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\title{Interval Neural Networks}
\author{Rajendra B. Patil}

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\markright{APIC'95, El Paso,
Extended Abstracts,
A Supplement to the international journal of {\rm Reliable
Computing}\ \ \ \ \ \ \ \ \ \ \  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ }

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\begin{abstract}
Traditional neural networks use {\it patterns}, i.e., pairs of 
observation results $(\vec x^{(p)},y_p)$, $1 \le p\le P$,
to reconstruct the dependency $y(\vec x)$. To determine the parameters
of the approximation, a special version of the gradient descent method
called {\it backpropagation} is normally used. 

In real life, observations are not precise; instead of a precise value
$y$, after measuring $y$, 
we only have an {\it interval} ${\bf y}=[\tilde y-\Delta,\tilde
y+\Delta]$ of possible values of $y$, where $\tilde y$ is the
measurement result, and $\Delta$ is the accuracy of the measuring
instrument. Similarly, instead of the precise values of inputs $\vec
x=(x_1,...,x_n)$, we only have intervals of possible values. So, the
input data for extrapolation consists of {\it interval patterns}
$(\vec {\bf x}^{(p)}, {\bf y}^{(p)})$.  

We have designed and implemented an interval modification of 
backpropagation technique. 
Experimental and theoretical results will be presented in the talk.
\end{abstract} 
  
\auffil{The author is with 
Computing Research and Applications (CIC-3),
MS -  M986,
Los Alamos National Laboratory,
Los Alamos, NM 87545,
email rbp@killdeer.lanl.gov.}

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