Learnability, representation, and language : a Bayesian approach

Abstract

Within the metaphor of the "mind as a computation device" that dominates cognitive science, understanding human cognition means understanding learnability not only what (and how) the brain learns, but also what data is available to it from the world. Ideal learnability arguments seek to characterize what knowledge is in theory possible for an ideal reasoner to acquire, which illuminates the path towards understanding what human reasoners actually do acquire. The goal of this thesis is to exploit recent advances in machine learning to revisit three common learnability arguments in language acquisition. By formalizing them in Bayesian terms and evaluating them given realistic, real-world datasets, we achieve insight about what must be assumed about a child's representational capacity, learning mechanism, and cognitive biases. Exploring learnability in the context of an ideal learner but realistic (rather than ideal) datasets enables us to investigate what could be learned in practice rather than noting what is impossible in theory. Understanding how higher-order inductive constraints can themselves be learned permits us to reconsider inferences about innate inductive constraints in a new light. And realizing how a learner who evaluates theories based on a simplicity/goodness-of-fit tradeoff can handle sparse evidence may lead to a new perspective on how humans reason based on the noisy and impoverished data in the world. The learnability arguments I consider all ultimately stem from the impoverishment of the input either because it lacks negative evidence, it lacks a certain essential kind of positive evidence, or it lacks suffcient quantity of evidence necessary for choosing from an infinite set of possible generalizations.

(cont.) I focus on these learnability arguments in the context of three major topics in language acquisition: the acquisition of abstract linguistic knowledge about hierarchical phrase structure, the acquisition of verb argument structures, and the acquisition of word leaning biases.