Accounting for the Relational Shift and Context Sensitivity in the Development of Generalization

Accounting for the Relational Shift and Context Sensitivity in the Development of Generalization Paul H. Thibodeau (paul.thibodeau@oberlin.edu) Erin M. Tesny (erin.tesny@oberlin.edu) Oberlin College; Department of Psychology Stephen J. Flusberg (stephen.flusberg@purchase.edu) Purchase College, State University of New York; Department of Psychology Abstract Similarity-based generalization is fundamental to human cognition, and the ability to draw analogies based on relational similarities between superficially different domains is crucial for reasoning and inference. Learning to base generalization on shared relations rather than (or in the face of) shared perceptual features has been identified as an important developmental milestone. However, recent research has shown that children and adults can flexibly generalize based on perceptual or relational similarity, depending on what has been an effective strategy in the past in a given context. Here we demonstrate that this pattern of behavior naturally emerges over the course of development in a domain-general statistical learning model that employs distributed, sub-symbolic representations. We suggest that this model offers a parsimonious account of the development of context-sensitive, similarity-based generalization and may provide several key advantages over other popular structured or symbolic approaches to modeling analogical inference. Keywords: Analogy; similarity; relational shift; distributed connectionist model; generalization; statistical learning Introduction Is a lemon more similar to a small yellow balloon or a green grape? The answer, it turns out, is not so straightforward. All three objects are small and round(ish), but the lemon and balloon are somewhat larger than the grape and both of them are yellow. On the other hand, the lemon and grape are filled with juice, grow on trees, and belong to the same basic category (fruit), while the balloon is man-made and filled with air. Your response, therefore, may depend on what type of similarity (you believe) the questioner has in mind; the lemon looks more similar to the yellow balloon but is structurally (and functionally) more similar to the grape. Without any additional information, most adults would probably say that the lemon is more similar to the grape. The shared taxonomy and structural elements of the lemon and grape trump the superficial similarity of the lemon and balloon. However, this relational match requires relatively sophisticated knowledge of lemons and grapes; without it, the lemon will seem more similar to the balloon. Indeed, experimental research has found that young children typically base similarity judgments on perceptual features before they have the relevant domain knowledge to make relational matches (Gentner & Ratterman, 1998). In other words, until young children gain sufficient knowledge of fruit, they are likely to say that a lemon is more similar to a yellow balloon than a grape. This developmental change in similarity matching – from an early reliance on surface- level, perceptual features to a later reliance on structural or relational properties – is known as the perceptual-to- relational shift (Gentner, 1988; Goswami, 1996; Piaget, 1952; Ratterman & Gentner, 1998). Computational models have been instrumental in helping us understand the mechanistic underpinnings of relational reasoning, though they have focused primarily on adult- level competence (e.g., Falkenhainer, Forbus, & Gentner, 1989; Hummel & Holyoak, 1997). Recently, however, more attention has been given to the development of relational reasoning (Doumas, Hummel, & Sandhofer, 2008; Gentner, Rattermann, Markman, & Kotovsky, 1995; Leech, Mareschal, & Cooper, 2008; Morrison, Doumas, Richland, 2011; Thibodeau, Flusberg, Glick, & Sternberg, 2013). Notably, proponents of two modeling approaches that have been at the forefront of the field (SME, proposed by Falkenhainer, Forbus, & Gentner, 1989; and LISA, proposed by Hummel & Holyoak, 1997) have offered somewhat different (though arguably complementary) accounts of the emergence of relational reasoning. These two accounts highlight different aspects of cognitive development to explain the developmental trajectory of similarity-based generalization. Gentner et al. (1995) used SME to show how conceptual change and knowledge accretion could give rise to the relational shift. That is, they argue that relational reasoning emerges as domain-specific knowledge increases (Gentner & Rattermann, 1991; Gentner, 1988; but see, e.g., Goswami, 1995 for a different perspective). In SME, concepts are hand-coded in a predicate calculus that represents both objects and their relations in a structured, symbolic fashion. Knowledge accretion is achieved in the model by manually re-coding representations (and not, e.g. through experiential learning). While this model can accurately capture the perceptual-to-relational shift in this fashion (i.e., by using “object-centered” representations to model the performance of younger children and “relation- centered” representations to model the performance of older children and adults), it leaves open the question of how conceptual re-representation emerges as people acquire