Large-Scale Brain Area Functional Organization - Computational Explorations in Cognitive Neuroscience - page 216

cle, square, triangle). The binding problem arises when
you present both a red circle and a green square to such
a system — how does it know that it is the circle that
is red and the square that is green, and not the other
way around (see figure 7.8 for an illustration)? In other
words, how does the system bind these separate features
together as applying to the same object?
This is a good example of a problem that arises from
a simplified, transparent, symbol-like set of representa-
tional assumptions, which can be resolved by adopting
a more complex and less transparent distributed frame-
work. The simplification in question is that stimulus
information (e.g., shape and color) is represented com-
pletely separately — if instead representations incorpo-
rate aspects of both shape and color, then the conjunc-
tions between these stimulus dimensions (e.g., red-and-
circle, vs. green-and-circle) can be represented.
The standard objection to this conjunctive solution is
that it is impossible to represent all possible such com-
binations in the world — way too many units would be
required for realistic numbers of features. However, the
alternative implicit in this objection is also overly sim-
plistic — instead, individual units can represent multi-
ple combinations of conjunctions, thereby covering the
space much more efficiently (Wickelgren, 1969; Mel &
Fiser, 2000). We can analyze this solution by consid-
ering combinations of conjunctions used together with
the separate feature representations. The critical test is
whether the overall distributed pattern of activity across
all the units uniquely identifies the combination and
binding of features present in the input.
Table 7.1 shows how the combination-of-conjunc-
tions scheme works, with only a single additional unit
required. This additional unit responds to a red circle
or a green square or a blue triangle, and is enough to
disambiguate the cases where the network would oth-
erwise be confused on the basis of the separate fea-
tures alone (e.g., confusing a red square and a green
circle for a green square and a red circle). Thus, the
total number of units required is 7 (6 separate features
and 1 conjunction unit), which is only 2 less than the 9
units that would be needed to encode all possible con-
junctions. However, when you scale the problem up,
the advantages become more apparent. For example,
if you have 4 colors and 4 shapes, then 16 conjunctive

? ?

Red Green Blue

? ?

Triangle Circle Square

Figure 7.8: Illustration of the binding problem, where en-
coding in terms of separate features leads to confusion when
multiple items are present in the input. Here, a red circle and
green square are present in the input, but the same representa-
tion would be activated by a green circle and a red square, so
the system does not really know which was present (as illus-
trated by the “imagination bubble” above the representation).

We will discuss in more detail examples of struc-
tured approaches in the context of object recognition
(i.e., having a full 3-D structured representation akin
to one you might find in a computer-aided design pro-
gram) and sentence-level processing (i.e., representing
the full parse-tree grammatical structure of a sentence)
in chapters 8 and 10, respectively. We will find that the
alternative distributed approach adopted in the models
we explore offers a number of advantages in these con-
texts. Finally, note that although we focus on examples
from visual perception in the following discussion, the
issues generalize to many other aspects of cognition.

7.6.1 The Binding Problem for Distributed

Representations of Multiple Items

One of the most commonly raised problems with neu-
ral networks is known as the binding problem ,which
arises whenever different features of a given stimulus
are represented completely separately by different un-
derlying representations, and multiple items need to be
represented. Let's imagine we have a set of units that
encode color information (e.g., red, green, and blue),
and another set that encode shape information (e.g., cir-