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{A Visualization of Weight Solutions \\
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of \\
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a Neural Network Model of Associative Memory
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\vspace{1in}
Akira Imada\\
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Conputer Engineering Department\\
Dokuz Eylul University\\
Izmir, Turkey
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%%%%%%%%%%  To be More Specific.  %%%%%%%%%%
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\begin{itemize}
\item We evolve neural network model of associative memory,\\
   \begin{itemize}
   \item[-]where many issues such as \\
      \begin{itemize}
      \item[$\star$]the location of weight solutions \\
      \end{itemize}
   \item[]are still unknown.\\
   \end{itemize}
\item We approach this issue also by an EC.
\end{itemize}

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%% I don't think this topic is very familar for all of us. So I start ...
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$\Box${\bf Contents:}\\

\begin{itemize}
\item What is Associative Memory?
%\item How we evolve it?\\
\item[] \underline{\hspace*{5in}} \\
\item Exploration on High-D Weight Space.\\
\item[]\underline{\hspace*{5in}} \\
\item Concluding Remarks.
\item Future Work.
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$\Box${\bf Associative Memory:}\\

\begin{itemize}
\item[-] stores patterns:
   \begin{itemize}
   \item[] in a distributed way among neurons,\\
   \end{itemize}
\item[-] recalls patterns:
   \begin{itemize}
   \item[] from noisy and/or partial input
   \item[]\hspace*{2.1in}(using attraction of attractors).\\
   \item[]\hspace*{1.5in}$\Downarrow$ i.e.\\
   \end{itemize}
\item[-] evokes {\it perfect information} from {\it imperfect information} 
   \begin{itemize}
   \item[]with its capability depending on basin of attraction.\\
   \end{itemize}
\end{itemize}

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We should note that there exists:
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\item[]
   \begin{itemize}
   \item[$\star$]a trade-off between {\it storage capacity} and 
                 {\it basin size}.
   \end{itemize}
\end{itemize}


%%%%%%%%%% Conclusion %%%%%%%%%%
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{\bf $\Box$ Conclusions:}\\
\begin{itemize}
\item We have many different weight solutions for Associative Memory,\\
   \begin{itemize}
   \item[-] where questions are:
      \begin{itemize}
      \item[$\star$] Can we learn the distribution of them in weight space?
      \end{itemize}
   \item[] which is still one of the open issues.
   \end{itemize}
\item[]
\item The answer is (somehow) yes!
   \begin{itemize}
   \item[-] GA visualizes a high dimensional space.
   \end{itemize}
\item[]
\item We shed new light on the classical unknown issues by ECs.
\item Can we apply these techniques to real world problems too?
\end{itemize}


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Our concern here is to observe the high dimensional weight space