Consider a data set in which the two points $\{(1,1),(1,1)\}$ belong to one class, and the other two points $\{(1,1),(1,1)\}$ belong to the other class. Start with perceptron parameter values at $(0,0),$ and work out a few point$-$wise gradient$-$descent updates with $=1.$ While performing the gradient$-$descent updates, cycle through the training points in any order. $($a$)$ Does the algorithm converge in the sense that the change in objective function becomes extremely small over time? $($b$)$ Explain why the situation in $($a$)$ occurs.