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From: pluto@beowulf.ucsd.edu (Mark E. P. Plutowski)
Newsgroups: comp.ai.neural-nets
Subject: Re: : Step Function
Keywords: learning,generalization
Message-ID: <7000@sdcsvax.UCSD.Edu>
Date: 31 Aug 89 17:01:20 GMT
References: <1060@rex.cs.tulane.edu> <6980@sdcsvax.UCSD.Edu> <1989Aug30.162345.9569@elroy.jpl.nasa.gov> <1697@cbnewsl.ATT.COM>
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Reply-To: pluto@beowulf.UCSD.EDU (Mark E. P. Plutowski)
Organization: EE/CS Dept. U.C. San Diego
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In article <1697@cbnewsl.ATT.COM> apr@cbnewsl.ATT.COM (anthony.p.russo) writes:
>... someone commented that learnability should be defined dependent
>on architecture. I don't see why.

I mentioned this for concreteness' sake.  
More generally, you want to know whether the 
set of hypotheses your learning protocol has
at its disposal can represent the function
you wish to learn to a satisfactory level of
approximation - is the hypothesis space sufficient
to characterize the set of concepts you wish to
learn ?  A particular architecture can represent
a subset of some concept space - this is its 
hypothesis space - and it may be only capable
of effectively learning some subset of its
hypotheses space. 

In the case you mention, a single 2-input threshold gate
cannot learn x-or because it cannot represent x-or.
A 2-input threshold gate network with at least 1 hidden
unit may not be able to effectively (feasibly, satisfactorily)
learn x-or, perhaps due to the ineffectiveness of the 
learning law.  

With the definition of learning you initially proposed,
we can say very little about learning - except that it
will be impossible for all practical purposes.