A network of NPO’s may constitute anything from a SOM to a
preprogrammed detector, depending upon the relative amount of
preprogramming included. Two methods of preprogramming are: (1) Feeding
a signal out of a permanent storage into some of the inputs of the
network of NPO’s. This a priori copy need not be perfect, because the
SOM will measure the angles Θᵢ anyhow. (2) Feedback, which, after all,
is just a way of taking advantage of the storage inherent in any delay
line. (We implicitly assume that any reasonable physical realization
of an NPO will include a delay T between the x input and the ξ output
which is not less than perhaps 10⁻¹ times the time constant of the
internal feedback loop in the γ computation.)
Simulation of channels that possess a discrete component requires
feedback path(s) to generate the required free products of the finitely
generated groups. Then, such a SOM converges to a maximal subgroup of
the group describing the symmetry of the signal that is a free product
available to this SOM.
Because a single NPO with 1 ≤ n₀ ≤ K₀ is isomorphic (provides the same
input to output mapping) to a suitable network of NPO’s with n₀ = 1, it
suffices to study only networks of NPO’s with n₀ = 1.
Figure 10 is largely self-explanatory. Item a is our schematic symbol
for a single NPO with n₀ = 1. Items b, d (including larger feedback
loops), and f are typical of artificial intelligence networks. Item c
is employed to effect the level changing required in order to apply the
three channels in cascade algorithm to the solution of one-dimensional
coding problems. Observe that items c and e are the only configurations
requiring the γ output. Item d may be used as a limiter by making T⁻¹
high compared to the highest frequency present in the signal. Observe
that item e is the only application of NPO’s that requires either the
ξ₂ or β outputs. Item f serves the purpose of handling higher power
levels into and out of what effectively is a single (larger) NPO.
[Illustration]
[Illustration: Figure 10—Some possible networks of NPO’s]