SIMULATING ARTIFICIAL NEURAL SYSTEMS
	USING PARSIMONIOUS PARALLELISM

	Professor William W. Armstrong
	Department of Computing Science
	University of Alberta
	Edmonton, Alberta
	Canada
	T6G 2H1
	Tel. (403) 492 2374
	FAX: (403) 492 1071
	email: arms@cs.ualberta.ca

Many problems cannot be completely solved by mathematical techniques,
even though there may be a wealth of empirical data available.  For
example, consider a medical application where some measurement data
related to symptoms, treatments and history are given for each person
in a sample, together with a value indicating whether a certain
disease was found present or not after costly tests.  Suppose we want
to find a simple relationship between the given data and the presence
of the disease, which could lead to an inexpensive method for
screening for the disease, or to an understanding of which factors are
important for disease prevention.  If there are many factors, and
there are complex interactions among them, the usual statistical
techniques may be inappropriate.  In that case, one way of analysing
data is by use of adaptive logic networks, which can, in principle,
find simple relationships by means of an adaptive learning procedure.
Since the method uses only empirical data, very little human
intervention may be required to obtain an answer, hence making the
approach very easy to try out.

Adaptive logic networks belong to the class of artificial neural
systems (ANS).  Beyond applications in data analysis, such as the
above, these are being used in an increasing number of applications
where high-speed computation of functions is important.  For example,
to correct an industrial robot's positioning to take into account the
mass of an object it is holding would normally require time-consuming
numerical calculations which are impossible to do in a real-time
situation during use of the robot.  An ANS can learn the necessary
corrections based on trial motions, and can perform the corrections in
real time.  It is not necessary to use all possible masses and motions
during training, since ANS have the capacity to extrapolate smoothly
to cases not presented in training.

Speed and extrapolation ability would also be useful in situations
where agile motions of autonomous robots are required.  Extremely high
speed response is needed in electronic systems, when parameters have
to be adjusted, as in automatic equalizers for communication links.
Other applications are in pattern recognition, sensor fusion, sonar
signal interpretation, and many areas of data analysis.

The usual type of ANS depends on fast multiplications and additions.
Special chips have been built to do ANS computations at high speed,
even resorting to analog operations for greater speed.  A type of ANS
has been developed at the University of Alberta, following earlier
work at Bell Telephone Laboratories and the Universite de Montreal,
which uses only simple logical functions AND, OR, and NOT.  In
hardware, computations would be done in parallel in a tree of
combinational logic gates.  Comparisons with a recent chip using
standard techniques suggest that hardware based on adaptive logic
could evaluate functions at least one thousand times faster, and would
be in the trillion connections per second range.

Another advantage of the logic networks is that most of a computation
can often be left out.  For example if a logical zero is input to an
AND-node in a logical tree, then the output of the node can be
computed without computing the other input, or even knowing the inputs
which give rise to it.  This produces no speedup in a completely
parallel system, however in systems running on ordinary processors, or
in systems which re-use any ANS special hardware sequentially (the
usual case), it is of critical importance for speed.  Systems which
combine special hardware parallelism with the possibility of leaving
out unnecessary computations are using "parsimonious parallelism".  A
small amount of such parsimony applies to ordinary ANS, but in logical
networks, the speedups produced can amount to many orders of
magnitude, and confer a great advantage on this approach vis-a-vis the
usual one.

The backpropagation technique for training standard ANS is quite slow.
However, there is a technique for training adaptive logic networks
that runs at combinational speeds.  On-line learning would be quite
feasible.

Finally, although the networks are constructed using logical
operations, they can also be applied to functions of real values or
integers by using appropriate encodings of reals or integers into
logical vectors.  The results of logical computations are then decoded
to obtain the real or integer results.

Demonstration software in C-source form is available to researchers
for non-commercial purposes only.  The software is intended to be very
clear, rather than being highly optimized for performance.
Researchers are invited to copy it and modify it to suit their needs,
without a license.  Anyone requiring better performance should inquire
at the above address about other versions of the software, which will
be available later.  They will offer great improvements in adaptive
and evaluation algorithms, as well as numerous optimizations at the
coding level.  Such a version will be ready by 1991.

Best wishes for success in using the research version of the adaptive
logic network package!  Please let us know about your successes and
failures, so we can better serve the research community.