Incorporate L$2-$norm regularization into the loss function:

L$=$

$1$

$2(($y$1$t$1)2+($y$2$t$2)2)+$ w$2$

ij$.$

Assume a neural network with one hidden layer, two hidden nodes h$1,$h$2,$ and two

output nodes y$1,$y$2.$ The activation function is sigmoid. Derive the modified weight

update rule for the weights connecting the input layer to the hidden layer using gradient

descent. Assume $>0$ is the regularization parameter.