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matical apparatus that deals with networks in general, or these constraints
may be introduced by neurophysiological and neuroanatomical findings
which uncover certain functional or structural details in some specific cases.
It is tempting, but—alas—dangerous, to translate uncritically some of the
theoretical results into physiological language even in cases of some unde-
niable correspondences between theory and experiment. The crux of this
danger lies in the fact that the overall network response (NR) is uniquely
determined by the connective structure (
e
) of the network elements and the
transfer function (TF) of these elements, but the converse is not true. In
other words, we have the following inference scheme:
[
e
e
,
TF
]
Æ
NR
[
]
Æ
[]
,
NR
Class TF
[
]
Æ
[]
TF, NR
Class
e
Since in most cases we have either some idea of structure and function
of a particular network, or some evidence about the transfer function of the
neurons of a network giving certain responses, we are left either with a
whole class of “neurons” or with a whole class of structures that will match
the observed responses. Bad though this may sound, it represents a con-
siderable progress in reducing the sheer combinatorial possibilities men-
tioned before, and it is hoped that the following account of structure and
function in nervous nets will at least escape the Scylla of empty generali-
ties and the Charybdis of doubtful specificities.
The discussion of neural networks will be presented in three different
chapters. The first chapter introduces some general notions of networks,
irrespective of the “agent” that is transmitted over the connective paths
from element to element, and irrespective of the operations that are sup-
posedly carried out at the nodal elements of such generalized networks.
This generality has the advantage that no commitments have to be made
with respect to the adoption of certain functional properties of neurons, nor
with respect to certain theories as to the code in which information is passed
from neuron to neuron.
Since the overall behavior of neural networks depends to a strong degree
on the operations carried out by its constituents, a second chapter discusses
various modalities in the operation of these elements which may respond
in a variety of ways from extremely non-linear behavior to simple algebraic
summation of the input signal strength. Again no claims are made as to how
a neuron “really” behaves, for this—alas—has as yet not been determined.
However, the attempt is made to include as much of its known properties
as will be necessary to discuss some of the prominent features of networks
which filter and process the information that is decisive for the survival of
the organism.
The last chapter represents a series of exercises in the application of the
principles of connection and operation as discussed in the earlier chapters.
It is hoped that the applicability of these concepts to various concrete cases
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