Learning How to Generalize.

Generalization is a fundamental problem solved by every cognitive system in essentially every domain. Although it is known that how people generalize varies in complex ways depending on the context or domain, it is an open question how people learn the appropriate way to generalize for a new context. To understand this capability, we cast the problem of learning how to generalize as a problem of learning the appropriate hypothesis space for generalization. We propose a normative mathematical framework for learning how to generalize by learning inductive biases for which properties are relevant for generalization in a domain from the statistical structure of features and concepts observed in that domain. More formally, the framework predicts that an ideal learner should learn to generalize by either taking the weighted average of the results of generalizing according to each hypothesis space, with weights given by how well each hypothesis space fits the previously observed concepts, or by using the most likely hypothesis space. We compare the predictions of this framework to human generalization behavior with three experiments in one perceptual (rectangles) and two conceptual (animals and numbers) domains. Across all three studies we find support for the framework's predictions, including individual-level support for averaging in the third study.

Children's representation of abstract relations in relational/array match-to-sample tasks.

Five experiments compared preschool children's performance to that of adults and of non-human animals on match to sample tasks involving 2-item or 16-item arrays that varied according to their composition of same or different items (Array Match-to-Sample, AMTS). They establish that, like non-human animals in most studies, 3- and 4-year-olds fail 2-item AMTS (the classic relational match to sample task introduced into the literature by Premack, 1983), and that robust success is not observed until age 6. They also establish that 3-year-olds, like non-human animal species, succeed only when they are able to encode stimuli in terms of entropy, a property of an array (namely its internal variability), rather than relations among the individuals in the array (same vs. different), whereas adults solve both 2-item and 16-item AMTS on the basis of the relations same and different. As in the case of non-human animals, the acuity of 3- and 4-year-olds' representation of entropy is insufficient to solve the 2-item same-different AMTS task. At age 4, behavior begins to contrast with that of non-human species. On 16-item AMTS, a subgroup of 4-year-olds induce a categorical rule matching all-same arrays to all-same arrays, while matching other arrays (mixed arrays of same and different items) to all-different arrays. These children tend to justify their choices using the words "same" and "different." By age 4 a number of our participants succeed at 2-item AMTS, also justifying their choices by explicit verbal appeals using words for same and different. Taken together these results suggest that the recruitment of the relational representations corresponding to the meaning of these words contributes to the better performance over the preschool years at solving array match-to-sample tasks.