The conceptual basis of function learning and extrapolation: Comparison of rule-based and associative-based models

The purpose of this article is to provide a foundation for a more formal, systematic, and integrative approach to function learning that parallels the existing progress in category learning. First, we note limitations of existing formal theories. Next, we develop several potential formal models of function learning, which include expansion of classic rule-based approaches and associative-based models. We specify for the first time psychologically based learning mechanisms for the rule models. We then present new, rigorous tests of these competing models that take into account order of difficulty for learning different function forms and extrapolation performance. Critically, detailed learning performance was also used to conduct the model evaluations. The results favor a hybrid model that combines associative learning of trained input-prediction pairs with a rule-based output response for extrapolation (EXAM).