Using one$-$dimensional and two$-$dimensional input xi$,$ explain that the above neural network

defines a piecewise linear function si $=$ f $($xi$).$

$(2)$ Explain that the last line can be expressed in terms of vectors and matrix.

$(3)$ Let $=($k$,$ kj $,$k$,$ j$).$ Find the gradient J$($$)$ by calculating $$J$/$k and $$J$/$kj $,$ and

write down the gradient ascent algorithm with momentum.