Information Technology Reference
In-Depth Information
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:
Let us call the initial distribution of the states of neurons in the network an initial
image. It is transformed by the network during its evolution in accordance with the
rules defined by the matrix of neural connections.
A neural network can memorize a certain number of images, whose number is
determined by the network structure. One of the most famous memory circuits is the
so-called Hebb's rule.
Assume that the following images are stored:
V
1
; ...;
V
N
V
ʼ
¼
ʼ ¼
1, 2,
...
,
M
:
Then, for binary vectors, the Hebb's rule is defined as
T
ij
¼
X
ʼ
:
ð
2
V
i
1
Þ
2
V
j
1
It can be shown that this means that:
Two elements of the connection matrix of the neurons
T
ij
that are in the same
state are connected in most of the memorized patterns, and the power of the
connection depends on the number of structures in which these elements are in
the same condition.
Elements that are in different states in the majority of memorized patterns are not
connected.
In the case of chemical neural networks, the Ross group used a modified Hebb's
rule. In this case, the strength of connection between the elements
i
and
j
is defined
as
(
)
,
X
2
R
j
1
2
R
i
1
T
ij
¼ ʻˑ
ʼ
is the coupling constant, which is determined in the case of chemical
networks as a flow rate of reagents through the reactor:
where
ʻ
ˑ
fg¼ x
,
if
x
0,
ˑ
fg
¼
0,
if
x
<
:
0
It was shown that when using this rule, steady states are generated corresponding
to the stored patterns.
These theoretical considerations were the basis for an experimental realization
of chemical neural networks. A set of eight reactors of complete mixing with a
continuous flow of reagents was used for storing the three images (they were some
