Computation in Neural Nets - Understanding Understanding: Essays on Cybernetics and Cognition - page 24

FIGURE 1. Network as directed graph (a) and its connection matrix (b).

the n 2 ordered pairs, and for each entry there are two choices, namely 0 and
1 for disconnection or active connection respectively, the number of ways
in which “zeros” and “ones” can be distributed over n 2 entries is precisely

2

n

2 .

For n = 10 we have 2 100 ª 10 30 different nets and for n = 100 we must be pre-
pared to deal with 2 10000 ª 10 3000 different nets. To put the reader at ease, we
promise not to explore these rich possibilities in an exhaustive manner.
We turn to another property of our connection matrix, which permits us
to determine at a glance the “action field” and the “receptor field” of any
particular element e i in the whole network. We define the action field A i of
an element e i by the set of all elements to which e i is actively connected.
These can be determined at once by going along the row e i and noting the
columns e i which are designated by a “one”. Consequently, the action field
of element e 3 in fig. 1 is defined by

= [

]

Aee

, .

3 3 4

Conversely, we define the receptor field R i of element e i by the set of
all elements that act upon e i . These elements can be determined at once by
going down column e i and noting the rows e j which are designated by a
“one”. Consequently, the receptor field of element e 3 in fig. 1 is defined by