What is a "hybrid" model?

[Ron Sun]

That's a tricky question. I don't know if there is any
clear-cut answer. (I really hate to answer this, Lev :-) )

One might simply say hybrid models involve both symbolic and
subsymbolic processes. But then, what are these?
One is NN and the other is LISP code?? A deeper  answer is needed.
Smolensky attempted to distinguish the two types in his PTC paper
in 1988. And there is the (still continuing) discussion in terms of
systematicity etc. (Fodor and Pylyshyn 1988, Clark 1991).
But I am still not clear about the difference.

In relation to mathematical forms as alluded to in Lev's message,
one possible answer is that  while symbolic processes can be better modeled
by discrete math, subsymbolic processes are better modeled
by continuous math.  Thus, hybrid models may involve a variety of
mathematical forms. But obviously, this is an (over) simplification.
(Just consider the approximate equivalence of discrete and continuous
math: one can be approximated by the other.)

Another possible answer is that while one involves explicit representation
the other involves implicit representation. But then the question is:
what is difference between the two representations?  If I remember correctly,
there was a paper recently in Mind and Machine on exactly this topic.
But again I was not convinced by the answer provided by the author.
Motivated by this dissatisfaction,
I was trying to develop my own solution, but it fared no better.

Recently, however, I stumbled upon something that I believe may provide
a fruitful way of looking into this and other related issues.
What I am looking at is psychological literature on implicit learning
(and to a lesser extent, literature on implicit memory, unconscious
perception, etc.). What these bodies of work may give us is a scientific
(experimental) way of getting a handle on the issues. Instead of
philosophizing on the differences and so on (no offense intended), 
we may actually examine
the issues experimentally in human subjects and thus make some head ways
towards understanding the differences in a rigorous and well-grounded way. 

As demonstrated by the work of e.g. Reber (1989), Berry and Broadbent (1989),
Stanley et al. (1989), Willingham et al (1989),  humans may actually
learn in two different ways (at least):
either explicitly or implicitly (symbolically or subsymbolically?).
These two types of learning may interact sometimes (Stanley et al 1989).
The distinction and dissociation of these two different types of learning
have been demonstrated in a variety of domains, including artificial
grammar learning, dynamic control, sequences, covariations, and so on
(Seger 1994).  Of course, in these experiments, an operational 
(experiment-based) definition of explicitness
and implicitness has to be assumed, and indeed much controversy resulted
from definitional differences. However, despite  the  shortcomings,
given the breadth and consistency of results
of this line of research, the distinction seems to be well established.
I believe this distinction may be beneficial
to the understanding of the symbolic vs. subsymbolic and related differences,
and ultimately, may lead to a better understanding of what hybrid models
are and how we should structure hybrid models.

I will announce a TR that contains a thorough discussion of this shortly.

--Ron 


========================================================================
Dr. Ron Sun                      http://cs.ua.edu/faculty/sun/sun.html
101 K  Houser Hall               ftp://aramis.cs.ua.edu/pub/tech-reports/
Department of Computer Science                      phone: (205) 348-6363
The University of Alabama                           fax:   (205) 348-0219
Tuscaloosa, AL 35487                                email: rsun at cs.ua.edu
========================================================================