Questions for the machine learning homework

Question 5: Assuming the following CONV layer in a NN with a 3x3x3 filter and 3x4x4 input fmaps. 12 6 1 4 0.1 -0.5 0,2 12 3 3 3 Channel 3 Channel 3 0.2 -0.5.0.2 2 3 3 5 0.1 -0.2 0.3 4 3 1 2 0.2 -0.6 0.1 14 6 4 Channel 2 0.5 0.2 0.1 3 1 514 Channel 2 0.2 -0.4 0.1 2 3 -13 6 3 2 2 0.1 0.4 0.2 Channel 1 0.2 -0.1 0.1 12 3 1 5 0.3 -0.2 0.1 4 3 2 1 Channel 1 1 2 4 3 1 2 3 1 2 a) Demonstrate the corresponding CONV in the form of Matrix Multiplication (assuming a stride of 1) and calculate the output feature map. Please show the flattened filter, and corresponding Toeplitz Matrix for the input fmap. You can assume RELU as an activation function. [20 points) Question 5: Assuming the following CONV layer in a NN with a 3x3x3 filter and 3x4x4 input fmaps. 12 6 1 4 0.1 -0.5 0,2 12 3 3 3 Channel 3 Channel 3 0.2 -0.5.0.2 2 3 3 5 0.1 -0.2 0.3 4 3 1 2 0.2 -0.6 0.1 14 6 4 Channel 2 0.5 0.2 0.1 3 1 514 Channel 2 0.2 -0.4 0.1 2 3 -13 6 3 2 2 0.1 0.4 0.2 Channel 1 0.2 -0.1 0.1 12 3 1 5 0.3 -0.2 0.1 4 3 2 1 Channel 1 1 2 4 3 1 2 3 1 2 a) Demonstrate the corresponding CONV in the form of Matrix Multiplication (assuming a stride of 1) and calculate the output feature map. Please show the flattened filter, and corresponding Toeplitz Matrix for the input fmap. You can assume RELU as an activation function. [20 points)