Path: utzoo!attcan!uunet!wuarchive!cs.utexas.edu!helios!guansy
From: guansy@cs.tamu.edu (Sheng-Yih Guan)
Newsgroups: comp.ai.neural-nets
Subject: Re: Reference for sufficiency of two layers
Message-ID: <8728@helios.TAMU.EDU>
Date: 2 Oct 90 21:32:17 GMT
References: <12626564934017@osu-20.ircc.ohio-state.edu>
Sender: usenet@helios.TAMU.EDU
Organization: Computer Science Department, Texas A&M University
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It has been proved (see, for instance, Funahashi, 1989; Moore and Poggio, 1988)
that a network with two layers of hidden sigmoidal units can approximate
arbitrarily well any continuous function.  It is interesting to notice that 
this statement still holds true if there is just one hidden layer (Carrol and
Dickinson, 1989; Cybenko, 1989; Funahashi, 1989).

S. M. Carrol and B. W. Dickinson.  Construction of neural nets using the 
Radon transform.  In Proceedings of the International Joint Conference
on Neural Networks, pages I-607-I-611, Washinton D. C., June 1989.
IEEE TAB Neural Network Committee.


K. Funahashi.  On the approximate realization of continuous mappings by 
neural networks.  Neural Networks, 2:183-192, 1989.

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