The network given in the figure is trained by backpropagation algorithm. The sigmoidal activation functions used in the network are parametric $(a_i\text{'}$s are the parameters and they are updated at each iteration together with the weights$).$

The activation functions are given as ${}_1(v)=\frac{1}{1+e^{-a_{1}v}},{}_2(v)=\frac{1}{1+e^{-a_{1}v}},{}_3(v)=\frac{1}{1+e^{-z_{3}v}},{}_4(v)=\frac{1}{1+e^{-a_{4}v}},{}_5(v)=\frac{1}{1+e^{-a_{3}v}}$ and ${}_6(v)=\frac{1}{1+e^{-a_{4}v}}$ with $a_l=a_2=a_3=a_4=a_5=a_6=1.$ The weights are given as $w_l=0\mathrm{.}1,w_2=0\mathrm{.}3,w_3=0\mathrm{.}4,w_4=0\mathrm{.}2,w_5=0\mathrm{.}6,w_6=0\mathrm{.}5,w_7=0\mathrm{.}9,w_8=0\mathrm{.}8,w_9=0\mathrm{.}1,w_{l0}=1\mathrm{.}2,w_{11}=0\mathrm{.}2$ and $w_{12}=1,w_{13}=0\mathrm{.}4,w_{14}=0\mathrm{.}9,w_{15}=0\mathrm{.}5,w_{16}=1\mathrm{.}5.$

Assume: and $d_2$ are desired outputs for output neurons and $$ is the learning rate$).$

$($a$)$ For one forward pass, calculate $y_l$ and $y_2.$

$($b$)$ Write down the update rule for $w_9$ and determine the updated value of $w_9$ for one iteration.

$($c$)$ Write down the update rule for $w_l$ and determine the updated value of $w_l$ for one iteration.

$($d$)$ Write down the update rule for $a_l$ and determine the updated value of $a_l$ for one iteration.