Discussion: Numbers - Connectionist Symbols analogy

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Consider the following analogy between ways of representing
numbers and connectionist representations (proposed to me by
a professor of psychology at NMSU, Roger Schvanevelt).

There are many ways of representing numbers. '238',
'11101110', 'CCXXXIIX', 'two-hundred and thirty-eight',
'e^5.4722706736' (e^ln(238)),
'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa',
and 'X', a pointer to any of the above, are all
representations of 238. Some are more useful than others,
and sometimes the usefulness of a representation depends on
what we want to do with it.

All of these representations for 238, with the exception of
the last two, have some structure.  What makes some of these
representations useful in certain situations is that the
structure of the representation itself makes immediately
apparent the relevant properties of the thing it refers to.
And when all properties of the symbol are irrelevant to what
is being done with it, the pointer representation is a
perfectly adequate representation.

The roman numeral representation is horrible for arithmetic,
(though quite suitable for some other tasks, such as
labelling).  In Roman times very few people knew how to
multiply, and one reason was that the algorithm for
multiplying with roman numbers is very long and tedious, and
difficult to understand and remember.  Some historians have
suggested that the Roman's representation for numbers is the
reason that their acheivements in arithmetic and mathematics
did not match their technical acheivements in other areas.

Now, taking language as a domain, and words and their
meanings as the things to be represented, what is it that
some people like about connectionist representations of
them?  I think it is that the connectionist representations
make the relevant properties immediately apparent.  This is
the case in distributed 'micro-feature' representations of
words and meanings.

So, the upshot of this analogy is that doing AI with
list-based representations is like doing arithmetic with
roman numbers, i.e. possible, but difficult and a hindrance
to the development of the field.

And the final question is: Can connectionism provide the
"positional base-encoding" for symbols that represent
the objects that AI needs to manipulate?.

All of these points have been made previously, but it seems
to me that putting them in the context of this analogy adds
a certain (false?) coherence and force to them.

Comments?

-----------------------------
Tony Plate
Computing Research Laboratory
Box 30001
New Mexico State University
Las Cruces, New Mexico 88003
(505) 646-5948
CSNET: tap%nmsu