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Fig.7.16.
Hereditary mechanism of Darwinian type.
7.4.3.1 Adaptive Evolutionally Learning Method
In feedforward neural networks, when the input pattern
p
is set to input neurons,
the output activity in the
m
th layer is given by the following equations:
( )
m
ip
o
=
s
net
(7.23)
ip
∑
m
jp
−
1
net
=
j
w
o
,
(7.24)
ip
j
where
w
is a connection weight from the
j
th neuron in the
m
−
1
layer to the
i
th
j
i
()
neuron in the
m
th layer and
s
x
is a sigmoid function as follows:
1
()
s
x
=
,
(7.25)
1
+
exp(
−
x
)
where ε is a constant.
The error is estimated by the sum of square error as follows:
2
K
1
(
)
()
∑
=
E
W
=
o
−
o
(7.26)
p
kp
kp
2
k
1
()
()
=
p
E
W
E
W
,
(7.27)
p
where
o
is a teaching signal,
k
o
is an output activity,
K
is the number of
output neurons, and
W
denotes the vector of all connection weights.
The connection weight is adjusted by the following equation:
()
kp
∂
E
W
m
p
∆
w
(
t
+
1
=
−
η
o
+
α
∆
w
(
t
),
(7.28)
j
i
j
∂
w
j
where
t
is the time index,
is the coefficient of momentum term, and
is the
α
η
learning rate.
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