Computation in Neural Nets - Understanding Understanding: Essays on Cybernetics and Cognition - page 76

(iii) McCulloch Element; Synchronism
We finally change the modus operandi of our net to synchronous operation
with McCulloch element (q=1). Clearly, for uniform stimulus distribution,
strong or weak, steady or flicker, all effectors will be silent; the net shows
no response. Nevertheless, an edge will be readily observed.
However, a net incorporating much simpler elements will suffice. A
McCulloch element with only two inputs computing the logical function
“either A or B ” (see function No. 6, table 1) clearly computes an “edge”.
This function represents again a symmetric action function. Asymmetry
may be introduced by choosing a McCulloch element that computes, say,
function No. 2: “ A only”. A net incorporating this element in layer L 1 is
given in fig. 28a. The result is, of course, the detection of an asymmetric
stimulus property, the presence of a “right hand edge”. Hence, in order to
detect directionality in the stimulus field the net must mirror this direc-
tionality in the connectivity of its structure or in the operation of its ele-
ments. Utilizing synaptic delays that occur in layer L 1 we have attached a
second layer L 2 that computes in D the function “ C only”. Consequently,
layer L 2 detects right edges moving to the right. While C computes the pres-
ence of a right hand edge D will be silent, because the presence of a right
edge implies a stimulated B which, simultaneous with an active C , gives an
inactive D . Similarly, a left edge will leave D inactive; but C is inactive
during the presence of a left edge. However, D will be active at once if we
move the right hand edge of an obstruction to the right. Under these cir-
cumstances the synaptic delay in C will cause C to report still a right hand
edge to D , while B is already without excitation. Of course, movements to
the left remain unnoticed by this net. The equivalent net using the appro-
priate McCulloch formal neurons is given in fig. 28b.
Thanks to the remarkable advances in experimental neurophysiology, in
numerous cases the existence of abstracting cascaded action networks in
sensory pathways has been demonstrated. In their now classic paper “What
the frog's eye tells the frog's brain” Letvvin et al. (1959) summed up their
findings: “The output from the retina of the frog is a set of four distributed
operations on the visual image. These operations are independent of the
level of general illimunation and express the image in terms of: (1) local
sharp edges and contrast; (2) the curvature of edge of a dark object; (3) the
movement of edges; and (4) the local dimmings produced by movement or
rapid general darkening”.
To these properties Maturana (1962) adds a few more in the eye of the
pigeon. Here anti-symmetric action functions produce strong directionali-
ties. There are fibers that report horizontal edges, but only when they move.
A vertical edge is detected whether it is moving or not. A careful analysis
of the receptor function G ( q , p ) in the visual system in cats and monkeys
has been carried out by Hubel (1962); Mountcastle et al. (1962) explored
the complicated transformations of multilayer mixed action-interaction net-