Information Technology Reference
In-Depth Information
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f
X
N
s
i
¼
T
ij
s
j
:
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Successive repetition of this transformation leads to subsequent changes in the
original image.
This transformation can be performed in different ways. A neuron can be selected
at random and its condition recalculated, then another neuron gets randomly selected
and subjected to the same procedure, etc. Such process of network transformation
is called asynchronous. If the network transformation is performed in “cycles”
simultaneously for all neurons, then such a process is called synchronous.
Dynamical evolution of the Hopfield model, for which
T
ij
¼
0, and
the transformation of the image happens synchronously, corresponds to reducing
the function usually called “energy”
T
ji
and
T
ii
¼
2
X
ij
1
E
¼
T
ij
s
i
s
j
:
The steady state of the network corresponds to the local minimum of this
function. Sequential transformation of the original image involves the motion
along the phase surface to the point (more precisely, to one of the points) of a
local minimum corresponding to the solution of the given problem (Fig.
4.3
).
Particular properties as well as computing, information, and logical capabilities
of the Hopfield model were studied in detail in the 1980s of the last century.
Moreover, this model stimulated the development of a wide range of variants of
both single-layer and multilayer neural networks. But the most important conse-
quence of the rapid development of the theory of neural networks was apparently
engineering development of commercial
information processing devices—
neurocomputers.
Let us try to understand what advantages of neural networks were considered
particularly promising by the developers of neurocomputers.
The basis of the neural network approach is constituted by the biological
principles of information processing and, above all, the general principles of
functioning of the cerebral cortex. Therefore, one could expect that the devices
that mimic biological neurons will be able, at least partially, to reproduce their
function.
Over a long period of biological evolution the human brain developed properties
inaccessible to modern digital computers with von Neumann architecture. These
include:
Distributed representation of information and parallel computing
Ability to learn and generalize
Adaptability
Tolerance to faults and errors in the structure
Low power consumption
