Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!uwm.edu!uwvax!goat!honavar
From: honavar@goat.cs.wisc.edu (A Buggy AI Program)
Newsgroups: comp.ai.neural-nets
Subject: Re: Minimum # of internal nodes to form boolean function
Message-ID: <8837@spool.cs.wisc.edu>
Date: 12 Oct 89 18:03:12 GMT
References: <1989Oct12.050402.9790@boingo.med.jhu.edu>
Sender: news@spool.cs.wisc.edu
Reply-To: honavar@goat.cs.wisc.edu (Vasant Honavar)
Distribution: usa
Organization: U of Wisconsin CS Dept
Lines: 17

In article <1989Oct12.050402.9790@boingo.med.jhu.edu> heath@cs.jhu.edu (David Heath) writes:
>
>  I've been told that Robert Heicht Neilson recently proved that any
>boolean function of n inputs to n outputs can be realized with a neural
>net having n input nodes, n output nodes and 2n-1 intermediate nodes
>(a total of 3 layers). Is there any truth to this statement? Please
>forgive me if this has been discussed here before.
>

I don't know anything about the proof. However, I have made runs with backprop
on a net with 2 input units, 3 hidden units, and 16 output units (all possible
boolean functions of 2 variables) and have gotten it to learn successfully to
meet the preset criterion. I used real valued activations between 0 and 1,
sigmoid output function, and real valued weights.

Vasant Honavar
honavar@cs.wisc.edu