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Posted-Date: Fri, 20 Nov 92 08:59:19 PST
Newsgroups: bit.listserv.csg-l
Date:         Fri, 20 Nov 1992 08:59:19 PST
From:         marken@AERO.ORG
Subject:      Grandmother cells

[From Rick Marken (921120.0800)]

In a personal reply to my perceptibly rude public reply to
him, Martin Taylor did answer my question about the
"Grandmother cell" -- the question being "what's wrong
with it"? I will take the liberty of posting Martin's
very helpful description of the Grandmother cell problem
along with my apologies for responding testily to his
previous post. Sorry Martin -- really.

Now, on to Grandma.

Martin Taylor (in a private post to me -- 921118) says:

>The argument that has always been used, I think successfully, is that
>there would have to be too many of them to fit into a brain.  That
>problem is finessed by distributed representations, since the amount
>that can be stored is not limited by the number of storage places, but
>by the differences that can be discriminated among vectors.

I think this is an important point because it reveals
another area (perception modelling) which has been strongly
influenced (tainted?) by the digital computer metaphor of the
brain. Your statement of the "Grandmother cell" problem implies
that perceptions are either present or not; the grandmother
perception is present if the grandmother cell fires (above a
threshold level, perhaps) and is absent if it does not (or fires
below threshold). This implies that perceptions are either/or
phenomena -- and they are indicated by the presense or absense
of "signal" in a cell. This model does seem to require a different
cell for every different perception; and this could, presumably
be a huge number of cells.

The "Grandmother cell" is not a problem for the PCT model because
perceptions are not either/or phenomena; they are VARIABLES
(just like the rate of firing in neurons). So you don't
need a different cell for every different, say, configuration
you can experience; just cells that respond in proportion to the
degree that certain configurations are present; a roundness
detector cell,for example, where the firing rate is low for something
like a compressed elipse, increases as the elipse becomes less
eccentric and peaks out when it is a perfect circle. Perceptions
vary continuously -- and there are many different types
of perceptions that vary within type (so to speak); warmth
(a sensation) varies as you adjust the water to the right temp;
grip (a configuration of force sensations) varies as you adjust
your hand to the steering wheel; transition varies smoothly
and can be changed easily by varying the pressure on the gas
pedal. All these different sensations, configurations and
transitions can be represented as different rates of
firing in individual neurons. One can even perceive different
degrees of "grandmotherliness" (probabaly a category level
perception) running from Joanne Woodward (least like) to
Barbara Bush (most like).

At some level in the hierarchy, perceptual signals do seem to be
treated in either/or form; it might even be that there are
percpetual variables treated in either/or form at all levels
of the hierarchy; in these cases, each neuron does function like
a grandmother cell; but there is no reason to think that the
number of such "categorical perceptions" is anywhere near the
number of perceptual cells available at each level of the
brain.  A few hundred phomemes, a few hundred thousand categories,
etc. With something on the order of 10 billion neurons (and
maybe 5 billion available for perceptual signals) I don't think
there is a real storage problem.

Anyway, the presumed solution to the Grandmother cell storage
problem -- distributed representation -- is only a solution
in the minds of the people watching these distributed systems;
at some point, some resource (a cell or cell assembly) is going
to have to represent the state of the distributed representation
to someone other than the person watching the model -- ie. there
will have to be a perceptual signal that represents the state
of the distributed representation -- and that requires storage.

Best regards

Rick

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

Richard S. Marken                   USMail: 10459 Holman Ave
The Aerospace Corporation                   Los Angeles, CA 90024
E-mail: marken@aero.org
(310) 336-6214 (day)
(310) 474-0313 (evening)
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