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

phase, pairs of to-be-associated patterns simultaneously activate the input and
output units in Figure 4-1. With each presented pair, all of the connection weights—
the strength of each connection between an input and an output processor—are
modified by adding a value to them. This value is determined in accordance with
some version of Hebb’s (1949) learning rule. Usually, the value added to a weight is
equal to the activity of the processor at the input end of the connection, multiplied
by the activity of the processor at the output end of the connection, and multiplied
by some fractional value called a learning rate. The mathematical details of such
learning are provided in Chapter 9 of Dawson (2004).
The standard pattern associator is called a distributed memory because its
knowledge is stored throughout all the connections in the network, and because
this one set of connections can store several different associations. During a recall
phase, a cue pattern is used to activate the input units. This causes signals to be sent
through the connections in the network. These signals are equal to the activation
value of an input unit multiplied by the weight of the connection through which the
activity is being transmitted. Signals received by the output processors are used to
compute net input, which is simply the sum of all of the incoming signals. In the
standard pattern associator, an output unit’s activity is equal to its net input. If the
memory is functioning properly, then the pattern of activation in the output units
will be the pattern that was originally associated with the cue pattern.
The standard pattern associator is the cornerstone of many models of memory
created after the cognitive revolution (Anderson, 1972; Anderson et al., 1977; Eich,
1982; Hinton & Anderson, 1981; Murdock, 1982; Pike, 1984; Steinbuch, 1961; Taylor,
1956). These models are important, because they use a simple principle—James’
(1890a, 1890b) law of habit—to model many subtle regularities of human memory,
including errors in recall. In other words, the standard pattern associator is a kind
of memory that has been evaluated with the different kinds of evidence cited in
Chapters 2 and 3, in an attempt to establish strong equivalence.
The standard pattern associator also demonstrates another property crucial
to modern connectionism, graceful degradation. How does this distributed model
behave if it is presented with a noisy cue, or with some other cue that was never
tested during training? It generates a response that has the same degree of noise as
its input (Dawson, 1998, Table 3-1). That is, there is a match between the quality of
the memory’s input and the quality of its output.
The graceful degradation of the standard pattern associator reveals that it is
sensitive to the similarity of noisy cues to other cues that were presented during
training. Thus modern pattern associators provide some evidence for James’ (1890a)
attempt to reduce other associative laws, such as the law of similarity, to the basic
law of habit or contiguity.
138 Chapter 4