a$)$ Suppose you design a multilayer perceptron with a single hidden layer that has a hard threshold activation function. The output layer uses the softmax activation function. What will go wrong if you try to train this network using gradient descent?

b$)$ Consider the following two multilayer perceptrons, where all of the layers use linear activation functions.

Which one is more advantageous in terms of the following?

i$)$ Expressive power:

ii$)$ The number of operations for backpropagation:

iii$)$ Overfitting:

Please first write Network $1$ or Network $2,$ then explain your argument.