$(20$pts$)$ Multilayer Neural Networks.

$($a$)$ Draw a $d-n_H-c$ fully connected three$-$layer neural network and give the

proper notations.

$($b$)$ Suppose the network is to be trained using the following criterion

function.

$J=\frac{1}{4}{\displaystyle \underset{k=1}{\overset{c}{}}}(t_k-z_k{)}^4$

Derive the learning rule ${}_{kj}$ for the hidden$-$to$-$output weight.