Biomedical Engineering Reference
In-Depth Information
Broadly interpreted, this means that an articial neuron can be consid-
ered to be of the form
0
1
X
n
X
v
@
A
x
i
=
w
ij
X
js
i
+
i
j=1
s=1
where X
sik
is some transformation of x
i
and where
i
is a small random
number modeling uctuations in V
initial
: For example, if I
j
() is constant
in (2), then
Z
t
1e
js
t
e
js
t
e
js
I
j
() d =
1
I
j
js
0
and the corresponding articial model is
0
@
1
A
X
n
X
v
x
i
=
w
ij
sj
x
j
i
+
i
j=1
s=1
where
sj
= C
js
1
1e
js
T
for some xed T > 0: Although this
model is mathematically equivalent to (1)|thus allowing back propagation
training|comparison to (2) suggests that the
sj
should be trained at
dierent \time scales" and that small amounts of \noise" may be added at
each iteration.
This conrms recent models obtained without biological inspiration in
which Monte Carlo techniques and extensions of the back propagation train-
ing method have been used to improve neural network performance
14;19
.
Conversely, it suggests that more recent models of the neuron can produce
improved articial neural network models. If vision is interpreted to be
feature extraction on a grand scale, then real world neural networks can
be considered to be the ultimate data mining tools, behooving us to con-
tinually revisit our understanding of real neurons in our quest to develop
suitable articial models designed to perform similar tasks.
js
Acknowledgements
The authors wish to thank the referees for their several excellent sugges-
tions. This research was supported in part by the National Science Foun-
dation under Grant No. 0126682.
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