Learning Conceptual Hierarchies by Iterated Relational Consolidation - eScholarship (2012)

Learning Conceptual Hierarchies by Iterated Relational Consolidation James M. Foster, Fabian Canas, & Matt Jones {james.m.foster, canas, mcj}@colorado.edu University of Colorado, Department of Psychology & Neuroscience Boulder, CO 80309 USA Abstract levels of abstraction by chunking systems of relations at one level into building blocks at the next level. In computer architecture, digital logic gates are composed to form adders, which are composed with other digital circuits to form an arithmetic logic unit (ALU), which is a building block in a computer’s CPU. Software design manages complexity by continuing this hierarchy, composing primitive functions into more complex functions, and from there to objects and design patterns. The conceptual progression in mathematics proceeds similarly, composing the counting operation to define adding, which is further composed to form multiplying, and then exponentiation. In traditional views of linguistics, phonemes, morphemes, words, and sentences form another example of a relational hierarchy. 1 These examples motivate our basic research questions. How are relational hierarchies mentally represented? How are these representations learned or constructed through experience? Once a relational concept is learned, how can one discover the higher-order relations in which it can participate? Here we consider the proposal that much of concept learning is driven by recognizing relational structure through analogy. Research on analogical reasoning has converged on a view that episodes or scenarios are represented as patterns of role binding, in which objects are bound to roles of relations (Gentner, 1983; Hummel & Holyoak, 2003). For example, the fact that the earth revolves around the sun is represented by binding earth and sun to the first and second roles of a revolves_around relation. An analogy between two scenarios constitutes a determination that they share a common pattern of role binding. For example, in the analogy between the solar system and the atom (Gentner, 1983), each system has the property that the object playing role 1 of revolves_around is the same as the object playing role 2 of more_massive_than. Analogy formation can thus be viewed as a search for a pattern of linkage among relations (i.e., in terms of how they are bound to shared objects) that holds in two different scenarios. This linkage pattern is a type of higher-order relation among the linked relations. Theories of schema induction (e.g., Doumas, Hummel, & Sandhofer, 2008) offer one way for such higher-order relations to be learned. When an analogy is formed, an abstract schema is created that captures the common structure discovered by the Learning new concepts is critical to making sense of the world. Research on analogical reasoning suggests structure mapping and schema induction can enable discovery of new relational concepts. However, existing theories of schema induction and refinement are insufficient to explain acquisition of rich, compositional hierarchies of relational concepts. This paper offers a proposal for this sort of representation construction, founded on reinforcement learning to evaluate the predictive usefulness of higher-order relations, together with a mechanism of relational consolidation by which systems of relations (schemas) can be chunked into unitary entities. A computational model of these ideas is outlined and partially tested in simulations and human experiments. Implications and moderating factors for relational consolidation are considered. Keywords: Relational Consolidation; Analogy; Schema Induction; Predication; Refinement; Concept Learning Introduction Consider a second-order same-different task, in which the subject is presented with two pairs of objects and must recognize whether the pairs match in terms of whether their objects are the same or different. The pairs match if both are instances of sameness (e.g., A-A, B-B) or if both are instances of difference (e.g., A-B, C-D), and they mismatch if one is an instance of sameness and the other an instance of difference (e.g., A-A, B-C). Thompson, Oden, and Boyson (1997) tested naive chimpanzees on this task and found them unable to learn it, unless they were first trained on a first-order same-different task. In the first-order task, a single pair of objects was presented, and subjects learned to associate sameness and difference to two plastic tokens (e.g., a yellow triangle and a red circle, respectively). Thompson et al. argued this training enabled subjects to reduce the second-order same-different task to a first-order task, by mentally replacing each pair of objects with its associated token, and then determining whether those tokens matched (see also Clark, 2006). Learning higher-order relations, such as in the second- order same-different task, is arguably critical to abstract conceptual development. In this paper, we argue that many concepts reside in relational hierarchies (relations among relations, and so on), and we investigate how such concepts might be learned. Our basic premises are that much structure in the world (or at least its mental representation) is hierarchically compositional, and that discovering (or creating) this structure is a powerful cognitive mechanism for both learning and designing complex systems. For example, computer architecture, mathematical functions, and natural languages all exemplify multiple Relational hierarchies are not taxonomic hierarchies. In a taxonomic hierarchy, each concept or category is a union of lower- level categories. In a relational hierarchy, each instance of a concept is a configuration of instances of lower-order concepts.