Modeling the acquisition of domain structure and feature understanding

Modeling the Acquisition of Domain Structure and Feature Understanding Amy Perfors, Charles Kemp, Joshua B. Tenenbaum Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology Address correspondence to perfors@mit.edu Abstract Young children face a difficult learning task: without having access to the cues that full language mastery would provide, they must acquire conceptual knowl- edge about the world; likewise, they must somehow learn words while lacking the full conceptual structure that the words refer to. We present a Bayesian frame- work that can model aspects of the acquisition of the- ory knowledge as a function of different types of input. We describe a set of developmental phenomena that our model can address.  Acquiring theories of the world, particularly as they vary from domain to domain, is one of the most difficult tasks confronting young children. This is especially the case for infants and children in the earliest stages of language learning, since they are faced with two simultaneous problems: learning words without yet fully grasping the conceptual theory underlying the domain to which those words refer, and learning the knowledge underlying a do- main without yet fully understanding the language that would give cues to that knowledge. What constitutes theory knowledge? The question is the focus of some debate, but for this paper we wish to limit our focus to two aspects that are believed to be important facets of theories. The first is structure: knowledge about the organization of relationships be- tween objects in a domain. For instance, biological ob- jects are organized hierarchically with respect to each other, but political views may be better characterized by a linear spectrum [2, 12]. The other is knowledge about feature weights: which features are the most important or central in that domain. For example, the generaliza- tion of novel nouns for animals is best done on the basis of shape or internal features, while for foods it depends more on color [10, 13, 21]. Of course, feature biases and domain structure are not independent of each other. Important features are those that are the most coherent and informative in that do- main; when that domain is structured, this means that important features are those that are most coherent with respect to the structure. For instance, animals organized in a taxonomic structure would be expected to share important features (e.g., warm-bloodedness) only with those animals close to them on the structure (i.e., other mammals); unimportant features, such as skin color, could be shared – or not – with objects arbitrarily far away in the structure. The interdependence between structures and features means that learning about structures and learning about features goes hand-in-hand: initially knowing that some features are more important than others can constrain the best structures to ones on which those features to co- vary coherently. Similarly, initially knowing that some structure is most appropriate limits the important fea- tures to those than cluster tightly on that structure. Though the empirical phenomena underlying the ac- quisition of knowledge about domain structure and fea- ture biases are well studied (e.g., [10, 15, 21, 23]), there are few computational models for them. The main mod- els involve connectionist networks (e.g., [4, 19]), which have proven quite useful to cognitive psychologists in many ways, but which suffer from the disadvantage of opacity. It is often difficult to understand exactly what the model is doing and what its representation actually consists of. Particularly if one is interested in the repre- sentation and acquisition of structure – such as the tree- structured taxonomy in folk biology – an unstructured connectionist approach may not only be less transparent, but may also perform worse on tasks that specifically rely on that structure . The Bayesian model of concept acquisition we present here allows for a tractable and clear exploration of the interplay between the acquisition of information about the world and the development of domain theories. Be- cause we operate in a framework for Bayesian inference, we incorporate one of the primary advantages of con- nectionist algorithms – their domain-general statistical learning character – while still providing the clarity and explicitness of a more structured approach. In the following sections we first describe a set of phe- nomena that arise while children acquire domain-specific theory knowledge; we then explore how our approach can naturally model them. Learning about structure Little is known about at what age and to what extent children realize that some domains are organized taxonomically. Some argue that the tendency to group living kinds into hierarchies re- flects an “innately determined cognitive structure” . However, children’s behavior changes in ways that sug- gest they may not initially begin with an accessible tax- onomic structure. Very young children have a hard time learning superordinate categories [9], especially if they