Computation in Neural Nets - Understanding Understanding: Essays on Cybernetics and Cognition - page 51

for

1 .

e= 1 x <<

Under these conditions eq. (40) becomes simply:

yx

=

or

= (

)

fSqq *.

o

This “nice” feature of our element is, of course, spoiled by the considera-
tions which were presented earlier, namely, that the activation frequency S ,
which is the sum-total of the impinging frequencies (see eq. (33)) might be
too high to be handled by a physiological neuron. In order to adjust for the
frequency limit that is expected from our element, we proceed in precisely
the same way as was suggested in eq. (30): we introduce into eq. (41) a
formal interaction term that reduces its potential activity x commensurate
with its actual activity:

( ) (42)

y =- 1 m y ,

o o

where the factor m will become evident in a moment. Solving for y o

x

y

o =

(43)

1 m x

and for x Æ•we have

y o max = 1 m. (44)

Denormalization according to (38) and comparison with (32) gives

l
m

1
DD ,

f == + (45)

o max

t t

R

or

( )

ml = DD t + t R . (46)

In other words, the parameter m expresses all neuronic delays in units of
the agent's decay constant.
In order to make the high frequency correction applicable for the
whole operational range of our element, we simply replace x in eq. (40) by
x /(1 +m x ) of eq. (43) which is the adjusted equivalent to the unadjusted
eq. (41).
With this adjustment we have the output frequency of our element
defined by

1

y

o =

(47)

x

ln

( ) -

x 1 - m 1