[Eisenstein Chapter 3 Problem 8] The ReLU activation function can lead to "dead neurons", which can never be activated on any input. Consider a feedforward neural network with a single hidden layer and ReLU nonlinearity, assuming a binary input vector, xf{0,1}D and scalar output y : zi=ReLU(i(xz)x+bi)y=(zy)z Assume the above function is optimized to minimze a loss function (e.g., mean squared error) using stochastic gradient descent. 1. (2 pts) Under what condition is node zi "dead"? Your answer should be expressed in terms of the parameters i(xz) and bi 2. (2 pts) Suppose that the gradient of the loss on a given instance is yl=1. Derive gradients bil and j,i(xz)l for such an instance. 3. (2 pts) Using your answers to the previous two parts, explain why a "dead" neuron can never be brought back to life during gradient-based learning