Connectionists: New technical report available

[mjhealy@ece.unm.edu]

A new University of New Mexico technical report is available on DSpace,
ECE-TR-08-0010.  It describes an experiment in cognitive psychology that
tests a (mathematical) category-theoretic model of categorization by
humans.  The model is part of a comprehensive theoretical model of the
declarative semantics of neural networks.   The report can be obtained by
going to DSpaceUNM, or directly to  http://hdl.handle.net/1928/6724  .

Questions and comments are welcome.

Mike Healy
Electrical and Computer Engineering
University of New Mexico
Albuquerque, NM
USA

Abstract

Categorization and the judgement of similarity are fundamental in
cognition. We propose that these and other activities are based upon an
underlying structure of knowledge, or concept representation, in the
brain. Further, we propose that this structure can be represented
mathematically in a declarative form via category theory, the mathematical
theory of structure. We test the resulting mathematical model in an
experiment in which human subjects provide judgements of similarity for
pairs of line drawings using a numerical scale to represent degrees of
similarity. The resulting numerical similarities are compared with those
derived from the category-theoretic model by comparing diagrams. The
diagrams represent distributed concept structures underlying the line
drawings. To compare with a more conventional analysis technique, we also
compare the human judgements with those provided by a two-dimensional
feature space model equipped with a distance metric for the line drawings.
 The results are equally favorable for both models. Because of this and
the putative explanatory power of the category-theoretic model, we propose
that this model is worthy of further exploration as a mathematical model
for cognitive science.

Keywords

categorization, (mathematical) category, cognition, colimit, concept,
diagram, feature, morphism, similarity, theory