Path: utzoo!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!usc!henry.jpl.nasa.gov!elroy.jpl.nasa.gov!news
From: eric@jane.Jpl.Nasa.Gov (Eric Majani)
Newsgroups: comp.ai.neural-nets
Subject: Re: nn implementation of "max" function
Keywords: max, winner-take-all, weights
Message-ID: <1989Nov30.004621.24751@elroy.jpl.nasa.gov>
Date: 30 Nov 89 00:46:21 GMT
References: <4616@arctic.nprdc.arpa> <80766@linus.UUCP> <9202@spool.cs.wisc.edu>
Reply-To: eric@jane.Jpl.Nasa.Gov (Eric Majani)
Organization: Image Analysis Systems Grp, JPL
Lines: 39

In article <9202@spool.cs.wisc.edu> finton@cs.wisc.edu (David Finton) writes:
>Can anyone describe to me what an implementation of the function
>max{xi} looks like in a connectionist net?  I'm using linear-sum,
>sigmoid-output units.  
>
>What I want is a layer which outputs a "1" from the unit whose
>input (from outside the layer) is greatest, with the other nodes
>in the layer outputing a "0".  
>
>Assume that each node in the layer has an input from outside the 
>layer, and these inputs are clamped to their values.  Node 
>activation is in the range [0,1], while link weights are in the 
>range [-1, 1].
>
>The obvious thing is to have mutual inhibition within the layer,
>possibly with each unit also sending itself some activation (or,
>equivalently, each unit retains some fraction of its previous
>activation level).  But what I've come up with so far seems 
>to give me a net which sends out "1" for *each* unit whose input
>is above the *average*.
>
>I bet this has been done before;  can someone show me where I'm 
>going wrong?  
>
>--David Finton ( finton@cs.wisc.edu )

Check out the following paper which I presented at the Neural Information
Processing Systems Conference in Denver last year (88):

On the K-Winners-Take-All Network
by E. Majani, R. Erlanson, Y. Abu-Mostafa
pp. 634-642
Advances in N.I.P.S., (David Touretzky Editor)
Morgan Kaufmann Pub.

PS: With your approach, you get 1 for each unit above the median
I believe.

-eric