$5\mathrm{.}2[28$ points$]$ The following sigmoid network has $3$ units labeled $1,2,$ and $3.$ All units are negative sigmoid units, meaning that their output is computed using the equation:

$n(z)=-\frac{1}{1+e^{-z}}$

This differs from standard sigmoid by a minus sign. The derivative of $n(z)$ is:

$\frac{dn(z)}{dz}=n(z)(1+n(z))$

Additionally, this network uses a non$-$standard error function:

$E=\frac{1}{2}(2y^{**}-2y{)}^2$

$(1)$ Using the initial weights provided below, and the input vector $[x1,x2]=[2,0\mathrm{.}5],$

compute the output at each neuron after forward propagation $(6$ points$).$ Use the

negative sigmoid values given in the table on the tear$-$off sheet at the end of the exam in

your computation.

$(2)$ Using a learning rate of $1,$ and a desired output of $0,$ backpropagate the network by computing the derivatives for all parameters, and write the new values in the table below. Assume the initial values for the weights are as specified in Part $(1).$ Write down your calculation process. $(22$ points$)$

$\backslash$table$[[\backslash$table$[[$Param$],[$eters$]],$b$1,$w$11,$w$12,$w$13,$b$2,$w$21,$w$22,$w$23,$b$3],[\backslash$table$[[$Deriva$],[$tives$]],,,,,,,,,],[\backslash$table$[[$New$],[$values$]],,,,,,,,,]]$