interpolation vs generalisation

[Ross Gayler]

The people following this thread might want to consider where analogical
inference fits in.  Analogical inference is a form of generalisation that
is performed on the basis of structural or relational similarity rather
than literal 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 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 input space instead of
the structural representation space.

In brief: Generalisation can occur without interpolation in a data space
that you can observe, but it may involve interpolation in some other space
that is constructed internally and dynamically.

Ross Gayler
ross at psych.psy.uq.oz.au