Newsgroups: comp.ai,comp.ai.neural-nets,comp.ai.philosophy
Path: cantaloupe.srv.cs.cmu.edu!bb3.andrew.cmu.edu!newsfeed.pitt.edu!scramble.lm.com!news.math.psu.edu!news.cse.psu.edu!uwm.edu!math.ohio-state.edu!howland.reston.ans.net!torn!tortoise.oise.on.ca!tortoise!dyeo
From: David Yeo <dyeo@tortoise>
Subject: Re: * how many neurons for basic cognition? 
In-Reply-To: <4r7mb3$2pte@lamar.ColoState.EDU> 
Content-Type: TEXT/PLAIN; charset=US-ASCII
Message-ID: <Pine.SOL.3.91.960701072344.1529B@tortoise>
Sender: news@oise.on.ca
Nntp-Posting-Host: tortoise
Organization: Ontario Institute for Studies in Education, Toronto
References: <4r7mb3$2pte@lamar.ColoState.EDU> 
Mime-Version: 1.0
Date: Mon, 1 Jul 1996 11:48:22 GMT
Lines: 36
Xref: glinda.oz.cs.cmu.edu comp.ai:39664 comp.ai.neural-nets:32279 comp.ai.philosophy:43480

On 30 Jun 1996, Steven Eisenberg wrote:

> I am interested to see what anyone has come up with to determine what the 
> size of a neural network should be whose sole function is to do logic 
> processing.  For example, taking in some information about the world 
> around it, going through essentially some thought processes, and 
> producing some kind of conclusion(s).  Not to perform some specific 
> task, but basically to think about a problem.  
> 
> What work has been done on this?  How do you determine how many neurons
> and/or layers work best for this kind of cognition?  How would you design
> a network whose sole purpose is to compare and contrast ideas and
> information? 

It is rather difficult to answer your question in its present form since
it not clear (at least to me) what you mean by "to do logic processing". 
If you mean how many neurons are required to implement the and, or, not
circuits which base logic (actually a single "nand" circuit may suffice)
then that answer is directly provided in the 1943 McCulloch and Pitts work
"A logical calculus of the ideas immanent in nervous activity".  If, as I
suspect is more your goal, you wish to implement the rules of inference in
neurons, then that is quite another problem. One way might be to build
these rules of inference out of their logical primitives (and, or, not)
and then count.  That's just a guess though. In any event, I would start
with the seminal McCulloch-Pitts work.

Two words of caution: 1) there are an infinite number of ways to build any
circuit using neurons, so you will likely need to use parsimony to guide
your selection and 2) it may be impossible to represent a true variable. 
Some good work is being done to address this problem, however (see Hinton,
G. E., 1990, "Connectionist Symbol Processing", Bradford: The MIT Press)

Cheers,

- David Yeo (Applied Cognitive Science, University of Toronto)

