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i w connecting the output of the perceptron i and the input of the perceptron j will
increase by an amount
' ,
wx y
K
ij
j
i
where x is the output of the perceptron j , y the output of the perceptron i , and Ș is
a measure controlling the learning step size (Figure 3.14). Accordingly, the
Hebbian learning updating the weights, or the Hebbian learning rule , can be
expressed as
K
wt
( )
wt
()
xtyt
()()
.
ij
ij
j
i
p i
w ij
p j
y i
x j
Figure 3.14. Interconnected perceptrons
x 1
w 1
w 2
x 2
y
:
:
:
:
:
:
x n
w n
Figure 3.15. Multiple interconnected perceptron
The rule can be generalized and applied to a multiple-input perceptron as
T
wt
( ) ()
wt
K
x wx
,
where the relation
n
y
wx
wx
T
x w
T
¦
j
j
j
1
is taken into account (Figure 3.15).
Nevertheless, the direct application of the Hebbian rule bears the risk of an
endless increase of weight values, which could saturate the output neurons. As a
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