2) a) Design three single-layer perceptrons, each having a single neuron, which implement the Boolean functions AND, OR and NAND, respectively. Assume that there are two binary inputs to each neuron, xI and x2, and no bias. Which activation function should be used in each neuron? Evaluate the three perceptrons for all four possible combinations of x 1 (having a value 0 or ) and x2 (having a value 0 or 1). Combine the above neurons in two layers such that the resulting network implements the XOR function. Provide a geometric interpretation of the network and explain which region of the 2D input space is classified as and which region is classified as 0. b) Regularization is one way to avoid overfitting while training a neural network. Explain how and why it works. You should also explain how the error function of the neural network should be modified. c) Assume that you test classifier A on a dataset of 100 examples with the classification rate of 80%. Suppose that more examples (=10000) become available and another classifier B is tested on this new dataset achieving a classification rate of 77%. Compute the 99% confidence intervals for both classifiers and discuss what these intervals mean and which classifier you would trust more for an important application. Provide the equation for d) calculating confidence interval. The constant following table: can be computed from the N%:150% 68% 80% 90% 95% 98% 99% 10.67 1.00 1.28 1.64 1.96 2.33 2.58 2) a) Design three single-layer perceptrons, each having a single neuron, which implement the Boolean functions AND, OR and NAND, respectively. Assume that there are two binary inputs to each neuron, xI and x2, and no bias. Which activation function should be used in each neuron? Evaluate the three perceptrons for all four possible combinations of x 1 (having a value 0 or ) and x2 (having a value 0 or 1). Combine the above neurons in two layers such that the resulting network implements the XOR function. Provide a geometric interpretation of the network and explain which region of the 2D input space is classified as and which region is classified as 0. b) Regularization is one way to avoid overfitting while training a neural network. Explain how and why it works. You should also explain how the error function of the neural network should be modified. c) Assume that you test classifier A on a dataset of 100 examples with the classification rate of 80%. Suppose that more examples (=10000) become available and another classifier B is tested on this new dataset achieving a classification rate of 77%. Compute the 99% confidence intervals for both classifiers and discuss what these intervals mean and which classifier you would trust more for an important application. Provide the equation for d) calculating confidence interval. The constant following table: can be computed from the N%:150% 68% 80% 90% 95% 98% 99% 10.67 1.00 1.28 1.64 1.96 2.33 2.58