ASME's Mechanical Engine…ing Toolkit 1997 December/ASME's Mechanical Engineering Toolkit 1997 December.iso/win_eng/atre27.exe/ATREE_27/EXPERT.TXT

Text File | 1992-08-01 | 14KB | 305 lines

WHAT IS AN ALN?

An ALN (adaptive logic network) is a kind of artificial neural
network.  It is a special case of the familiar multilayer perceptron
(MLP) feedforward network and has been designed to perform basic
pattern classification computations at extremely high speed --
literally at the upper limit of speed for any digital system.

WHAT COULD ONE USE ALNS FOR?

They are currently being tried out in simulations using the atree
software for various applications:

1. Optical Character Recognition (OCR) -- a demo of OCR is included in
atree release 2.7; the great immunity of ALN trees to noise is made clear
(Thomas)

2. Discriminating between two kinds of particles produced by an
accelerator, where a decision must be made in less than 1/2
microsecond
(Volkemer).

3. Designing control systems for prostheses to enable people with
spinal cord damage to walk by means of functional electrical stimulation.
Simplicity of fabrication, safety and lightness are important here.
(Stein, et al.)

4. Analyzing spectra of tarsands to determine the composition; data
analysis was used to cut down the number of spectral measurements
required from 700 to 25.
(Parsons).

5. Classifying the amount of fat in beef based on texture measures
taken of ultrasound images of beef cattle.
(McCauley et al.)

INPUTS

The following assumes the reader has read something about typical
feed-forward neural nets.  In the case of ALNs, the input data to the
learning system must be boolean.  Non-boolean data is coded into
boolean vectors before entering the learning part.  This may involve
arithmetic and table lookup operations.  Several boolean outputs may
be used to provide outputs which are more complex than boolean, say
continuous values.  There are no a priori limitations on the kind of
functions that can be treated using ALNs.

ARCHITECTURE OF THE NET

The interconnections of nodes usually take the form of a binary tree,
except that there are multiple connections of inputs to the leaf nodes
of the tree, some involving inversions.  There is no limit to the
number of hidden layers in practice.  Ten or fifteen is typical.
A small net might have 255 nodes, a large one 65,535 nodes.

One doesn't have to worry about the shape of the net as much as with
other networks.

THE ELEMENTS OF THE NEURAL NETWORK

The nodes (or adaptive logic elements) have two input leads. The input
signals x1, x2 are boolean ( 0 or 1).  A connection "weight" to be
used for each input ( to use the term for the usual kind of neural
net) is determined by a single bit of information.  The nonlinearity,
or "squashing function", used in ALNs is just a simple threshold
(comparison to a constant).  Specifically, if b1 and b2 are boolean,
then the element computes a boolean value which is 1 if and only if

     (b1 + 1) * x1 + (b2 + 1) * x2 >= 2.

The four combinations of b1 and b2 ( 00, 11, 10, 01) generate the four
boolean functions of two variables: AND, OR, LEFT, and RIGHT, where
LEFT(x1, x2) = x1 and RIGHT(x1, x2) = x2.  For example 1 * x1 + 1 * x2
>= 2 if and only if both x1 AND x2 are 1.

The LEFT and RIGHT functions, in effect, serve to provide some
flexibility in the interconnections.  They disappear after training is
complete.

Two counters in the node count up and down in response to 0s and 1s
desired of the network when the input to the node is 01 or 10
respectively.  They try to determine the best function for the node
even in the presence of noise and conflicting training data.  The
counters also disappear after training is complete.

THE TRAINING OF THE TREE

A tree of such elements is randomly connected to some boolean input
variables and their complements.  Inputs enter the tree at the leaves
and the output is at the root node.  The input variables are
components of a vector representing a pattern, such as a handwritten
character.  Training on a set of input vectors, furnished with the
desired boolean outputs, consists of presenting input vectors in
random sequence, along with the desired outputs.  It results in an
assignment of functions to nodes that allows the tree to approximate
the desired outputs specified by the training data.

