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

Finally, different degrees of superposition may be reflected in the number of different
contents that a given resource can represent. For example, it is well known that
one kind of artificial neural network, the Hopfield network (Hopfield, 1982), is of
limited capacity, where if the network is comprised of N processors, it will be only
to be able to represent in the order of 0.18N distinct memories (Abu-Mostafa & St.
Jacques, 1985; McEliece, et al., 1987).
Nonetheless, van Gelder (1991) expressed confidence that the notion of superposition
provides an appropriate characteristic for defining a distributed representation.
“It is strong enough that very many kinds of representations do not count as
superposed, yet it manages to subsume virtually all paradigm cases of distribution,
whether these are drawn from the brain, connectionism, psychology, or optics” (p. 54).
Even if van Gelder’s (1991) definition is correct, it is still the case that the concept
of superposition does not universally distinguish connectionist representations
from classical ones. One example of this is when concepts are represented as collections
of features or microfeatures. For instance, in an influential PDP model called
an interactive activation and competition network (McClelland & Rumelhart, 1988),
most of the processing units represent the presence of a variety of features. Higherorder
concepts are defined as sets of such features. This is an instance of superposition,
because the same feature can be involved in the representation of multiple
networks. However, the identical type of representation—that is, superposition
of featural elements—is also true of many prototypical classical representations,
including semantic networks (Collins & Quillian, 1969, 1970a, 1970b) and feature set
representations (Rips, Shoben, & Smith, 1973; Tversky, 1977; Tversky & Gati, 1982).
The discussion up to this point has considered a handful of different notions
of distributed representation, and has argued that these different definitions do
not appear to uniquely separate connectionist and classical concepts of representation.
To wrap up this discussion, let us take a different approach, and consider
why in some senses connectionist researchers may still need to appeal to local
representations.
One problem of considerable interest within cognitive neuroscience is the issue
of assigning specific behavioural functions to specific brain regions; that is, the localization
of function. To aid in this endeavour, cognitive neuroscientists find it useful to
distinguish between two qualitatively different types of behavioural deficits. A single
dissociation consists of a patient performing one task extremely poorly while performing
a second task at a normal level, or at least very much better than the first. In
contrast, a double dissociation occurs when one patient performs the first task significantly
poorer than the second, and another patient (with a different brain injury)
performs the second task significantly poorer than the first (Shallice, 1988).
Cognitive neuroscientists have argued that double dissociations reflect damages
to localized functions (Caramazza, 1986; Shallice, 1988). The view that dissociation
Marks of the Classical? 341