We are going to build a computation graph and evaluate it using the data from the car collision $($XOR$)$ example from class. Using the computation

graph for a simple linear classifier with hinge loss from pg$.38$ of the notes, perform a feedforward pass with the following samples:

$w=[0\mathrm{.}25,0\mathrm{.}5]$

$(x)=[0,2],y=1$

$(x)=[2,0],y=1$

$(x)=[0,0],y=-1$

$(x)=[2,2],y=-1$

Draw $4$ computation graphs, one for each sample. Show your work using it to calculate the output the loss for each sample, performing a "forward

pass". Write the value of each node on the lefthand side to keep track. What is the overall average loss?

Now, for each sample whose loss was non$-$zero, use the computation graph $($along with the values calculated in the forward pass$)$ to calculate the

gradient of the loss with respect to w $($i$.$e a "backward pass"$).$ Using stochastic gradient descent, what would be w after updating it with the gradient

of these $4$ samples?

Will this ever converge? If not, how could you modify your computation graph?