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Date:         Mon, 23 Nov 1992 10:51:33 MET
From:         Maler <maler@IMAG.FR>
Subject:      Distributed control and G-ma signals
              and Neural nets" (Nov 20,  9:15)

[From: Oded Maler 921123]

First I owe an answer about the possibility of distributed
control which looks "as-if" it is hierarchical. Suppose
x and y are the elemantary perceptual variables and that the
higher level variable is z=ax+by (assume a=1 and b=-1 in the
following example). According to the difference z*-z, the higher
system sets references for x and y, which essentially are of
the form "increase" or "decrease" according to the sign of a, b
and z*-z. Graphically, if everything works well (we are in the
range of controllability of x and y, etc.) our system will lead
us from every point in the x/y plane toward the diagonal line
representing ax+by=z*. An observer of this system will certainly
say that z is contolled.

Now consider the case when there is no explicit signal representing z,
but rather two low-level ECS controlling independently for x* and y*,
such that ax*+by*=z*. Graphically the system will move from every
point to the point (x*,y*) which is one point on the diagonal.
An external observer who sees only z, will again conclude that z
is a controlled variable, although it is not explicitly rperesented
inside the system.

Which is better? It depends on the simplifying assumptions. If you
assume that the controllabilty range of x and y are unlimited,
and that z corresponds to some really-important CEV, then the
hierarchical mode is better because it takes the shortest path to
the diagonal, while the distributed control system will try to
reach (x*,y*) form everywhere, even from other points (x',y')
which satisfy ax'+by'=z*. On the other hand the hierarchical
control scheme does not "care" about pushing x and y into extreme
values beyond their capabilites. If x and y reflect some important
EVs, this might be a problem. (My association are soldiers dying
for their country, or if you prefer, Lymphocites dying for their
body).

Last year Bill demonstrated that under certain conditions hierarchical
control can be achieved of two higher-level perceptions e.g., z=x+y,
w=x-y. Again, I think that under the same assumption you can achieve
a dsitributed version.

I don't have any ideological bias against "signal for every percept",
and hierarchy is very useful (when it works), especially when the
reference signals for the higher variables may change, but I just
wanted to demonstrate that a dsitributed control system can fool
an external observer and look like a hierarchical one.

*****************

Consider now the "special status" of those perceptual variables
which have a "dedicated" scalar signal. If you take their neural
correlates to be currents on some neuronal wires, you may have some
problem to explain the devlopment of new "concepts" and any
other "learning" phenomena in adults, beacuse according to the
current dogma in neurobiology (please correct me if
I'm wrong) the changes in the connectivity patterns of neurons
cease at some stage, so how are new controlled perceptual
varibles acquired? What is the perceptual "meaning" of a signal
on some wire before it became dedicated to some variable? This
is why I think one should not be so dogmatic about the actual
realization of variables, and be ready to accept more sophisticated
forms using which virtual signals can exist.

(I don't think that the question of all-or-none vs. degree, is relevant
here, because both can be realized either by a scalar or in a
distributed manner.)


*******************

Bill & Science: It takes an enormous amount of time to develop the
perceptual capability to tell geniosity from charletanism and
crackpothood, and I'm sure the editors of Science don't have the time
nor the real motivation. If I were you, I would, in parallel to the
development of a full version for Biol. Cyb., send the rejected stuff
to Nature (it's already in a similar format, so it costs you nothing).


Best regards

--Oded


--
===============================================================
Oded Maler, LGI-IMAG (Campus), B.P. 53x, 38041 Grenoble, France
Phone:  76635846  Fax: 76446675   e-mail: maler@vercors.imag.fr
===============================================================