Connectionists: Complete account of category-theoretic ART modification

[mjhealy@ece.unm.edu]

Our full account of an application of colimits and limits to improving
the performance of the ART 1 neural architecture with complement
coding is to appear in the journal Neurocomputing.  A preprint
is available on my website, http://www.ece.unm.edu/~mjhealy , or
by contacting me for a copy.

Applying Category Theory to Improve the Performance of a Neural Architecture

Michael J. Healy, Richard D. Olinger, Robert J. Young,
Shawn E. Taylor, Thomas P. Caudell, and Kurt W. Larson

Abstract:

A recently developed mathematical semantic theory explains the relationship
between knowledge and its representation in connectionist systems. The
semantic
theory is based upon category theory, the mathematical theory of structure. A
product of its explanatory capability is a set of principles to guide the
design of future
neural architectures and enhancements to existing designs. We claim that this
mathematical semantic approach to network design is an effective basis for
advancing the state of the art. We offer two experiments to support this
claim. One
of these involves multispectral imaging using data from a satellite camera.

Keywords: Category theory; Mathematical semantics; ART 1; Stack intervals;
Multispectral imaging