Path: utzoo!attcan!uunet!wuarchive!mit-eddie!media-lab!minsky
From: minsky@media-lab.MEDIA.MIT.EDU (Marvin Minsky)
Newsgroups: comp.ai.neural-nets
Subject: Re: Reference for sufficiency of two layers
Message-ID: <3528@media-lab.MEDIA.MIT.EDU>
Date: 2 Oct 90 19:45:19 GMT
References: <12626564934017@osu-20.ircc.ohio-state.edu>
Reply-To: minsky@media-lab.media.mit.edu (Marvin Minsky)
Organization: MIT Media Lab, Cambridge MA
Lines: 14




WHITELEY-J@osu-20.ircc.ohio-state.edu (J. Whiteley) asks

 > I'm looking for a reference which shows that two layers are
 > sufficient to approximate any function using a BP network.  All
 > I've dug up so far is ...

Any boolean function has a disjunctive (and a conjunctive) normal form
hence can be expressed exactly by two layers, one with threshold 1 and
the other with threshold N, for the number of inputs.  However, if the
fan-out is less than N, then the question is much more serious, and
you have to read "Perceptrons", etc.