Studies in the learning function

The error function of the theoretical learning curve developed by Thurstone has been fitted to maze data from rats that have been subjected to cerebral cortical insult. There is a high degree of relationship between the number of errors necessary to complete learning as predicted from the curve and the experimental measure of learning, total-errors-minus-errors-first-trial. The procedure provides a method of analysis for individual learning records and it may be used to shorten the training period. The goodness of fit indicates that the underlying logic of the learning curve is plausible.A grant-in-aid from the National Research Council has made the present analysis possible. We are indebted to Professor L. L. Thurstone for aid and encouragement.     

Nonmonotonic extrapolation in function learning

This article reports the results of an experiment addressing extrapolation in function learning, in particular the issue of whether participants can extrapolate in a nonmonotonic manner. Existing models of function learning, including the extrapolation association model of function learning (EXAM; E. L. DeLosh, J. R. Busemeyer, & M. A. McDaniel, 1997), cannot account for this type of extrapolation pattern. We present the results of an experiment in which participants were shown a series of paired stimulus-response magnitudes where the relationship between these 2 dimensions conformed to a cyclic function. Participants were shown to extrapolate from these training data in a nonmonotonic way, contrary to predictions from EXAM. A new model of function learning is presented, which predicts responses more accurately than EXAM.     

Simplified learning in complex situations: knowledge partitioning in function learning

The authors explored the phenomenon that knowledge is not always integrated and consistent but may be partitioned into independent parcels that may contain mutually contradictory information. In 4 experiments, using a function learning paradigm, a binary context variable was paired with the continuous stimulus variable of a to-be-learned function. In the first 2 experiments, when context predicted the slope of a quadratic function, generalization was context specific. Because context did not predict function values, it is suggested that people use context to gate separate learning of simpler partial functions. The 3rd experiment showed that partitioning also occurs with a decreasing linear function, whereas the 4th study showed that partitioning is absent for a linearly increasing function. The results support the notion that people simplify complex learning tasks by acquiring independent parcels of knowledge.     

Adult age differences in function concept learning

Function concept learning and knowledge use was explored across adulthood. During training older and younger adults predicted an amount of physiological arousal produced as a negative and positive function of a chemical substance. Knowledge use was evaluated with two transfer conditions requiring a switch between contextual contingencies: a relationship inversion, predicting the chemical amount given the physiological arousal, and a change from graphic based to text based stimuli. Older adults were impaired in applying the negative slope concept. However, there was no relative deficit in switching between the negative and positive function slopes or inverting the learned relationship. Our results suggest that age-related differences in relational reasoning tasks vary not only with processing efficiency, but also task related conceptual knowledge.     

Induction of combination rules in two-dimensional function learning

Previous studies have typically found that when people learn to combine two dimensions of a stimulus to select a response, they learn additive combination rules more easily than nonadditive (e.g., multiplicative) ones. The present experiments demonstrate that in some situations people can learn multiplicative rules more easily than other (e.g., additive) rules. Subjects learned to produce specified response durations when presented with stimulus lines varying in length and angle of orientation. When stimuliand correct responses were related by a multiplicative combination of power functions, learning was relatively easy (Experiment 1). In contrast, systematic response biases occurred during the early phases of learning an additive combination of linear functions (Experiment 2) and a more complex (nonadditive and nonmultiplicative) combination of linear functions (Experiment3), suggesting that people have a tendency to induce a multiplicative combination of power functions. However, the initial biases decreased with practice. These results are explained in terms of a revised adaptive regression model of function learning originally proposed by Koh and Meyer (1991). Differences between the present results and previous results in the literature are discussed.     

A generalization of Thurstone's learning function

Thurstone's equation giving the probability of a correct response (p) as a function of practice time (t) when punishment and reward have equal effects has been generalized to the case where the effect of punishment is not necessarily equal to the effect of reward. Since the general equation is somewhat unwieldy, three special cases are considered, where reward has no effect, where punishment has no effect, and where these effects are equal. Equations are given together with tables for making a rectified plot for each of the three special cases.This study was supported in part by contract N6onr 270-20 between the Office of Naval Research and Princeton University. The opinions expressed are, of course, those of the author and do not represent attitudes or policies of the Office of Naval Research.