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and let the parameters of the moves of the neurons from the
i
-th layer be given by
the IM
a
1
,
i
...
a
1
,
s
i
B
i
=
b
i
,
s
i
.
p
0
b
i
,
1
...
Let us have the IM for the
(
i
1
)
-st layer
a
1
,
1
...
a
1
,
s
i
−
1
a
i
−
1
=
s
i
−
1
.
p
0
a
i
−
1
a
i
−
1
...
1
Then
a
i
−
1
a
i
W
i
B
i
=
(
)
⊕
a
1
,
1
...
a
1
,
s
i
k
=
1
(
R
k
=
1
(
R
=
a
i
−
1
k
a
i
−
1
k
W
k
,
1
+
b
k
,
1
)...
W
k
,
s
i
+
b
k
,
s
i
)
p
0
a
1
,
1
...
a
1
,
s
i
=
p
0
a
i
1
a
s
i
...
and for
i
=
M
a
M
,
1
...
a
M
,
s
M
−
1
a
M
−
1
=
s
M
−
1
.
p
0
a
M
−
1
a
M
−
1
...
1
is defined. We see that the above
formulas can be interpreted as results of identical function
F
, i.e., for every real
number
x
In [38], the transfer function
F
:
R
→
R
x
. Below, firstly, we discuss the case, when
F
is a real function,
different from the identical one. For example, in [37] this function is sigmoidal or
hyperbolical tangent function.
Now, following [23], for a fixed real function
F
, we define over the IM
,
F
(
x
)
=
l
1
l
2
...
l
n
k
1
a
k
1
,
l
1
a
k
1
,
l
2
...
a
k
1
,
l
n
k
2
a
k
2
,
l
1
a
k
2
,
l
2
...
a
k
2
,
l
n
A
=
.
k
m
a
k
m
,
l
1
a
k
m
,
l
2
...
a
k
m
,
l
n
the operator
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