Computation in Neural Nets - Understanding Understanding: Essays on Cybernetics and Cognition - page 66

The second deficiency becomes obvious if we have to answer the ques-
tion of where we localize the operation that transmits “a certain fraction
a ij ” of the activity of element e i to element e j . Is this a property of the trans-
mitting or of the receiving element? Clearly, our simple model of elements
does not yet take care of this possibility. However, at this stage of the devel-
opment it is irrelevant to decide whether we make transmitter or receiver
responsible for the regulation of the amount of the transmitted agent (see
fig. 22a). However, it is necessary to bestow on at least one of them the
capacity to regulate the transmitted agent. We decide to make the receiver
responsible for this operation, justifying this decision by the possibility of
interpreting this regulatory operation—at least for neural synaptic con-
tacts—as the number of facilitatory or inhibitory synaptic junctions of a
fiber that synapses element e i onto e j . Hence, for our present purposes we
adopt a representation of our linear elements (fig. 22b) which modifies the
transmitted signal at their inputs according to the numerical value of the
active connection coefficient a ij . Later, however, we shall see that both,
transmitter and receiver define this coefficient.
4.4. Active Networks of Discrete, Linear Elements
We draw directly from our definitions for action nets and for the various
operational modalities of elements as discussed in earlier paragraphs;
however, we shall introduce in this paragraph for the first time some con-
straints on the spatial distribution of elements. These constraints will be
tightened considerably while we proceed.
FIGURE 22. Formal equivalence of localization of operations.