Associative-Projective Neural Networks (APNNs) - Neural Networks and Micromechanics - page 74

where a i is the signal at the associative input i of the neuron; w i is the synaptic
weight of the input i of the neuron; and th is the threshold value at the input Th . w i
can take only two values: 0 or 1.
Earlier investigations of neuron assemblies were made by Hebb and Milner
[ 12 , 13 ]. Many of the mechanisms that they proposed were used later by other
authors. For example, the biological neural network does not contain primordial
knowledge about the world; it obtains knowlege gradually. During training, the
neural networks are modified and are capable of memorizing new information. How
does training occur, and what processes occur in the neural network? These ques-
tions became the subject of consideration in Hebb's topic [ 12 ]. The fundamental
rule (law of training) is formulated by Hebb as follows: if neuron A excites neuron B
and this process is repeated, then the synaptic weight of the connection between
these neurons increases. This rule of the training of neural networks proposed by
Hebb is used frequently and with only small modifications in the newest models of
neural networks.
In our case, the modified Hebbian rule of training is used. The training of the
neuron is accomplished due to a change of its synaptic weight, which occurs in
cases when the signal at the training input is not equal to 0 ( tr

0). We will
distinguish training with the positive signal tr (positive reinforcement) and negative
signal tr (negative reinforcement). With positive reinforcement, a change of the
synaptic weight is accomplished in accordance with the expression:

6¼

w i ¼ w i U ð a i & q & h i Þ; (5.2)

where U is a disjunction; & is a conjunction; w i * is the synaptic weight after
training; w i is the synaptic weight before training; a i is the signal at the associative
input i ; q is the signal at the neuron output; and h i is the binary random variable,
whose probability of unit value is equal to the absolute value of reinforcement tr :

ph i ¼ ð 1 Þ¼ j : tr (5.3)

With negative reinforcement, a change in the synaptic weight is described by other
expressions:

;

w i ¼ w i & a i & q & h i (5.4)

p ð h i ¼ 1 Þ¼ j ; tr (5.5)

where the line above the expression means negation. Such neurons will be used for
constructing the associative-projective neuron structures.
The neurons described above will be used in the associative fields. In order to
understand the work of the associative field, let us give more detailed ideas about
the work of the neuron. Fig. 5.2 depicts the detailed functional diagram of the
neuron in which the foregoing designations are used, and new ones are added: SUM
is the adder, which is followed by the threshold element; TG is the flip-flop; Q * is