Problem $1)$ Binary Hopfield Model $(50$ points$)$

Step $1$: Given a set of literals, $($for example you can select A$,$ B$,$ C and D$),$ build a Binary Hopfield Model such that these sampler patterns are stored as equilibrium points of the network.

$($Hint: Build a $8$x$8$ grid to represent for each literal. Then convert each $88$ matrix to a $64-$dimensional vector.$)$

Step $2$: Show each sampler pattern graphically on this $88$ grid.

Step $3$: Start the system by initializing the outputs of each neuron with an arbitrary pattern. Choose arbitrary pattern such that the original patterns are distorted by zero mean white noise with changing variance. Show each starting pattern graphically, followed by iterative steps.

Step $4$: Show that if there is too much noise, there is no convergence to the desired state.

Ex: $44$ grid to represent the literal $"T"$

pattern$\_T=[+1,+1,+1,-1,-1,+1,-1,-1,-1,+1,-1,-1,-1,+1,-1,-1{]}^T$

distorted image:

Take screenshots for each step and insert these screens into MS$\_$Word file. Save the MS$\_$word file as a pdf with the following naming convention: firstname$\_$lastname$\_$HW$2\_$p$1.$pdf and upload it to BilgiLearn. Upload the $m-$file as well.