereevaluate one version of this argument with a Bayesianmodel of grammar induction, and show that a rationallearner without any initial language-specific biases couldlearn this dependency given typical child-directed input.This choice enables the learner to master aspects of syn-tax, such as the auxiliary fronting rule in interrogativeformation, even without having heard directly relevantdata (e.g., interrogatives containing an auxiliary in arelative clause in the subject NP).IntroductionModern linguistics was strongly influenced by Chomsky’sobservation that language learners make grammaticalgeneralizations that do not appear justified by the ev-idence in the input (Chomsky, 1965, 1980). The no-tion that these generalizations can best be explainedby innate knowledge, known as the argument from thePoverty of the Stimulus (henceforth PoS), has led to anenduring debate that is central to many of the key issuesin cognitive science and linguistics.The original formulation of the Poverty of Stimulus ar-gument rests critically on assumptions about simplicity,the nature of the input children are exposed to, and howmuch evidence is sufficient to support the generaliza-tions that children make. The phenomenon of auxiliaryfronting in interrogative sentences is one example of thePoS argument; here, the argument states that childrenmust be innately biased to favor structure-dependentrules that operate using grammatical constructs likephrases and clauses over structure-independent rulesthat operate only on the sequence of words.English interrogatives are formed from declaratives byfronting the main clause auxiliary. Given a declarativesentence like “The dog in the corner is hungry”, the in-terrogative is formed by moving the is to make the sen-tence “Is the dog in the corner hungry?” Chomsky con-sidered two types of operation that can explain auxiliaryfronting (Chomsky, 1965, 1971). The simplest (linear)rule is independent of the hierarchical phrase structureof the sentence: take the leftmost (first) occurrence of theauxiliary in the sentence and move it to the beginning.The structure-dependent (hierarchical) rule – move theauxiliary from the main clause of the sentence – is morecomplex since it operates over a sentence’s phrasal struc-ture and not just its sequence of elements.The “poverty” part of this form of the PoS argumentclaims that children do not see the data they would needto in order to rule out the structure-independent (linear)hypothesis. An example of such data would be an in-terrogative sentence such as “Is the man who is hungryordering dinner?”. In this sentence, the main clause aux-iliary is fronted in spite of the existence of another aux-iliary that would come first in the corresponding declar-ative sentence. Chomsky argued that this type of datais not accessible in child speech, maintaining that “it isquite possible for a person to go through life withouthaving heard any of the relevant examples that wouldchoose between the two principles” (Chomsky, 1971).It is mostly accepted that children do not appear togo through a period where they consider the linear hy-pothesis (Crain and Nakayama, 1987). However, twoother aspects of the PoS argument are the topic of muchdebate. The first considers what evidence there is inthe input and what constitutes “enough” (Pullum andScholz, 2002; Legate and Yang, 2002). Unfortunately,this approach is inconclusive: while there is some agree-ment that the critical forms are rare in child-directedspeech, they do occur (Legate and Yang, 2002; Pullumand Scholz, 2002). Lacking a clear specification of howa child’s language learning mechanism might work, it isdifficult to determine whether that input is sufficient.The second issue concerns the nature of the stimulus,suggesting that regardless of whether there is enoughdirect syntactic evidence available, there may be suf-ficient distributional and statistical regularities in lan-guage to explain children’s behavior (Redington et al.,1998; Lewis and Elman, 2001; Reali and Christiansen,2004). Most of the work focusing specifically on aux-iliary fronting uses connectionist simulations or n-grammodels to argue that child-directed language containsenough information to predict the grammatical status ofaux-fronted interrogatives (Reali and Christiansen, 2004;Lewis and Elman, 2001).While both of these approaches are useful and the re-search on statistical learning in particular is promising,there are still notable shortcomings. First of all, the sta-tistical models do not engage with the primary intuitionand issue raised by the PoS argument. The intuitionis that language has a hierarchical structure – it usessymbolic notions like syntactic categories and phrasesthat are hierarchically organized within sentences, whichare recursively generated by a grammar. The issue iswhether knowledge about this structure is learned or in-nate. An approach that lacks an explicit representa-tion of structure has two problems addressing this issue.First of all, many linguists and cognitive scientists tendto discount these results because they ignore a principalfeature of linguistic knowledge, namely that it is basedon structured symbolic representations. Secondly, con-nectionist networks and n-gram models tend to be diffi-cult to understand analytically. For instance, the mod-els used by Reali and Christiansen (2004) and Lewis andElman (2001) measure success by whether they predictthe next word in a sequence, rather than based on ex-amination of an explicit grammar. Though the modelsperform above chance, it is difficult to tell why and whatprecisely they have learned.In this work we present a Bayesian account of lin-guistic structure learning in order to engage with thePoS argument on its own terms – taking the existenceof structure seriously and asking whether and to whatextent knowledge of that structure can be inferred by arational statistical learner. This is an ideal learnabilityanalysis: our question is not
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