Subject: Re: Query

From: categories <[email-masked]>
Date: Tue, 1 Jul 1997 15:14:42 -0300 (ADT)

Date: Tue, 1 Jul 1997 09:49:21 -0700
From: Michael J. Healy 206-865-3123 <[email-masked]>

Since there have been some replies to the query about artificial perception, 
I suppose it's OK to mention my own work in progress.  I have been doing 
research in the formal semantics of neural networks.  I am working on a 
mathematical model in which concepts (formulas) are formed in memory as 
colimits.  The diagrams involve neural structures representing other 
concepts, going all the way back to simple percepts.  A concept is stored 
in memory as a neuron or neuron pool together with its attendant synaptic 
connections.  Logically closed portions of memory are theories.  Functors 
and natural transformations enter in in the usual fashion of categorical 
model theory.  

There is still a lot of work to do on this, and I am still learning the 
mathematics.  I do have a proposed neural implementation of it, and am 
working on a paper.  Previous work along these lines has involved geometric 
logic, so that I could understand some of the basics of learning, which for 
me involves working with an observational logic.  I have a paper on this, 
too.  Finding reviewers for this kind of material in the neural network 
community has been difficult.  If any of this sounds interesting enough 
to discuss, I certainly wouldn't mind getting some feedback from category 
theorists.

Sincerely, 
Mike Healy
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