Associative-Projective Neural Networks (APNNs) - Neural Networks and Micromechanics - page 94

If the connection exists, then its synaptic weight equals “1;” otherwise, it is “0.” The
associative-projective neural networks are stochastic networks, meaning that the
connections between the active neurons are established with a certain probability. If
the same vectors are input to the network, the probability of connections forming
between the active neurons will increase. Thus, in the network are formed the sets
of neurons having a higher probability of connection than the mean probability of
connection in the whole network. We term such sets the neural ensembles [ 12 ].
In the ensemble, it is possible to distinguish the nucleus and fringe [ 13 ]. Neurons
of the ensemble having a higher probablity of connection correspond to the nucleus.
The most typical information about the presented object corresponds to the nucleus.
The individual differences of the representatives of the object class correspond
to the fringe. If we extract the different quantities of neurons with the greatest
activity, for example, those assigning a high threshold of neural activity, then we
can ensure a different level of concretization in the description of the object. For
example, if the nucleus of the formed ensemble is named “apple,” the extended
description (taking into account the neurons entering the fringe of the ensemble)
can contain the information “red, round, large.” The description of the object of a
different level makes it possible to speak about existence in the neural network
hierarchy as “class - element of class,” reflecting the subsumption relations.
The neural ensemble is the basic information element of all hierarchical levels of
the neural network. It is formed from the elements of lower hierarchical levels
and can correspond to the feature, to the description of an object, to the descrip-
tion of a situation, to the relation between the objects, and so forth. Its internal
structure reflects the structure of the corresponding object. The fact that part of the
ensemble is entirely excited allows us to consider the ensemble as a united and
indivisible element in one hierarchical level. However, when it is transferred to
other hierarchical levels, it is divided in such a way that only a part of its neurons is
included into the descriptions of the more complex objects of upper hierarchical
levels.
Assume, for example, that it is necessary to build the description of a tree, which
consists of the stem, branches, and leaves. Each element has its own description.
Thus, for example, leaves can have form, color, and texture. Let each of the named
features in the associative field of the neural network's lower level be coded in the
form of the subset of the neurons. Then, the neural ensembles corresponding to
stem, leaves, and branches can be formed at the following hierarchical level. The
neurons that describe its form, color, and texture at the lower level will enter into
the ensemble that corresponds to the stem. So the sizes of the ensemble at the upper
level will not be too large; only the part of the neurons from the ensembles of the
lower level falls into the ensemble of the upper level. For example, during the
construction of the ensemble that corresponds to the entire tree, only the parts of
each of the ensembles describing the stem, branch, and leaves are included in it. We
term the procedure for selecting the part of the neurons for transfer to the upper
level the normalization of the neural ensemble. The ensemble is formed in such a
way that, using the neurons that entered into the ensemble of the upper level, it
would be possible to restore the ensembles of the lower level due to the associative