(Answered): 2. Multi-Layer Perceptron (MLP). As you remember in class, the activation functions (S) used in Neu ...

2. Multi-Layer Perceptron (MLP). As you remember in class, the activation functions (S) used in Neural Networks can be of different kinds, such as elu, Sigmoid, and Step functions. For MLP, we worked with Sigmoid activation function for input and hidden layers in class. That is how we achieved the net gradient for one weight between the input and hidden layer 8) = z;(1 - 2)2-18 = 2(1 - 2)Wºgº and the gradient for weights between hidden and output layer 8 - (o; - y).04- (1 - 0). We used these to calculate the gradients and updates in the backpropagation and gradient descent phases in the MLP training algorithm. In this ex- ercise, we would like to explore other activation functions for a specific MLP. Consider the following MLP with 1 hidden layer, 2 input neurons and 1 output neuron: 2 be O W 2 Figure 1: Simple MLP Architecture (a) (25 pts. Suppose that, instead of the sigmoid activation function, we use incar activation function in all neurons. This way, the output of unit g in the hidden layer is 2) - eX( wa) - cx (..+bzo). where is the augmented input vector for some fixed constant scalar Similarly, the output of unity in the outpat layer is o; - cx + V. Suppose that you are given all weight parameter values (W" and were given). Re-design the MLP to compute the same function (the same output o besed on given inputs x) withou using any hidden units (no hidden layer). Calculate the weights of this network based on the old weights and the cost () (15 ptal According to your solution to the previous part, is it was possible to represent a neural network that only Bear me without a hide layer? Explain who