Associative Memory for Holographic Retrieval
The employment of a nonlinear processing unit, as shown in this
figure , will prove essential in oreder to eliminate unwantede perturbation.
Given a test pattern t, we define a (matching) score vector s
in terms of the inner-product between
and the test pattern t denoted by .
where the inner product operation for real-valued input is defined as
The score vector s is proceede by a nonlinear processing, leading
to a binary decision vector v,
which is expected to have only one non-zero element. If the non-zero element
is correctly positioned, then a Holographical retrieval can be obtained.
The pattern to be retrieved is the output value
where A is the matrix formed from the column vectors .
The purpose of the nonlinear operator
is to select one (and only one) winning node and simultaneosly supress
all other nodes. The purpose is to supress the noise, thus leading to holographic
retrieval. The nonlinear operators can be manifested as eithera thresholding
device or a
Threshold Units A basic threshold circuit is depicted in this
figure. It is necesary to first estimate an optimal threshold .
Suppose that we have a test pattern
and that the noise level is low and the pattern vectors are approximately
orthogonal. Then and
should be sufficiently small so that the perturbational components are
lower than the threshold. More exactly,
then the k-th pattern
can be holographically retrieved. If the threshold is set to be too low,
then some inappropiate components may be falsely selected. On the other
hand, if the threshold is set too high, then, in a noisy environment, it
is possible that even the correct node will fail the threshold. The threshold
is set commonly to 0.5.
MAXNET A MAXNET can be used to pick the winner
as the one which has the maximum node value. See this figure.
In terms of digital implementation, a typical sorting or tree structure
could be adopted. In anolog implementation, however, it requires a dynamic
circuit implementation. The MAXNET selects the correct winner when
An important advantage of the MAXNET is that it avoids altogether the need
to stimate the threshold .
Artificial Neural Networks