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{\it The Final-exam of the Advanced Course of Neural Networks
             (24 Jan 2001)}\\
\noindent
Name [ \hspace{2in} ] \hspace{.1in} Student-ID [ \hspace{1in} ]
\begin{itemize}
\item[1.] Assume that we want to store two patterns:
\begin{displaymath}
\begin{array}{cccccccccc}
(+1 & +1 & +1 & +1 & +1 & +1 & +1 & +1 & +1 & +1) \\
(+1 & -1 & +1 & -1 & +1 & -1 & +1 & -1 & +1 & -1) \\
\end{array}
\end{displaymath}
in the fully connected neural network with 10 neurons. 
Answer the following questions.
   \begin{itemize}
          \item[(1)] By using the Hebbian learning algorithm, 
                     obtain the $10 \times 10$ weight matrix. 
\vspace{1.4in}
          \item[(2)] Under the weights obtained above, 
                     calculate the {\it energy} of the network when
                     a noisy input of one of the stored patterns:
                     \begin{displaymath}
                     \begin{array}{cccccccccc}
                       (-1 & -1 & -1 & +1 & +1 & +1 & +1 & +1 & +1 & +1) \\
                     \end{array}
                     \end{displaymath}
                     is given to the network.
\vspace{.7in}
          \item[(3)] If you assume that the $i$-th neuron corresponds to
                     the $i$-th bit of patterns to be stored and the order
                     of update is according to this $i$, then which 
                     neuron will be first updated under the input of (2). 
\vspace{.7in}
          \item[(4)] Obtain also the energy 
                     when the input above converges to the original one.
\vspace{.7in}
          \item[(5)] Obtain the Hamming distance of the two stored patterns.
\vspace{.7in}
          \item[(6)] Give me an example of the patterns that is located
                     just at the center of the two energy minimum.
   \end{itemize}
\end{itemize}


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