Asking help with detailed steps: The small neural net in the figure below uses ReLU as the nonlinearity at the output of each neuron. The values specified in the hollow circles are biases, and the values along the edges are gains.

$($a$)$ Are all the layers in the network above fully connected?

$($b$)$ What is the output $y$ from the net above when the input is as follows?

$x_1=0$ and $x_2=3$

$($c$)$ What is the gradient $g$ of the output $y$ of the network above with respect to the weight vector

$w=[w_1,w_2,w_3,w_4,w_5,w_6,w_7,w_8,w_9{]}^T$when the input has the values given in the previous problem? Just give the result if you are confident of your answer.

$($d$)$ With image data convolutional neural networks are much more popular than fully connected neural networks. Why is this?

$($e$)$ Especially deep convolutional neural networks have proven to be effective. What function do the earlier layers $($a$.$k$.$a$.$ the base network$)$ of a deep convolutional neural network serve and why are they often re$-$used from pre$-$existing networks such as VGG$16.$

$($f$)$ SSD object detector evaluates only a small set $($e$.$g$.4)$ of default boxes of different aspect ratios at each location. How can it detect large and small objects if the boxes are of fixed size?