1000
1010
0010
0100
0110
0001
0000
1111
|
1 |
0 |
0 |
1 |
|
0 |
0 |
1 |
0 |
|
0 |
1 |
0 |
1 |
|
0 |
0 |
0 |
1 |
1000
1010
1001
0100
0110
0101
1001
1111
Figure 5: Representing feature conjunctions. A network consisting of four nodes and four inputs (‘black’,
‘white’, ‘square’ and ‘triangle’) is wired up so that the first node receives input from ‘black-square’, the
second from ‘white-square’ the third from ‘black-triangle’ and the fourth from ‘white-triangle’ (all weights
have a value of 1). The first four figures in the top row show the response of the network to valid conjunc-
tions of features from a single object. The last figure in the top row shows the response to an ambiguous
input that could either be caused by the presentation of a black-square and a white-triangle, or by a black-
triangle and a white-square. The second row shows responses to the same inputs as used in first row, but
with the first node (which represents ‘black-squares’) receiving a small bias input during competition. It
can be seen that for input patterns where activation of the first node is not justified by the input the bias
has no effect on the outcome. However, for the ambiguous case the bias causes a parsing of the input into
‘black-square’ + ‘white-triangle’.
response (Marshall and Gupta, 1998). However, this approach is also unsatisfactory since it suggests that
one-quarter of each pattern is present, when this is not the case. Neither of these activity patterns seem to
provide an appropriate representation. Any response in which both nodes generate equal activity suggests
that a single piece of data provides evidence for two interpretations simultaneously. While any response
in which one node has higher activity than the other is making an unjustified, arbitrary, selection. Pre-
integration lateral inhibition avoids generating responses that are not justified by the available data by
preventing any response (Figure 4). It thus produces no representation of the input rather than a potentially
misleading representation.
As an example ofa situation in which such an approach would be advantageous consider again using a
network to represent the color and shape of an object. However, in this situation the network is wired up to
generate localist representations of conjunctions of color and shape from a distributed input representation
of these separate features. For example, consider a network with four nodes representing ‘black-squares’,
‘white-squares’, ‘black-triangles’ and ‘white-triangles’ (with the inputs to this network signaling ‘black’,
‘white’, ‘square’ and ‘triangle’). In this case the ambiguous situation occurs when multiple objects are
presented to the network simultaneously: a black-square and a white-triangle would cause an identical
input pattern as a black-triangle and a white-square (Thorpe, 1995). Given such a situation it is important
to prevent illusory conjunctions from being represented (Roelfsema et al., 2000), pre-integration lateral
inhibition does so by suppressing all responses (Figure 5). One solution to this ‘binding’ problem would
be the action of expectation or attention in disambiguating the situation (Reynolds and Desimone, 1999;
Roelfsema et al., 2000). If such modulatory effects are modeled by adding a small increase to the activity
of one node during competition then this succeeds in causing a response from those nodes compatible
with the biased interpretation, while suppressing activity in the other two nodes (Figure 5). A similar bias
applied to a network using post-integration inhibition would cause the biased node to be the most active,
but would also suppress the response of the node representing the second object. An alternative solution
would be for inputs representing the features of one object to be active simultaneously but out-of-phase
with those inputs representing the other object (Gray, 1999; Singer, 1999; von der Malsburg, 1981). In this
case the network succeeds (as would a network using the standard method of competition) by responding
alternately to the non-ambiguous patterns generated by each individual object presented in isolation.