TR available:Inverting Neural Nets Using LP and NLP

[Bao-Liang Lu]

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TITLE: Inverting Feedforward Neural Networks Using   
       Linear and Nonlinear Programming   

       BMC Technical Report BMC-TR-97-12
AUTHORS:
       Bao-Liang Lu (1)
       Hajime Kita (2)
       Yoshikazu Nishikawa (3)

ORGANISATIONS:
       (1) The Institute of Physical and Chemical Research (RIKEN)
       (2) Tokyo Institute of Technology
       (3) Osaka Institute of Technology
 
ABSTRACT:
The problem of inverting trained feedforward neural networks is to 
find the inputs which yield a given output. In general, this problem 
is an ill-posed problem because the mapping from the output space to 
the input space is an one-to-many mapping. In this paper, we present 
a method for dealing with this inverse problem by using mathematical 
programming techniques. The principal idea behind the method is to 
formulate the inverse problem as a nonlinear programming problem. 
An important advantage of the method is that multilayer perceptrons 
(MLPs) and radial basis function (RBF) neural networks can be inverted 
by solving the corresponding separable programming problems, which 
can be solved by a modified simplex method, a well-developed and 
efficient method for solving linear programming problems. As a result, 
large-scale MLPs and RBF networks can be inverted efficiently.  
We present several examples to demonstrate the proposed inversion 
algorithms and the applications of the network inversions to examining 
and improving the generalization performance of trained networks. 
The results show the effectiveness of the proposed method.

(double space, 50 pages)

Any comments are appreciated.

Bao-Liang Lu
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Bio-Mimetic Control Research Center
The Institute of Physical and Chemical Research (RIKEN)
Anagahora, Shimoshidami, Moriyama-ku
Nagoya 463-0003, Japan
Tel: +81-52-736-5870
Fax: +81-52-736-5871
Email: lbl at bmc.riken.go.jp