Shepard (Probabilistic Concepts)

Universal Law of Generalization

The probability that a response learned to one stimulus will generalize to another is an invariant monotonic function of the distance between them in psychological space

To a good approximation, this probability decays exponentially as the distance between stimuli increases (this is robust)

Consequential Region

A region in psychological space containing all stimuli that belong to the same natural kind

Natural Kind

Meaning they have the same significant consequences for an individual’s survival or reproduction

Cognitive Act

Generalization is not a "failure of sensory discrimination", it is a cognitive act of inferring whether a new, similar-looking stimulus belongs to the same consequential region as a previously encountered one

Probabilistic Geometry

An individual estimates the conditional probability that a second stimulus (point x) falls within the same consequential region as a first stimulus (point 0), given that the first stimulus was found to be consequential

Nonmetric MDS

A numerical method used to determine the coordinates of stimuli in psychological space; Takes a matrix of generalization data (probabilities of confused responses) and finds the most parsimonious spatial configuration where the rank order of distances matches the rank order of the generalization measures

Purely psychological process

Generalization

Generalization stems from uncertainty about the distribution of consequential stimuli

What does Discrimination Failure stem from?

Discrimination failure stems from uncertainty about the relative locations of individual stimuli in psychological space

Gaussian Decay

In cases of protracted training or "noise" in internal representation, the generalization function may deviate from exponential decay toward a Gaussian (bell-shaped) function