Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!rutgers!bellcore!wind!ackley
From: ackley@wind.bellcore.com (David H Ackley)
Newsgroups: comp.ai.neural-nets
Subject: Re: : Step Function
Summary: "known function" implies bias
Keywords: learning,generalization
Message-ID: <17538@bellcore.bellcore.com>
Date: 31 Aug 89 18:02:23 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: ackley@wind.UUCP (David H Ackley)
Organization: Bellcore, Morristown, NJ
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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".

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

| David Ackley   Cognitive Science Research Group |
| "There are     Bell Communications Research Inc.|
|     no facts,          ackley@flash.bellcore.com|
|       only factors"          ...!bellcore!ackley|