What is a "hybrid" model?

[Lev Goldfarb]

On Wed, 27 Mar 1996, Ron Sun wrote:

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

Ron,
Please note that the question is not really tricky. The question simply
suggests that there is no need to attach the term "hybrid" to the model,
because the combination (hybrid model) is both "ugly" and is likely to
lead almost all researchers involved in the wrong direction: there are
really no "hybrid" mathematical structures, but rather "symbiotic
structures", e.g. topological group, (although I would also hesitate to
suggest this combination as a research direction).

In other words, once we find the right model that captures the necessary
"symbiosis" of the discrete and the continuous, we will give it the name
that reflects its unique and fundamentally new features, which it MUST
exhibit.

By the way, I do believe that the inductive learning model proposed by me
- evolving transformation system (see the publications in my homepage) -
embodies a fundamentally new symbiosis of the discrete and the continuous.


> 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.

It is also important to understand why the nature of the above symbiosis
should be radically different from that of the classical mathematical
structures, which embody, basically, the symbiosis of the NUMERIC
mathematical structures.


> 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?

> 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 simply cannot imagine how such (of necessity) relatively "superficial"
experimental observations will in the foreseeable future lead us to the
insight into the nature of the fundamentally new MATHEMATICAL STRUCTURE
(of course, if one at all cares about it).

For that matter, many neuroscientists, for example, with equal
justification, may also claim to be on the "right trail". And why not?

Remember what Einstein said?
(But as long as no principles are found on which to base the deduction,
the individual empirical fact is of no use to the theorist; indeed he
cannot even do anything with isolated general laws abstracted from
experience. He will remain helpless in the face of separate results of
empirical research, until principles which he can make the basis of
deductive reasoning have revealed themselves to him.)

To our area of research this observation applicable even to a larger
extent: we are dealing with information processing.


 -- Lev

http://wwwos2.cs.unb.ca/profs/goldfarb/goldfarb.htm