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From: finton@cambizola.cs.wisc.edu (David Finton)
Newsgroups: comp.ai.neural-nets
Subject: nn implementation of "max" function
Summary: how do you do it?
Keywords: max, winner-take-all, weights
Message-ID: <9202@spool.cs.wisc.edu>
Date: 21 Nov 89 20:38:45 GMT
References: <4616@arctic.nprdc.arpa> <80766@linus.UUCP>
Sender: news@spool.cs.wisc.edu
Reply-To: finton@cs.wisc.edu (David Finton)
Organization: U of Wisconsin CS Dept
Lines: 24

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 )