IJCNN 2000 paper available (fwd)

[M. Healy]

My paper accepted for IJCNN 2000, 

M. J. Healy (2000), 
"Category Theory Applied to Neural Modeling and Graphical Representations"

is available (with minor revisions) on the web in postscript format at 

http://cialab.ee.washington.edu/pubs.htm .  I can supply .pdf format 
for anyone who requests it from me at mjhealy at u.washington.edu .

This has a larger scope than my IJCNN 99 paper.  Following a brief 
tutorial on category theory, it shows a simplified view of how functors 
implement concept hierarchies in a category of neural architecture
components through the use of colimits (the content of the 1999 paper).  
It goes on to show how natural transformations between the functors 
interconnect the hierarchies at all their levels of abstraction.  This 
yields a mathematical model of the semantics of the formation of 
ever-more-complex concepts in a connectionist memory during adaptation, 
and multiple implementations in subnetworks associated with different 
processing functions (vision, tactile and other sensors, association 
regions, motor function, etc.).  The multiple implementations are 
hierarchies directed from the abstract to the specialized.  These must 
be interconnected in a manner consistent with abstraction.  Here, we mean 
that, first, different implementations of concepts at different abstraction 
levels must maintain the same relative positions in the implementation 
hierarchies.  Second, performing a cross-hierarchy association and then 
abstracting or specializing (moving "down" or "up" in the associated 
hierarchy) must be interchangeable with first moving "down" or "up" 
and then moving across, so that the order of different stages in a 
perception or reasoning exercise does not change the semantics of what 
is being perceived or reasoned about.  My claim is that the functors 
and natural transformations capture these peoperties mathematically.  
A full paper is under construction.

Mike
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