From: erwin@trwacs.fp.trw.com (Harry Erwin)
Subject: Cognition
Organization: TRW Systems Division, Fairfax VA
Date: Thu, 19 Nov 1992 19:32:33 GMT

A couple of postings I accumulated while my news server was ill:


Subject: The Chaotic Brain
Summary: Discusses chaos in the brain--function and implications
Keywords: chaos neuroscience



>Take a look at
>Freeman, W.J.,  and Skarda, C.A.(1987).
>How brains make chaos in order to make sense of the world.
>Behavioral and Brain Sciences, 10, 16-195.
 
 
>It would be even better if someone could
>explain and/or challenge this work in terms which I am likely to
>understand.

OK, I've heard Freeman speak, I've discussed this with colleagues, and
I've done related work, so let's see if I can provide what you want...

Walt Freeman has shown that a chaotic process (probably quasiperiodic, if
you know what that means) underlies the processing in the olfactory nucleus
of rabbits. Bernardo Huberman seems to think that the claim is valid.
Although I haven't seen the real evidence (estimates of the Lyapunov
exponent for the process for example), the pictures I've seen are
convincing, and it's probably as chaotic as the "computer chaos" I studied
back in 87-90. (All I was able to show was mixing and sensitive dependence
on initial conditions.)

OK, it's chaotic. What does that mean?

Not much, unless you've been following the recent work on controlling
chaotic systems. Chaotic systems are _easy_ to control. This is because
they are not "living" at a fixed point or on a limit cycle. Since they
operate in a state space with hyperbolic fixed points, it's easy to
perturb them slightly and send them whereever you want. Pecora and
Stafford have shown that you can capture them with a non-linear
perturbation, and then use a linear perturbation to restrict them to a
specific point or orbit. Alternatively, you can perturb them as they
approach a hyperbolic fixed point and send them anywhere on their
manifold. The energy needed to control a chaotic process is many orders of
magnitude less than the energy needed to control a process that has a
fixed point or stable limit cycle.

So?

Now consider the olfactory nucleus. With each breath, the system is placed
into a chaotic state. The information provided by the olfactory cortex
cells serves as controls on the system. It _rapidly_ converges to a
terminal state, which is then reported to the cerebral cortex.

What is reported?

This gets interesting. The cerebral cortex downloads commands to monitor
specific semantic objects. The olfactory nucleus reports back on a
specific semantic object. Or--if the system doesn't converge--it reports
back the novelty. A novelty detection system in the cerebral cortex (which
has been evaluating each report) responds by shunting the novel sense data
to an evaluation process elsewhere in the cortex, which then performs an
orienting response. 

The interesting point is that Freeman has demonstrated semantic grounding
in the sensory peripherals of the mammalian brain. (He has shown that
there is a basic lack of invariance in the olfactory nucleus, although the
olfactory cortex does show invariance.) The chaos is interesting, but
peripheral--it occurs because it is efficient in the context of object
recognition.

Since the cerebral cortex is connected closely with the olfactory system,
I would expect that the same processing has been adapted for cognition.
The mechanism in the olfactory nucleus appears to involve competition
between neural columns and sets of neural columns. If the "evidence"
matches the pattern associated with a set of columns, they are
(non-linearly) amplified. If the amplification is able to overcome the
competition of alternative sets, then the system rapidly converges to a
state where those columns have "won." Then the system is reset into its
initial state (although the "winning" set of columns has been activated
and so is likely to be reactivated), new data are fed in, and the process
is repeated. The system appears to have evolved for sensitive dependence
on initial conditions, unlike the systems seen in many invertebrates.
Hence, we're naturally chaotic (deterministically unpredictable). 

The implications of this for the "self" are unclear.

To: zeleny@husc.harvard.edu
Subject: Re: Theories of meaning not relying solely on sym
Status: RO

I think we're talking past each other. Let me describe Freeman's
experiments to you.

What Freeman is doing is installing a permanent array of probes in the
olfactory nucleus of rabbits and hedgehogs. He habituates the
experimental animal to the set-up and then repeats the experiments over a
period of months. What he has seen is invariance in the olfactory nucleus
over each series of experiments, but upon repetition after a period of
months, the pattern of activation in the nucleus is entirely different.
Bernardo Huberman tells me that he thinks Walt's work is good, and he's
not alone in that evaluation.

What does that mean? It means that for a given stimulus, the response of
the animal at the cortical level is invariant, but the response of the
olfactory nucleus is _not_ invariant. In fact, the correlation between
nucleus response during separate trials is nil. 

Stimulus invariance is associated with semantic invariance, but _not_ with
syntactic invariance (at the level of the olfactory nucleus). The _same_
pattern in the nucleus _means_ different things from month to month. I've
speculated that the cortex downloads a "semantic" model to the olfactory
nucleus, the nucleus then monitors the stimulus using the model, reporting
minor novelties (discrepancies between the model and the stimulus) and
major novelties (unmatchable stimulus patterns) to the cortex (in a
distributed manner).

 Harry Erwin    erwin@trwacs.fp.trw.com

-- 
Harry Erwin
Internet: erwin@trwacs.fp.trw.com

Newsgroups: sci.cognitive,sci.philosophy.tech,sci.lang