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From: saswss@hotellng.unx.sas.com (Warren Sarle)
Subject: Re: Back ... something ??!
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Date: Mon, 3 Mar 1997 20:30:15 GMT
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In article <5f682n$t2m$1@okapi.ict.pwr.wroc.pl>, mnowak@cyber.ict.pwr.wroc.pl (Marcin Nowak) writes:
|> ...
|> Lets suppouse, we have multilayer neural network. The network
|> recognizes characters. The input is array (e.g. 5x8) and number
|> of outputs is equal to number of characters being recognized.
|> 
|>   When on input is letter 'A', first output node has on its output
|> '1', and the rest '-1', when there is 'B', the second node has
|> '1', and the rest '-1', and so on.
|> 
|>   The problem is to find set of input values that make the net
|> saying 'This is the letter A'.
|> 
|>   In a fact, that's not a big problem. Big problem is how to name
|> this in english :-)

That's usually called "inverting" the network. It's just a matter of
solving nonlinear equations (not that it's a trivial matter, by any
means!). Here are some references collected from previous posts by
Dave DeMers:

Ronald L. Williams (1986),
``Inverting a connectionist network mapping by backpropagation
of error'', {\em Proc. 8th Conf. Cognitive Science Soc.}.

J\"{o}rg Kindermann \& Alexander Linden (1990),
``Inversion of Neural Networks by Gradient Descent'',
{\em Parallel Computing}, {\bf 14}, 277--286.

Sukhan Lee \& Rhee M. Kil, ``Bidirectional Continuous
Associator Based on Gaussian Potential Function Network'', {\em Proc.
1989 IJCNN}, Washington, D.C..

Sukhan Lee \&  Rhee M. Kil, ``Robot Kinematic Control
Based on Bidirectional Mapping Network'', {\em Proc. 1990 IJCNN}, San Diego.

Michael I. Jordan and David E.  Rumelhart (1992),
``Forward Models: Supervised Learning with a Distal
Teacher''. {\em Cognitive Science} {\bf 16}, 307--354.

from the Robotics world:
Pasquale Chiacchio, Stefano Chiaverini, 
Lorenzo Sciavicco \& Bruno Siciliano (Aug. 1991), 
``Closed--Loop Inverse Kinematics Schemes for Constrained Redundant
Maniulators with Task--Space Augmentation and Task--Priority
Strategy'', {\em Int. J. Robotics Research}, {\bf 10}:4, 410--425.


-- 

Warren S. Sarle       SAS Institute Inc.   The opinions expressed here
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