Predicting transfer performance: a comparison of competing function learning models.

The population of linear experts (POLE) model suggests that function learning and transfer are mediated by activation of a set of prestored linear functions that together approximate the given function (Kalish, Lewandowsky, & Kruschke, 2004). In the extrapolation-association (EXAM) model, an exemplar-based architecture associates trained input values with their paired output values. Transfer incorporates a linear rule-based response mechanism (McDaniel & Busemeyer, 2005). Learners were trained on a functional relationship defined by 2 linear-function segments with mirror slopes. In Experiment 1, 1 segment was densely trained and 1 was sparsely trained; in Experiment 2, both segments were trained equally, but the 2 segments were widely separated. Transfer to new input values was tested. For each model, training performance for each individual participant was fit, and transfer predictions were generated. POLE generally better fit the training data than did EXAM, but EXAM was more accurate at predicting (and fitting) transfer behaviors. It was especially telling that in Experiment 2 the transfer pattern was more consistent with EXAM's but not POLE's predictions, even though the presentation of salient linear segments during training dovetailed with POLE's approach.