Computation in Neural Nets - Understanding Understanding: Essays on Cybernetics and Cognition - page 26

For obvious reasons we shall call all elements belonging to class N 1 “gen-
eralized receptors” and all elements belonging to class N 2 “generalized
effectors”. The justification of this terminology may be derived from
general usage which refers to a receptor as an element that is not stimu-
lated by an element of its own network but rather by some outside agent.
Likewise, an effector is usually thought of as an element that produces an
effect outside of its own network.
This observation permits us to use hybrid networks or action networks
as compound elements in networks that show some repetition in their con-
nection scheme. An example is given in fig. 3 in which the net suggested in
3a is to be inserted into the nodes of the net indicated in 3b. The repetition
of this process gives rise to the concept of periodic networks, features
almost ubiquitous in the physiological situation. To expect such periodicity
is not too far-fetched if one realizes for a moment that many net structures
are genetically programmed. The maximum amount of information neces-
sary to program a net of n elements is H n = n 2 . If this net is made up of k
periods of n / k elements each, the maximum information required is only
H k , n = k ( n / k ) 2 = n 2 / k . Consequently, periodicity—or redundancy—repre-
sents genetic economy.
Keeping this point in mind let us investigate further constraints in the
structure of networks.
Consider for the moment an action net consisting of n = 2 m elements
where the number of elements in set N 1 , the generalized receptors, equals
the number of elements in N 2 , the generalized effectors. In this case the con-
nection matrix has precisely half of its rows and columns empty (0), and the
FIGURE 3. Replacement of elements by
networkers. Periodic networks.