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P Niyogi

Publications and source records attributed to P Niyogi.

5 recordsLinked to original sources
PubMed2001

The evolutionary dynamics of grammar acquisition.

Grammar is the computational system of language. It is a set of rules that specifies how to construct sentences out of words. Grammar is the basis of the unlimited expressibility of human language. Children acquire the grammar of their native language without formal education simply by hearing a number of sample sentences. Children could not solve this learning task if they did not have some pre-formed expectations. In other words, children have to evaluate the sample sentences and choose one grammar out of a limited set of candidate grammars. The restricted search space and the mechanism which allows to evaluate the sample sentences is called universal grammar. Universal grammar cannot be learned; it must be in place when the learning process starts. In this paper, we design a mathematical theory that places the problem of language acquisition into an evolutionary context. We formulate equations for the population dynamics of communication and grammar learning. We ask how accurate children have to learn the grammar of their parents' language for a population of individuals to evolve and maintain a coherent grammatical system. It turns out that there is a maximum error tolerance for which a predominant grammar is stable. We calculate the maximum size of the search space that is compatible with coherent communication in a population. Thus, we specify the conditions for the evolution of universal grammar.

Algorithms↗
PubMed2001

Evolution of universal grammar.

Universal grammar specifies the mechanism of language acquisition. It determines the range of grammatical hypothesis that children entertain during language learning and the procedure they use for evaluating input sentences. How universal grammar arose is a major challenge for evolutionary biology. We present a mathematical framework for the evolutionary dynamics of grammar learning. The central result is a coherence threshold, which specifies the condition for a universal grammar to induce coherent communication within a population. We study selection of grammars within the same universal grammar and competition between different universal grammars. We calculate the condition under which natural selection favors the emergence of rule-based, generative grammars that underlie complex language.

Algorithms↗
PubMedDate not supplied

A language learning model for finite parameter spaces.

This paper shows how to formally characterize language learning in a finite parameter space, for instance, in the principles-and-parameters approach to language, as a Markov structure. New language learning results follow directly; we can explicitly calculate how many positive examples on average ("sample complexity") it will take for a learner to correctly identify a target language with high probability. We show how sample complexity varies with input distributions and learning regimes. In particular we find that the average time to converge under reasonable language input distributions for a simple three-parameter system first described by Gibson and Wexler (1994) is psychologically plausible, in the range of 100-150 positive examples. We further find that a simple random step algorithm-that is, simply jumping from one language hypothesis to another rather than changing one parameter at a time-works faster and always converges to the right target language, in contrast to the single-step, local parameter setting method advocated in some recent work.

Adult↗