Using Hebbian$-$type of learning rule to obtain a Hopfield network which can memorise the

following two patterns:

$\left[\begin{array}{cccccc}1& -1& -1& 1& -1& 1\end{array}\right],\left[\begin{array}{cccccc}1& -1& 1& -1& -1& 1\end{array}\right]$

a$)$ Draw the structure of the Hopfield network.

b$)$ Clearly indicate the following elements in the Hopfield network:

Weight

Threshold

Initial input

Output after the $1^{st}$ iteration

c$)$ Test the network with the following corrupted patterns:

$\left[\begin{array}{cccccc}-1& 1& -1& 1& 1& -1\end{array}\right],\left[\begin{array}{cccccc}-1& -1& 1& 1& -1& -1\end{array}\right]$

d$)$ Are the results from c$)$ expected and why?