Connectionist symbol processing: any progress?

[Mitsu Hadeishi]

Mitsu Hadeishi wrote:

> Lev Goldfarb wrote:
>
> However, the error measure is far more useful and important than
> the "metric" you might impose on the input space when conceiving of it as a
> vector space, since the input space is NOT a vector space.

Clarification:  I really should say you do not have to conceive of the input space
as a vector space.  It may in fact behave like a vector space (locally) if the
architecture of the network, the nature of the learning algorithm, and the
training sets are structured in a particular way.  However, it will not
necessarily behave this way as the network evolves---and particularly if you
conceive of the input space as spread out through time for a recurrent network,
the notion of it as a vector space doesn't work at all.  The main point is that it
is the feedback mechanism (error function or other mechanism) which is truly
important when considering how the learning algorithm is biased and will evolve,
not the "metric" on the initial input space.

Mitsu