Consider a simple Hopfield network made up of three neurons. The synaptic weight matrix of

the network is suggested to be:

$W=\left[\begin{array}{ccc}0& -2& 3\\ 2& 0& 3\\ 3& 2& 0\end{array}\right]$

The bias applied to each neuron is zero.

a$)$ Draw the architectural graph of the above Hopfield network $(5$ pts$)$

b$)$ Define the stable and non$-$stable states $(5$ pts$)$

c$)$ Calculate the matrix W$\text{'}$ using the equation of the optimized weight $(5$ pts$)$

Hopfield model: $,W_{\text{o}\text{p}\text{t}}=\frac{1}{N}[{\displaystyle \underset{=1}{\overset{M}{}}}{}_{}{}_{}^T-MI]$ and $y=sgn[Wy+b]$