Extrapolation: the sine qua non for abstraction in function learning.

Abstraction was investigated by examining extrapolation behavior in a function-learning task. During training, participants associated stimulus and response magnitudes (in the form of horizontal bar lengths) that covaried according to a linear, exponential, or quadratic function. After training, novel stimulus magnitudes were presented as tests of extrapolation and interpolation. Participants extrapolated well beyond the range of learned responses, and their responses captured the general shape of the assigned functions, with some systematic deviations. Notable individual differences were observed, particularly in the quadratic condition. The number of unique stimulus-response pairs given during training (i.e., density) was also manipulated but did not affect training or transfer performance. Two rule-learning models, an associative-learning model, and a new hybrid model with associative learning and rule-based responding (extrapolation-association model [EXAM]) were evaluated with respect to the transfer data. EXAM best approximated the overall pattern of extrapolation performance.