Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!mailrus!wuarchive!cs.utexas.edu!rutgers!bellcore!att!cbnewsl!apr
From: apr@cbnewsl.ATT.COM (anthony.p.russo)
Newsgroups: comp.ai.neural-nets
Subject: Re: : Step Function
Summary: "known-ness" -back to square one
Keywords: learning,generalization
Message-ID: <1727@cbnewsl.ATT.COM>
Date: 1 Sep 89 13:52:34 GMT
References: <1060@rex.cs.tulane.edu> <6980@sdcsvax.UCSD.Edu> <17538@bellcore.bellcore.com>
Organization: AT&T Bell Laboratories
Lines: 36

In article <17538@bellcore.bellcore.com>, ackley@wind.bellcore.com (David H Ackley) writes:
> In article <1697@cbnewsl.ATT.COM> apr@cbnewsl.ATT.COM (anthony.p.russo) writes:
> >Yes, I should stick to Valiant's paper. However, one thing: a known function
> 							       ^^^^^^^^^^^^^^
> >is, in most cases, more than a set of ordered pairs. It is a set of ordered
> >pairs related in some way. 
> 
> By referring to "known functions" you are implicitly incorporating a
> bias in your notion of learnability --- i.e., you are preferring
> functions that have some (presumably simple) relation between input
> and output.  I say "presumably simple" because I imagine you want to
> rule out properties like "appearing in the same truth table" as
> sufficient grounds for being "related in some way".
> 
I could have omitted the word "known" and had a perfectly legitimate statement.
That is, ANY deterministic FUNCTION is a set of related ordered pairs,
whether known or not.

> Can you make your criteria for "known-ness" explicit?  

No. You bring up a good point, because your argument is really, "What functions
shall we consider in the hypothesis space?" 

I can't tell you; this appears to be getting very deep. On the surface,
it seems that biases are  !necessary! for learning anything at all.
If so, then the biases are probably hard-wired and not learned, since
they would have to be learned in terms of other biases, etc.

Does this make sense to anyone else, or have I gone off the deep end?

 ~ tony ~

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	~  	 Tony Russo		" Surrender to the void."	~
	~   apr@cbnewsl.ATT.COM		   put disclaimer here		~
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