Representational principles of function generalization

Abstract

Generalization is at the core of human intelligence. When the relationship between continuous-valued data is generalized, generalization amounts to function learning. Function learning is important for understanding human cognition, as many everyday tasks and problems involve learning how quantities relate and subsequently using this knowledge to predict novel relationships. While function learning has been studied in psychology since the early 1960s, this thesis argues that questions regarding representational characteristics have not been adequately addressed in previous research. Previous accounts of function learning have often proposed one-size-fits-all models that excel at capturing how participants learn and extrapolate. In these models, learning amounts to learning the details of the presented patterns. Instead, this thesis presents computational and empirical results arguing that participants often learn abstract features of the data, such as the type of function or the variability of features of the function, instead of the details of the function. While previous work has emphasized domain-general inductive biases and learning rates, I propose that these biases are more flexible and adaptive than previously suggested. Given contextual information that sequential tasks share the same structure, participants can transfer knowledge from previous training to inform their generalizations. Furthermore, this thesis argues that function representations can be composed to form more complex hypotheses, and humans are perceptive to, and sometimes generalize according to these compositional features. Previous accounts of function learning had to postulate a fixed set of candidate functions that form a partic ipants’ hypothesis space, which ultimately struggled to account for the variety of extrapolations people can produce. In contrast, this thesis’s results suggest that a small set of broadly applicable functions, in combination with compositional principles, can produce flexible and productive generalization.