Connectionist symbol processing: any progress?

[George Reeke]

On Aug 16,  7:03pm, Mitsu Hadeishi wrote:

> The point I am making is simply that after one has transformed the
> input space, two points which begin "close together" (not
> infinitesimally close, but just close) may end up far apart and vice
> versa.  The mapping can be degenerate, singular, etc.  Why is the
> metric on the initial space, then, so important, after all these
> transformations? Distance measured in the input space may have very
> little correlation with distance in the output space.

I can't help stepping in with the following observation:

The reason that distance in the input space is so important is that the
input space is the real world.  It is generally (not always, of course)
useful for biological organisms to make similar responses to similar
situations--this is what we call "generalization".  For this reason,
whatever kind of representation is used, it probably should not
distort the real-world metric too much.  It is perhaps too easy when
thinking in terms of mathematical abstractions to forget what the
purpose of all these transformations might be.

Regards,
George Reeke
Laboratory of Biological Modelling
The Rockefeller University
1230 York Avenue
New York, NY  10021
phone:  (212)-327-7627
email:  reeke at lobimo.rockefeller.edu