preprint: Neural Networks, Knowledge and Cognition...

preprint: Neural Networks, Knowledge and Cognition...

[M. Healy]

A technical report on a categorical model of the semantics of neural
networks is now available on the Dspace archive in the collection 2004.
To access it, go to the University of New Mexico site at
https://repository.ece.unm.edu/dspace/  and search on
http://hdl.handle.net/1928/33 .

Here's an abstract:

   Neural Networks, Knowledge, and Cognition: A Mathematical Semantic Model
   Based upon Category Theory, by M. J. Healy and T. P. Caudell

   Category theory can be applied to mathematically model the semantics of
   cognitive neural systems.  We discuss semantics as a hierarchy of
   concepts, or symbolic descriptions of items sensed and represented in
   the connection weights distributed throughout a neural network.  The
   hierarchy expresses subconcept relationships, and in a neural network
   it becomes represented incrementally through a Hebbian-like learning
   process.  The categorical semantic model described here explains the
   learning process as the derivation of colimits and limits in a concept
   category.  It explains the representation of the concept hierarchy in a
   neural network at each stage of learning as a system of functors and
   natural transformations, expressing knowledge coherence across the
   regions of a multi-regional network equipped with multiple sensors.
   The model yields design principles that constrain neural network designs
   capable of the most important aspects of cognitive behavior.

Please let me know right away if there are any problems.  I'll warmly
receive any questions or comments.

- Mike