Associative-Projective Neural Networks (APNNs) - Neural Networks and Micromechanics - page 78

Projective and receptive connections .
The projective connections connect the outputs of one neural field with the
inputs of another (or the same) neural field, and they do not change during training.
The structure of connections can establish the one-to-one correspondence between
the neurons of one associative field and those of another associative field that
belong to different hierarchical levels. We shall say that two fields are connected
with a projective connection if each neuron of one field is connected with a
corresponding neuron of another field with a projective connection. The projective
connection between the fields can be displaced or undisplaced. In the case of
the undisplaced projective connection, the output of the neuron i of the first field
is connected with the inputs of the neuron i of the second field. In the case of
the displaced projective connection, the output of the neuron i of the first field is
connected with the input of | i+s | n of the second field, where s is the value of
the displacement, and | i+s | n is the sum on the module n .
Projective connections can be excitatory or inhibitory. In the functional dia-
grams, the projective exciting connection is depicted as a line with an arrow, while
the projective inhibitory connection is depicted as a line with a circle. Signals
between the fields are transferred by projective connections only in the presence of
the resolving signal. If there is no such signal, then the transfer of the signals
through the projective connections does not occur. The resolving signal is common
for all connections between the neurons of two fields. Projective connections are
used for organizing neural fields into complex hierarchical structures to solve
different problems of artificial intelligence.
Besides associative connections and projective connections, we will introduce
receptive connections. It is necessary to note that in the associative-projective
structures oriented toward solving image recognition problems, in which the
image is taken from the retina, projective as well as receptive connections are
used. Distinctly from projective connections, which map the neuron of one field
onto the neuron of another field, receptive connections map the subset of the
neurons of one field, called the receptive field (by analogy with the physiology of
sight), onto one neuron of another field. Two examples of receptive connections R
between the field of retina S 1 and the buffer field B 2 are given in Fig. 5.6 .
The receptive fields can have different sizes and shapes depending on the task
solved by the system. In order to take this variety into account, it is necessary to
provide the methods of their definition. The methods of the definition of receptive
fields will determine the methods of the definition of receptive connections.
Fig. 5.6 Receptive
connections R between
different fields