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From: sietsma@latcs1.oz.au (Jocelyn Sietsma Penington)
Newsgroups: comp.ai.neural-nets
Subject: Re: Lippmann paper
Message-ID: <8245@latcs1.oz.au>
Date: 2 Jul 90 00:56:02 GMT
References: <11441@rasp.eng.cam.ac.uk> <1085@carol.fwi.uva.nl>
Reply-To: sietsma@latcs1.oz.au (Jocelyn Sietsma)
Organization: Comp Sci, La Trobe Uni, Australia
Lines: 39

In article <1085@carol.fwi.uva.nl> smagt@fwi.uva.nl (Patrick van der Smagt) writes:
>In article <11441@rasp.eng.cam.ac.uk> mww@uk.ac.cam.eng writes:
>>A few weeks ago there was a summary of papers and books on neural
>>networks. Several people referred to Richard Lippman's well known
>>paper "An introduction to Computing with Neural Nets: IEEE ASSP
>>magazine April 1987"
>>
>>More than one person said that this paper contained errors.  As this
>>is such an influential and often read paper, particularly by those who
>>are new to the field, I wonder if anyone would care to say exactly
>>what these errors are.
>
>Here they are (or, at least, some of them):
        [2 criticisms deleted]

>	p. 14  figure 14 (serious)
>		rather misleading.  A ff-network with --**ONE**-- layer of
>		hidden units suffices.  For references, see

I have to disagree with you here a little.  This geometric analysis is 
valid if the outputs of the units are approximated by step-functions 
(= hard-limiters).  Using continous output functions gives more power
and allows a single hidden layer to suffice, but this analysis was useful
in giving an upper limit of 2 hidden layers 3 years before the 1-hidden-layer
proof arrived.
>	[2 more criticisms deleted]	
>	
    p. 16, second last paragraph
"There should thus typically be more than three times as many nodes in 
the second as in the first layer."
   The 'first' and 'second' should be exchanged - 3 times as many nodes
in the first as in the second layer.
This is clearly what is intended from the analysis preceding.

>Patrick van der Smagt                                               /\/\

Jocelyn Sietsma
USD, Materials Research Laboratory
DSTO