To orchestrate the changes to be made during training, a solution to
the credit assignment problem is used.  It is based on the idea that
if one input to an AND (OR) is 0 (1), then it doesn't matter what the
nodes of the subtree attached to the other input are doing.  According
to this simple rule, a node is responsible if a change in its output
would change the network output.  (This is like backprop, except that
the quantity being propagated backwards is either 0 or 1.)

The fact that all node functions are increasing causes a positive
correlation between the node output and the network output, which
indicates the direction of changes that must be made.  In addition,
there is a small refinement which goes beyond this simple scheme. (You
can look at the function starting

adapt(tree,vec,desired)

in atree.c to confirm that this is a very
simple yet effective mechanism).

After training, the ALN then has built-in capacity to generalize, i.e.
to give appropriate responses to other possible input vectors not
presented during training.  This comes about not because of any
additional hardware or software, but just because of the architecture
of the tree -- trees filter out perturbations of the inputs.  Hence no
speed is lost in order to generalize well -- the architecture does it.

The training set can contain contradictory samples, and the relative
numbers of such conflicting samples for the same input will be taken into
account in the training procedure to approximate maximum likelihood and
Bayes decision rules.

BUILDING HARDWARE FROM THE TRAINED SYSTEM

Training an ALN results in a combinational logic circuit.  After
adaptation, one eliminates LEFT and RIGHT functions, which are now
redundant and groups the connected subtrees of two-input ANDs together
to get ANDs of fanin >= 2.  Similarly for ORs.  The (alternating)
layers of ANDs and ORs are logically equivalent to layers consisting
entirely of NANDs.  (Use De Morgan's Law.)

The result is directly translatable into easily built hardware --
essentially a tree of transistors.  This is far, far simpler than any
other neural system.  There are no built in delays, flip-flops,
arithmetic units or table look-ups to slow the system down.

HARDWARE SPEED

The execution time of such a circuit depends on the depth, not the
size.  If we were using a twenty layer tree of transistors in
submicron CMOS, the entire function would be executed in a few
nanoseconds.

In the usual terms of numbers of one-bit connections per second, we
would get many trillions of connections per second from an ALN,
thousands of times more than existing special hardware systems for
implementing backprop.  The fastest we know of on the market for
backprop only allows a few billions of connections per second at peak
rate.

COST OF HARDWARE

For small problems, even one of the off-the-shelf programmable chips that exist
today can do the job, though at a slower rate than a custom chip.
Such fast, inexpensive hardware is being investigated at an accelerator
facility for making a fast trigger to recognize elementary particles in
under 1/2 microsecond.  A few hundred dollars should cover the materials.

This is in sharp contrast to other kinds of neural networks where you
need to have processors costing thousands of dollars just to get into
the game seriously, and even then the result of all their expensive,
learning will be a system that executes far more slowly than an ALN
tree of transistors.  With ALNs, you are seriously in the game from
day one with the atree simulators.

SPEED OF THE ATREE SIMULATOR

Even in the atree software simulator, evaluation is fast, thanks to
the fact that boolean logic can be lazily evaluated.  Once one input
to an AND gate is computed to be 0, we don't need the other input, so
we can suppress a whole subtree of the computation.  Laziness can
provide speedups by factors of 10 or 100 for typical problems.  On the
other hand, backprop systems do not enjoy such speedups.  Non-logical
MLPs compute *everything*.  It's like doing programming without any
"if"-statements.  (It's no wonder the usual neural networks need
massive parallelism -- they suffer from this serious omission.)

TRAINING SPEED

The adaptation algorithms are also designed to be fast: what
corresponds to backprop, a credit assignment computation, is also
combinational logic in hardware, so it will be possible to build systems
which will adapt a tree at a rate of, say, 25 million patterns per
second.

The difference in speed of training and execution of backprop systems
on the one hand, and ALN systems on the other, results from the
drastic simplification of the usual MLP paradigm to base it on boolean
logic.  The difference is immense.  One shouldn't think of it as
getting a racing car from a station wagon (twice as fast, say), it is
more like getting a rocket from a hot air balloon (thousands of times
faster).  As the problems get larger, the advantage of the ALN system
over the usual MLP just keep on growing.

