An integrated model of concept learning and word-concept mapping

An integrated model of concept learning and word-concept mapping Molly Lewis Michael C. Frank mll@stanford.edu Department of Psychology Stanford University mcfrank@stanford.edu Department of Psychology Stanford University Abstract To learn the meaning of a new word, children must solve two distinct problems: identify the referent under ambiguity and determine how to generalize that word’s meaning to new ob- jects. Traditionally, these two problems have been addressed separately in the literature, despite their tight relationship with one another. We present a hierarchical Bayesian model that jointly infers both the referent of a word in ambiguous con- texts and the concept associated with a word. As a first step in testing this model, we provide evidence that our model fits human data in a simple cross-situational concept learning task. Keywords: cross-situational word learning; Bayesian models Introduction Figure 1: Schema of the two problems associated with learn- ing the meaning of a word. Learning a new word requires that the child both identify which object the word refers to in the referential context (the Mapping Problem) and how to gener- alize that word to objects of the same kind (the Generalization Problem). Learning a new word requires drawing a link in your mental lexicon between a word and a concept. But, children do not observe associations between words and abstract concepts; they observe associations between words and exemplars of those concepts. Furthermore, the associations between words and objects are ambiguous: a single word uttered in any par- ticular context is consistent with an infinite number of possi- ble interpretations (Quine, 1960). There are thus two prob- lems a child must solve in order to learn the meaning of a new word: Determine which object is referred to by a word in context (the Mapping Problem) and determine the relevant concept of the object (the Generalization Problem; see Figure To understand these two problems more clearly, suppose you lived in an (impoverished) world with two words, “apple” and “cherry,” and three objects, a green apple, a red apple, and a cherry. You hear the word “apple” in the context of a single red apple on the table. You somehow infer that “apple” refers to the red object on the table, and thus correctly solve the Mapping Problem. But you have not yet succeeded in solving the Generalization Problem. To correctly solve the General- ization Problem, you must decide whether “apple” also refers to the green apple, which is similar in shape to your observed apple exemplar, or whether it also refers to the cherry, which is similar in color to your observed apple exemplar. Or, al- ternatively, whether “apple” refers to neither of these other objects (i.e. a proper name). Thus, to learn the word “apple” in this world, you must infer both that “apple” refers to the red object on the table, and that “apple” should be generalized to other apple-shaped objects. Separate learning mechanisms and constraints have been proposed to account for each of these problems. In the case of the Mapping Problem, one proposed constraint is cross- situational statistics (Pinker, 1984; Smith & Yu, 2008; Yu & Smith, 2007). Under this account, learners are hypothesized to aggregate the statistics of associations between words and objects across situations. When considered in an isolated sit- uation, the referent of a word may be ambiguous, but when situations are aggregated across, the learner is able to con- strain the hypothesis space of likely meanings. There is evi- dence that children as young as 12-months-old can learn word meanings in this way (Smith & Yu, 2008). A second class of constraints on the Mapping Problem are accounts of the disambiguation effect. The disambiguation effect refers to children’s tendency to select a novel, as op- posed to familiar, object as a referent for a novel word. One account of this phenomenon is the principle of mutual ex- clusivity (Markman & Wachtel, 1988; Markman, Wasow, & Hansen, 2003). Under this proposal, there is a constraint on the types of lexicons considered when learning the mean- ing of a new word. With this constraint, children are biased to consider only those lexicons that have a one-to-one map- ping between words and objects. Thus, when faced with an ambiguous referential context, the child solves the mapping problem by assuming that the novel word refers to the object for which she does not yet have a word in her lexicon. This is the inferred mapping because it is the only referent that al- lows the learner to maintain a one-to-one structure between words and concepts in the lexicon. Others have proposed that general pragmatic assumptions can also account for this ef- fect (Clark, 1987; Diesendruck & Markson, 2001). There are also a range of proposals about how children might solve the Generalization Problem. One proposal is that children have a bias to generalize by shape (Smith, Jones, Landau, Gershkoff-Stowe, & Samuelson, 2002). With this