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Speech and Chaos (corrected)

Harry Erwin erwin at trwacs.fp.trw.com
Sun Feb 7 18:00:18 EST 1993

(This is a corrected version taking into account a careful rereading of
Yao and Freeman)

If we look at what Freeman did we see the following: He postulated an
underlying high-dimensional perturbed quasi-periodic process--imagine
(this is how I see it) a field of dots, with the darkness of each dot
varying periodically (at different periodicities and not quite
sinusoidally) and now superimpose a scene, so the dots of the scene
vary in darkness each with their own period (and again not quite
sinusoidally). Over time the scene is apparent in the average value of
each dot (although the non-linear readout introduces distortions),
but at any given instant, the image is filtered through a haze.
(I envision the activity of virtual particles around a bare electron in
similar terms, although the haze is not quasiperiodic.) 

Now supplement this system with a collection of patterns "downloaded" to the
olfactory bulb from the cortex. Each pattern creates a set of neuronal
connections that are mutually excitory and that compete with those created
by other patterns. These perturb the quasiperiodic system described above
further. If any pattern matches the current state of the image+haze, it is
amplified, and, if it fails to match, it is weakened. This causes the overall
state of the system to evolve, with the components of the scene that match
patterns in the set becoming more and more distinct.  Eventually the system
converges to one of the patterns and that is what is reported back to the
cortex. If the system detects an unfamiliar image, this leads to a state
that causes an orienting reaction.

(My use of the term "download" has been controversial. If we examine the
neuronal connections shown on page 156 of Yao and Freeman, 1990. "Model of
Biological Pattern Recognition with Spatially Chaotic Dynamics," Neural
Networks, vol. 3, Nr. 2., we discover than the anterior olfactory nucleus
has connections that allow it to inject synthetic sensory data via the L2
path and to simulate the priming action of the prepyriform cortex via the
L1 pathway. This would seem to imply that the anterior olfactory nucleus
has a role to play in training the olfactory bulb to recognize a given
sensory object. Barry Richmond's work on the information content of the
neuronal pulse train indicates to me that most processing sequences in the
brain involve neurons transmitting not only their conclusions about the
data they see, but also the key data they are basing those conclusions on.
Hence a model of the sequence passing from sensory cell to cerebral cortex
that preserves the raw sense data seems reasonable and provides data to
the cerebral cortex that it can return to the anterior olfactory nucleus
for use in training the olfactory bulb. This is what I'm terming

Another way I envision this system is to ignore the high dimensionality,
and instead imagine the state of the system as evolving along a path.
Sometimes I'm on the inside of the path and sometimes I'm on the outside.
In part this results from the quasiperiodicity of the system and in part
from my interaction with the downloaded patterns. Sensitive dependence on
initial conditions and the other characteristics of chaos means that I'm
not stuck in a minimum energy rut, but rather can swing from side to side
easily. The downloaded patterns tend to attract me if there's a match.
If I'm attracted enough I discover that the path I was following has a
branching and I end up following it rather than the original path.
In Freeman's olfactory bulb model, I end up at a specific destination, (a
"near limit cycle"), which is recognized and reported back to the cortex,
and the system is reset for the next sniff. In the cortex, the new path
is like the old path, and I continue along indefinitely. Each decision
point is like a gate or a "y" where I can continue on the old path or
choose the new. 

The point is that the chaos is associated with the sequence of gates
(hyperbolic points) and the choice of "right or left" at each gate.
I should be able to replicate a train of thought by reporting "and here,
I decided this rather than that." Both speech and mental plans (as in
Paul Werbos' Heuristic Dynamic Programming) seem to have something of
this structure. 

(I've also been told that scientists in the former Soviet Union have
studied this type of system extensively, but little has been published
in English.)

Harry Erwin
Internet: erwin at trwacs.fp.trw.com

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