1. Consider a three layer neural network with one output unit, 10 hidden units at each hidden layer, and a five dimensional augmented feature vector as inputs.

(a) Draw the network.

(b) Write down the general expression on the derivative of the error function with respect to a weight using back error propagation (i.e., gradient decent).

(c) Verify the general expression by calculating the derivative of the error function with respect to a weight that connects the 5^th hidden unit at the first hidden layer with the 6 hidden unit at the second hidden layer.

(d) Write a pseudo algorithm that computes the increment of a weight that connects the 4^th input component with the 3^rd hidden unit at the first hidden layer.