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

unit activity via the existing connection weights. Second, output unit error is computed
by taking the difference between actual output unit activity and desired
output unit activity for each output unit in the network. This kind of training is
called supervised learning, because it requires an external trainer to provide the
desired output unit activities. Third, Hebb-style learning is used to associate input
unit activity with output unit error: weight change is equal to a learning rate times
input unit activity times output unit error. (In modern perceptrons, this triple product
can also be multiplied by the derivative of the output unit’s activation function,
resulting in gradient descent learning [Dawson, 2004]).
The supervised learning of a perceptron is designed to reduce output unit
errors as training proceeds. Weight changes are proportional to the amount of generated
error. If no errors occur, then weights are not changed. If a task’s solution can
be represented by a perceptron, then repeated training using pairs of input-output
stimuli is guaranteed to eventually produce zero error, as proven in Rosenblatt’s
perceptron convergence theorem (Rosenblatt, 1962).
Being a product of Old Connectionism, there are limits to the range of input-output
mappings that can be mediated by perceptrons. In their famous computational
analyses of what perceptrons could and could not learn to compute, Minsky and
Papert (1969) demonstrated that perceptrons could not learn to distinguish some
basic topological properties easily discriminated by humans, such as the difference
between connected and unconnected figures. As a result, interest in and funding for
Old Connectionist research decreased dramatically (Medler, 1998; Papert, 1988).
However, perceptrons are still capable of providing new insights into phenomena
of interest to cognitive science. The remainder of this section illustrates this by
exploring the relationship between perceptron learning and classical conditioning.
The primary reason that connectionist cognitive science is related to empiricism
is that the knowledge of an artificial neural network is typically acquired via
experience. For instance, in supervised learning a network is presented with pairs
of patterns that define an input-output mapping of interest, and a learning rule is
used to adjust connection weights until the network generates the desired response
to a given input pattern.
In the twentieth century, prior to the birth of artificial neural networks
(McCulloch & Pitts, 1943), empiricism was the province of experimental psychology.
A detailed study of classical conditioning (Pavlov, 1927) explored the subtle
regularities of the law of contiguity. Pavlovian, or classical, conditioning begins with
an unconditioned stimulus (US) that is capable, without training, of producing an
unconditioned response (UR). Also of interest is a conditioned stimulus (CS) that
when presented will not produce the UR. In classical conditioning, the CS is paired
with the US for a number of trials. As a result of this pairing, which places the CS
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