TY - JOUR
T1 - Measurement invariance explains the universal law of generalization for psychological perception
JF - Proceedings of the National Academy of Sciences
JO - Proc Natl Acad Sci USA
DO - 10.1073/pnas.1809787115
SP - 201809787
AU - Frank, Steven A.
Y1 - 2018/09/06
UR - http://www.pnas.org/content/early/2018/09/05/1809787115.abstract
N2 - When an animal is presented with two stimuli, it may consider them similar or different. Similarity often expresses a generalized notion of a category, such as two circles with different sizes, shadings, and colors both being circles. In many studies, perception of similarity declines exponentially with the measure of separation, a pattern often called the universal law of generalization. This article shows that the universal exponential law can be explained by simple properties any reasonable perceptual scale must have. A shift of the scale by a constant amount, or a stretch by a constant amount, should not change the animalâ€™s ability to perceive generalities or differences. Those invariant measurement properties by themselves explain why perceived generalization follows an exponential pattern.The universal law of generalization describes how animals discriminate between alternative sensory stimuli. On an appropriate perceptual scale, the probability that an organism perceives two stimuli as similar typically declines exponentially with the difference on the perceptual scale. Exceptions often follow a Gaussian probability pattern rather than an exponential pattern. Previous explanations have been based on underlying theoretical frameworks such as information theory, Kolmogorov complexity, or empirical multidimensional scaling. This article shows that the few inevitable invariances that must apply to any reasonable perceptual scale provide a sufficient explanation for the universal exponential law of generalization. In particular, reasonable measurement scales of perception must be invariant to shift by a constant value, which by itself leads to the exponential form. Similarly, reasonable measurement scales of perception must be invariant to multiplication, or stretch, by a constant value, which leads to the conservation of the slope of discrimination with perceptual difference. In some cases, an additional assumption about exchangeability or rotation of underlying perceptual dimensions leads to a Gaussian pattern of discrimination, which can be understood as a special case of the more general exponential form. The three measurement invariances of shift, stretch, and rotation provide a sufficient explanation for the universally observed patterns of perceptual generalization. All of the additional assumptions and language associated with information, complexity, and empirical scaling are superfluous with regard to the broad patterns of perception.
ER -