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

function, one can still translate Rescorla-Wagner learning into perceptron learning,
and vice versa (Dawson, 2008).
One would imagine that the existence of proofs of the computational equivalence
between Rescorla-Wagner learning and perceptron learning would mean that
perceptrons would not be able to provide any new insights into classical conditioning.
However, this is not correct. Dawson (2008) has shown that if one puts aside
the formal comparison of the two types of learning and uses perceptrons to simulate
a wide variety of different classical conditioning paradigms, then some puzzling
results occur. On the one hand, perceptrons generate the same results as the
Rescorla-Wagner model for many different paradigms. Given the formal equivalence
between the two types of learning, this is not surprising. On the other hand,
for some paradigms, perceptrons generate different results than those predicted
from the Rescorla-Wagner model (Dawson, 2008, Chapter 7). Furthermore, in
many cases these differences represent improvements over Rescorla-Wagner learning.
If the two types of learning are formally equivalent, then how is it possible for
such differences to occur?
Dawson (2008) used this perceptron paradox to motivate a more detailed comparison
between Rescorla-Wagner learning and perceptron learning. He found that
while these two models of learning were equivalent at the computational level of
investigation, there were crucial differences between them at the algorithmic level.
In order to train a perceptron, the network must first behave (i.e., respond to an
input pattern) in order for error to be computed to determine weight changes. In
contrast, Dawson showed that the Rescorla-Wagner model defines learning in such
a way that behaviour is not required!
Dawson’s (2008) algorithmic analysis of Rescorla-Wagner learning is consistent
with Rescorla and Wagner’s (1972) own understanding of their model: “Independent
assumptions will necessarily have to be made about the mapping of associative
strengths into responding in any particular situation” (p. 75). Later, they make this
same point much more explicitly:
We need to provide some mapping of [associative] values into behavior. We are
not prepared to make detailed assumptions in this instance. In fact, we would
assume that any such mapping would necessarily be peculiar to each experimental
situation, and depend upon a large number of ‘performance’ variables.
(Rescorla & Wagner, 1972, p. 77)
Some knowledge is tacit: we can know more than we can tell (Polanyi, 1966). Dawson
(2008) noted that the Rescorla-Wagner model presents an interesting variant of this
theme, where if there is no explicit need for a behavioural theory, then there is no
need to specify it explicitly. Instead, researchers can ignore Rescorla and Wagner’s
(1972) call for explicit models to convert associative strengths into behaviour
and instead assume unstated, tacit theories such as “strong associations produce
192 Chapter 4