GENERALIZATION AND NOISE IMMUNITY

Good generalization without loss of speed is the strong point of
ALNs.  Pattern classification problems generally require an output
which is the same for all patterns in a class.  Members of a class are
in some way similar.  Similarity could be based on all sorts of
criteria, but generally it can be defined by saying two individuals
have many features in common.  If a feature is represented by a
boolean variable, then the above says, similarity can be measured by
Hamming distance between boolean vectors.  In order to use ALNs, we
generally have to code other representations of individuals into
boolean vectors in such a way that similarity for pattern
classification purposes is reflected in Hamming distance.

Binary trees with node functions AND, OR, LEFT, and RIGHT have been
shown to have the property that the functions they realize tend to
have the same output value when the inputs are perturbed.  This
depends on averaging over all functions on the tree, weighted by the
number of ways each can be produced by setting the two bits at each
node which determine the node's function.  It is also necessary to
average over all vectors and all perturbations of a given number of
bits.

The plausible reasoning behind this is that when an input signal to a
gate changes, it may or may not change the output.  A change to an
input to an AND will not change its output if the other input to the
AND is 0.  Over all, the probability of a change is 0.5, if one input
changes.  So for a 10-layer tree, the probability of a single bit
change at a leaf causing a change of the tree output is 1/1024.

ALNs match the solution to the problem to provide fast pattern
recognition.  Simple properties of boolean logic provide speed,
immunity to noise, and offer the possibility of lazy evaluation.

THE FUTURE

In the Fall of 1992, we expect to have a much enhanced version,
embodying some recent developments, that have resulted in part thanks
to interaction with people on Internet via email and news.  It will
have

- superior adaptive algorithms for both continuous and boolean data

- an ability to deal with continuous values, without significant loss
  in speed, that will make other MLPs obsolete, including those using  variants of backprop

- a sound statistical basis for fitting continuous functions

- a design methodology that will be easy to understand and will result in
  provably *safe* systems; there will be no more problem of wild values being
  produced by a "black box", so ALNs can be applied in safety-critical areas

- an interface to common database management systems on micros and mainframes

- an interface to a popular spreadsheet program under Windows.

- facilities to encourage developers to apply ALNs to pattern recognition
  problems: OCR, voice, control of virtual realities etc.

- a price, since we can't carry on otherwise.

AN INVITATION

I hope the above arguments will be enough to convince the reader to
try the atree release 2.0 software for Unix and/or the new release f2.7
for Windows on the IBM PC and compatibles.  At the very least, you
should take a look at the OCR demo in release 2.7 to see the great
noise immunity which results from such simple means.

The lf language should make it easy to get started, and there are lots
of examples in release 2.7. (You could look at them even if you only
want the Unix version.)

If you like what you see, work with us.  Lots of researchers are doing
so, some via the net: physicists, engineers, neuroscientists, speech
pathologists, ...

Join the alnl mailing list (email to [e-mail]
providing a correct address that will last for a while please).

The interest in backprop-type neural networks which has blossomed in
the last few years is obviously fading fast and funding is less than
expected.  I heard that it is because "neural networks" were just
slightly better than standard techniques.  The problems that need high
speed pattern recognition are still there, though, and when speed is
an issue, ALNs are not just slightly better, but thousands of times
better than anything else.

As for the quality of ALN classifiers, you'll just have to try them
out in your area of application. For beef grading, at last report,
ALNs were the best technique they had.  A particle physicist, as far
as I know, is still trying to explain what information an ALN was
using that managed to learn even when he deprived it of momentum
information that was thought to be essential.  In prosthetics, the ALN
didn't make a mistake a physiotherapist did, even though the mistake
was in the training set.  A lot of people are pretty happy about their
results with ALNs.

Good luck with your results using them!

Bill Armstrong

The file for release 2.7 will be announced as soon as it is available.
Another posting will provide a list of references.