Mind, Body, World- Foundations of Cognitive Science, 2013a

esponse is interpreted as representing a class to which the input pattern is unambiguously
assigned.
What does the activity of a unit in a connectionist network mean? Under the
strict digital interpretation described above, activity is interpreted as the truth value
of some proposition represented by the unit. However, modern activation functions
such as the logistic or Gaussian equations have continuous values, which permit
more flexible kinds of interpretation. Continuous activity might model the frequency
with which a real unit (i.e., a neuron) generates action potentials. It could
represent a degree of confidence in asserting that a detected feature is present, or
it could represent the amount of a feature that is present (Waskan & Bechtel, 1997).
In this section, a computational-level analysis is used to prove that, in the context
of modern learning theory, continuous unit activity can be unambiguously
interpreted as a candidate measure of degree of confidence with conditional probability
(Waskan & Bechtel, 1997).
In experimental psychology, some learning theories are motivated by the
ambiguous or noisy nature of the world. Cues in the real world do not signal outcomes
with complete certainty (Dewey, 1929). It has been argued that adaptive systems
deal with worldly uncertainty by becoming “intuitive statisticians,” whether
these systems are humans (Peterson & Beach, 1967) or animals (Gallistel, 1990;
Shanks, 1995). An agent that behaves like an intuitive statistician detects contingency
in the world, because cues signal the likelihood (and not the certainty) that
certain events (such as being rewarded) will occur (Rescorla, 1967, 1968).
Evidence indicates that a variety of organisms are intuitive statisticians. For
example, the matching law is a mathematical formalism that was originally used
to explain variations in response frequency. It states that the rate of a response
reflects the rate of its obtained reinforcement. For instance, if response A is reinforced
twice as frequently as response B, then A will appear twice as frequently
as B (Herrnstein, 1961). The matching law also predicts how response strength
varies with reinforcement frequency (de Villiers & Herrnstein, 1976). Many results
show that the matching law governs numerous tasks in psychology and economics
(Davison & McCarthy, 1988; de Villiers, 1977; Herrnstein, 1997).
Another phenomenon that is formally related (Herrnstein & Loveland, 1975) to
the matching law is probability matching, which concerns choices made by agents
faced with competing alternatives. Under probability matching, the likelihood that
an agent makes a choice amongst different alternatives mirrors the probability associated
with the outcome or reward of that choice (Vulkan, 2000). Probability matching
has been demonstrated in a variety of organisms, including insects (Fischer,
Couvillon, & Bitterman, 1993; Keasar et al., 2002; Longo, 1964; Niv et al., 2002), fish
(Behrend & Bitterman, 1961), turtles (Kirk & Bitterman, 1965), pigeons (Graf, Bullock,
& Bitterman, 1964), and humans (Estes & Straughan, 1954).
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