Answer Happy

eta=0.05
2 Problem 2 (25 points) Your highway management department is planning to build a multilayer perceptron model for traffic moni- toring. You are asked to test and demonstrate the functionality of the model using a simple test sample. input layer 2 W13 W21 0.5 W12 W22 W23 hidden layer VIL 021 V31 (a) Single output output layer input layer O W13 W21 O W12 Figure 1: Two MLP models W22 W23 hidden layer V21 122 031 V32 (b) Two outputs output layer (1) The architecture of the model is demonstrated in Figure 1 (a). The feature vector of the test sample is (2,0.5), and the label is 1. Ignore bias terms and the activation function. The weights have already been initialized in the first row of the attached spreadsheet (see Problem-2.xlsx). Train the model until reaching zero loss using Excel or other tools that allows you to show all interme- diate calculations (but you are not expected to directly use off-the-shelf libraries like PyTorch for this problem). Use the stochastic gradient descent (SGD) optimizer with learning rate n = 0.05, and the loss is calculated by (y, y) = (y - y)². (15 points) (2) The department would like to investigate another variable at the same time, hence an additional output dimension in the model (see Figure 1 (b)). The square loss can be extended to ((y, ý) = ||y-ý||2- Show step by step how you use the chain rule to develop a formula of the gradient with respect to w12, and discuss the relationship between this MLP model and linear regression. (10 points)