Computation in Neural Nets - Understanding Understanding: Essays on Cybernetics and Cognition - page 49

to stimuli for which we changed our interpretation of what is a meaningful
signal. While in the synchronous case a string of OFFs and ONs was the
signal, in the asynchronous case pulse frequencies carried the information.
However, in both cases the element always operated on a “pulse by pulse”
basis, thus reflecting an important feature of a physiological neuron.
In this paragraph we wish to define an element that incorporates some
of the concepts which are associated with neurons as they were first postu-
lated by Sherrington (1952), and which are best described in the words of
Eccles (1952, p. 191): “All these concepts share the important postulate that
excitatory and inhibitory effects are exerted by convergence on to a
common locus, the neuron, and there integrated. It is evident that such inte-
gration would be possible only if the frequency signalling of the nervous
system were transmuted at such loci to graded intensities of excitation and
inhibition”.
In order to obtain a simple phenomenological description of this process
we suggest that each pulse arriving at a facilitatory or inhibitory junction
releases, or neutralizes, a certain amount q o of a hypothetical agent, which,
left alone, decays with a time constant 1/l. We further suggest that the
element fires whenever a critical amount q * of this agent has been
accumulated (see fig. 15).
Again we assume N fibers X i attached to the element, each having n i facil-
itatory (+) or inhibitory (-) synaptic junction. Each fiber operates with a
frequency f i . The number of synaptic activations per unit time clearly is the
algebraic sum:

N
= Â S n ii . (33)

1

Hence, the differential equation that describes the rate of change in the
amount of the agent q as a consequence of stimulus activity and decay is

d
d

q
t

= l, Sq q (34)

o

FIGURE 15. “Charging” process of an integrating element.