We’ll use a simple example of training a neural network to function as an “Exclusive OR” (“XOR”). The truth table of an XOR is given below.

i1	i2	Output
0	0	0
0	1	1
1	0	1
1	1	0

Let’s use a simple ANN to represent the XOR function. The ANN has three layers:

Input layer with two inputs neurons

One hidden layer with three neurons

Output layer with a single neuron

The initial weights are {0.8, 0.4, 0.3} from input neuron 1 to hidden neurons 1, 2, and 3. {0.2, 0.9, 0.5} from input neuron 2 to hidden neurons 1, 2, and 3. {0.3, 0.5, 0.9} from hidden neurons 1, 2, and 3 to the output neuron

To train our neural network, we need to find the weights that minimize prediction error. To answer this question, start with forward propagation, and then back propagation. Use the sigmoid function S(x) as an activation function. Show your steps for two rounds of output predictions and calculate the error in each case.

Marking Criteria

5 Marks for executing forward propagation correctly

5 Marks for executing back propagation correctly

5 Marks for adjusting the weights correctly

5 Marks for using the activation function correctly