Computation in Neural Nets - Understanding Understanding: Essays on Cybernetics and Cognition - page 87

Its usefulness becomes obvious if we assume that the stimulus of L q is a
contour that has been computed in L p from a preceding network say, L o ,
L p . On behalf of the d-function this contour, and nothing else, maps from
L p into L q . Take, for instance, a straight line with uniform intensity s o to be
the stimulus for L q (see fig. 34). Since two points symmetrical to any point
on this line contribute

( ( ) )

ak sf

o cos

+ cos 180 - f D A = 0 ,

2 1

because

( )

cos f =- cos 180 - f ,

a straight line gives no response. Curvature, however, is reported. The total
net-response

Ú r

()

Rr = d A

2 2

L

2

vanishes for bilateral symmetrical figures with their axis of symmetry par-
allel to the ori en tation of elements in L q . However, when turned away from
this position, R π 0 (see fig. 35).

4.8. Interaction Networks of Cell Assemblies
We consider the case where connections between all elements in the
network appear freely and a separation into layers of purely-transmitting
and purely-receiving elements is impossible. When all return connections
between interconnected elements are cut, the system reduces to an action
network. Clearly, we are dealing here with the more general case and con-
sequently have to be prepared for results that do not yield as easily as in
the previous case. However, the methods concepts developed in the previ-
ous section are immediately applicable to our present situation.

FIGURE 34. Insensitivity of antisymmetri-
cal action net to straight lines.