Induction of combination rules in two-dimensional function learning

Quick approximation of bivariate functions

This paper presents two experiments where participants had to approximate function values at various generalization points of a square, using given function values at a small set of data points. A representative set of standard function approximation models was trained to exactly fit the function values at data points, and models' responses at generalization points were compared to those of humans. Then one defined a large class of possible models (including the best two identified predictors) and the class maximal possible prediction accuracy was evaluated. A new model of quick multivariate function approximation belonging to this class was proposed. Its prediction accuracy was close to the maximum possible, and significantly better than that of all other models tested. The new model also provided a significant account of human response variability. Finally, it was shown that this model is more particularly suitable for problems in which the visual system can perform some specific structuring of the data space. This model is therefore considered as a suitable starting point for further investigations into quick multivariate function approximation, which is to date an inadequately explored question in cognitive psychology.

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.

Population of Linear Experts: Knowledge Partitioning and Function Learning

Knowledge partitioning is a theoretical construct holding that knowledge is not always integrated and homogeneous but may be separated into independent parcels containing mutually contradictory information. Knowledge partitioning has been observed in research on expertise, categorization, and function learning. This article presents a theory of function learning (the population of linear experts model--POLE) that assumes people partition their knowledge whenever they are presented with a complex task. The authors show that POLE is a general model of function learning that accommodates both benchmark results and recent data on knowledge partitioning. POLE also makes the counterintuitive prediction that a person's distribution of responses to repeated test stimuli should be multimodal. The authors report 3 experiments that support this prediction.

Limited attention and cue order consistency affect predictive learning: a test of similarity measures

The authors empirically tested the similarity metrics underlying 2 predictive-learning theories: J. K. Kruschke's (1992) attention learning covering map and J. M. Pearce's (1987, 1994) configural models. In Experiment 1, participants concurrently learned 3 types of discriminations: simple (A- vs. B+), common cue (XC- vs. XD+), and compound (YE- vs. ZF+). Accuracy was ordered: simple > compound > common cue. Neither model anticipated this ordering. In Experiment 2, cue order in 2-element configurations was either inconsistent (e.g., YE and EY) as in Experiment 1 or consistent (e.g., EY throughout). Although accuracy differences were smaller under consistent ordering, the relative difficulty of the tasks was the same as in Experiment 1. In Experiment 3, common cue and compound discriminations were tested in different participants to determine whether the ordering of difficulty in Experiments 1 and 2 was caused by differential generalization mediated by the number of elements; the ordering was the same as in Experiments 1 and 2. These results suggest the need for differential attention to event presence and absence and to mechanisms that incorporate limited attentional capacity.

Constrained scaling: the effect of learned psychophysical scales on idiosyncratic response bias

We report seven experiments in which subjects were trained to respond with numbers to the loudness of 1000-Hz pure tones according to power functions with exponents of 0.60, 0.30, and 0.90. Subjects were then presented with stimuli from other continua (65-Hz pure tones or 565-nm lights varying in amplitude) and were asked to judge the subjective magnitude of these stimuli on the same numerical scale. Stimuli from the training continuum were presented, with feedback, on every other trial in order to maintain the trained scale. Except for the 0.90 scale, subjects readily learned the predetermined scales and were able to use them to judge the non-training stimuli with group results consistent with those usually reported. Also, in contrast to the usual magnitude estimation results, these results produced extremely low levels of intersubject variability. We argue that such learned scales can be used as "rulers" for measuring perceived magnitudes, according to a common unit.

Binaural summation after learning psychophysical functions for loudness

Do response-related processes affect perceptual processes? Sometimes they may: Algom and Marks (1990) produced different loudness exponents by manipulating stimulus range, and thereby also modified the rules of loudness summation determined by magnitude scaling. The present study manipulated exponents by having a dozen subjects learn prescribed power functions with exponents of 0.3, 0.6, or 1.2 (re sound pressure). Subjects gave magnitude estimates of the loudness of binaural signals during training, and of monaural and binaural signals after training. During training, subjects' responses followed the nominal functions reasonably well. Immediately following training, subjects applied the numeric response scales uniformly to binaural and monaural signals alike; the implicit monaural-binaural loudness matches, and thus the basic rules underlying binaural summation, were unaffected by the exponent learned. Comparison of these results with those of Algom and Marks leads us to conclude that changing stimulus range likely influences underlying perceptual events, whereas "calibrating" a loudness scale through pretraining leaves the perceptual processes unaffected.