interpolation vs generalisation

On  Sat, 14 Sep 91 09:42:16 ADT  	Ross Gayler <ross at psych.psy.uq.oz.
au> writes:

>                                Analogical inference is a form of
> generalisation that is performed on the basis of structural or
> relational similarity rather than literal <fixed>  similarity.  It is
> generalisation, because it involves the application of knowledge from
> previously encountered situations to a novel situation.  However, the
> interpolation does not occur in the <some fixed> space defined by the
> input patterns, instead it occurs in the space describing the structural
> relationships of the input tokens.  The structural relationships
> between any set of inputs is not necessarily fixed by those inputs,
> but generated dynamically as an 'interpretation' that ties the inputs
> to a context.  There is an argument that analogical inference is the
> basic mode of retrieval from memory, but most connectionist research
> has focused on the degenerate case where the structural mapping is an
> identity mapping - so the interest is focused on interpolation in the
> <fixed> input space instead of the structural representation space.
>
> In brief: Generalisation can occur without interpolation in a <some
> fixed> data space that you can observe, but it may involve interpolation
> in some other space that is constructed internally and dynamically.


I also believe that the above point is of critical importance: an
intelligent system (at least if it is considered in the course of both
micro- and macro- evolution) must have the capacity to generate new
metrics based on the structural properties of the object classes.

In fact, I find this capacity of an intelligent process to be so
important, that I have suggested it to be the basic attribute of
an intelligent process. To ensure the presence of this attribute,
one can demand from the learning (test) environment some minimum
requirement:
"The requirement that I propose to adopt can be called structural
unboundedness of the environment. Informally, an environment is
called structurally unbounded if no finite set of "features", or
parameters, is sufficient for specifying all classes of events
<objects> in the environment."

See the paper mentioned in one of my resent postings ("Verifiable
characterization of an intelligent process").

If a proposed model can operate successfully in some such environments,
then it deserves a more serious consideration.

-- Lev Goldfarb