Feed-Forward Neural Networks 1. Consider a perceptron (a single unit with a sign function as activation function) with 3 binary inputs, Xi, and one bias input, b, that is constantly 1, and the following dataset (corresponding to a 3 input OR): X1 X2 X3 b y 1 1 1 1 1 1 1 1 1 -1 1 1 -1 1 1 1 -1 -1 1 -1 1 1 -1 1 -1 1 -1 1 1 -1 -1 -1 1 ------- 1 1 1 -1 a) Starting with weights of 0 for all connections, show 10 iterations of the Perceptron Learning rule. Each iteration here corresponds to randomly picking a data point and updating the weights accord- ingly. For each iteration show the sample picked, the update values (Aw resultin the learning rule) and the updated weights. b) Implement the Perceptron and the perceptron learning rule for 3-dimensional binary inputs (plus a constant bias input) c) Train your perceptron implementation from part b) using the 3-dimensional OR dataset and with the following dataset representing a 3-input XOR: X1 X2 X3 b Y 1 1 -1 1 1 1 1 1 -1 1 1 1 1 1 1 - 1 1 -1 -1 1 -1 1 1 1 1 1 -1 1-1 1 1 -1 -1 1 1 1 -1 -1 -1 1 -1 In both cases show how the perceptron converges by showing how the number of data items that are incorrectly classified changes over time. Discuss the results and the differences between the performance on the two datasets. Feed-Forward Neural Networks 1. Consider a perceptron (a single unit with a sign function as activation function) with 3 binary inputs, Xi, and one bias input, b, that is constantly 1, and the following dataset (corresponding to a 3 input OR): X1 X2 X3 b y 1 1 1 1 1 1 1 1 1 -1 1 1 -1 1 1 1 -1 -1 1 -1 1 1 -1 1 -1 1 -1 1 1 -1 -1 -1 1 ------- 1 1 1 -1 a) Starting with weights of 0 for all connections, show 10 iterations of the Perceptron Learning rule. Each iteration here corresponds to randomly picking a data point and updating the weights accord- ingly. For each iteration show the sample picked, the update values (Aw resultin the learning rule) and the updated weights. b) Implement the Perceptron and the perceptron learning rule for 3-dimensional binary inputs (plus a constant bias input) c) Train your perceptron implementation from part b) using the 3-dimensional OR dataset and with the following dataset representing a 3-input XOR: X1 X2 X3 b Y 1 1 -1 1 1 1 1 1 -1 1 1 1 1 1 1 - 1 1 -1 -1 1 -1 1 1 1 1 1 -1 1-1 1 1 -1 -1 1 1 1 -1 -1 -1 1 -1 In both cases show how the perceptron converges by showing how the number of data items that are incorrectly classified changes over time. Discuss the results and the differences between the performance on the two datasets