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From: joe@amos.ling.ucsd.edu (Shadow)
Newsgroups: comp.ai.neural-nets,comp.ai
Subject: Re: Learning arbitrary transfer functions
Message-ID: <5522@sdcsvax.UCSD.EDU>
Date: 17 Nov 88 20:48:52 GMT
References: <399@uvaee.ee.virginia.EDU> <380@itivax.UUCP>
Sender: nobody@sdcsvax.UCSD.EDU
Reply-To: joe@amos.UUCP (Shadow)
Organization: Univ. of Calif., San Diego
Lines: 47

in article, 399.uvaee.ee.virginia.EDU writes:

>>I am looking for any references that might deal with the following
>>problem:
>>
>>y = f(x);         f(x) is nonlinear in x
>>
>>Training Data = {(x1, y1), (x2, y2), ...... , (xn, yn)}
>>
>>Can the network now produce ym given xm, even if it has never seen the
>>pair before?
>>
>>That is, given a set of input/output pairs for a nonlinear function, can a
>>multi-layer neural network be trained to induce the transfer function

my response:

1. Neural nets are an attempt to model brain-like learning
   (at least in theory).

   So, how do human's learn non linear functions ?

      : you learn that x^2, for instance, is X times X.

   And how about X times Y ? How do humans learn that ?

      : you memorize it, for single digits, and
      : for more than a single digit, you multiply streams
	of digits together in a carry routine.

2. So the problem is a little more complicated. You might imagine
   a network which can perfectly learn non-linear functions if
   it has at its disposal various useful sub-networks (e.g., a
   network can learn x^n if it has at its disposal some mechanism
   and architecture suitable for multiplying x & x.)

   (imagine a sub-network behaving as a single unit, receiving
    input and producing output in a predictable mathimatical manner)

(promoting thought)


   What is food without the hunger ?
   What is light without the darkness ?
   And what is pleasure without pain ?

   joe@amos.ling.ucsd.edu