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Fig. 4.4.
Processing element that computes a feature cell. It consists of
P
kl
projection units
and one output unit that produces the activity
a
ijkl
. The output unit computes the weighted
sum of the potentials
b
tp
ijkl
of the individual projections and passes this sum through a transfer
function
ψ
kl
. Each projection unit computes the weighted sum of feature-cell activities and
passes it through a transfer function
φ
kl
. Bias weights of the projection units and the output
unit connect to a node with the fixed activity one.
Each projection computes a weighted sum of activities
a
t
∗
i
∗
j
∗
k
∗
l
∗
with the weighting
factors described by
w
pq
kl
R
. The number of contributions to a projection
p
is
Q
kl
. In addition, a bias value of
w
p
0
∈
kl
is added before the sum is passed through the
projection transfer function
φ
kl
.
The address
i
∗
j
∗
k
∗
l
∗
t
∗
of a source feature cell is described by:
t
∗
=
T
kl
(
t
);
(4.3)
l
∗
=
L
kl
;
(4.4)
k
∗
=
K
pq
kl
;
(4.5)
j
∗
=
J
pq
kl
(
j
) =
Υ
ll
∗
(
j
) +
J
p
kl
;
(4.6)
i
∗
=
I
pq
kl
(
i
) =
Υ
ll
∗
(
i
) +
I
p
kl
.
(4.7)
T
kl
(
t
)
determines if the source activity is accessed in a direct or in a buffered mode.
L
kl
describes the layer of the source.
K
pq
kl
addresses the feature array within layer
l
∗
.
J
pq
kl
(
j
)
and
I
pq
kl
(
i
)
describe the source location within the array
k
∗
as a function of
the destination location
(
i,j
)
. The source is accessed relative to the corresponding
position
(
Υ
ll
∗
(
i
)
,Υ
ll
∗
(
j
))
, where
Υ
ll
∗
(
x
)
maps coordinates from layer
l
to layer
l
∗
and
(
I
p
kl
,
J
p
kl
)
describes the source offset relative to the corresponding position.
Details of the addressing will be discussed later.
The choice of the basic processing element as feed-forward neural network with
a hidden layer of projection units and a single output unit is motivated as follows. It
is simple enough to be computed quickly and it is powerful enough to compute the
activity of a feature cell as a non-linear function of feature-cell activities.
Many aspects of biological neurons are not modeled by the basic processing
element. For instance, the discrete-time computation of activity is only a coarse
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