Consider the following neural network with weights w for the edges and offset b for the...

 

Transcribed Image Text:

Consider the following neural network with weights w for the edges and offset b for the nodes: 1 W = 0.4 1,3 W = 0.6 1,4 b= -0.3 3,5 Y3 W = 2.0 b = 0.0 Y_ b = 0.4 5 W23=-0.7 W2=-0.5 Y W4.5 1.0 4 Assume that the outputs of nodes Y3, Y4, and Y are based on rectified linear functions: Y3 = max(0,W,3 b3 Y5 = max (0, 2,40% a + b) or Y = max (0. + D). For the following problems, consider input values X = 1 and X2 = 1: (a) What is the value of Y3 for this input? (6 points) (b) What is the value of Y4 for this input? (6 points) (c) What is the value of Y5 for this input? (6 points) Assuming the desired output is 0.6 and the squared loss function, loss (Y5, 0.6) = (Y5 -0.6), is used: (d) What is the gradient of this loss for this example with respect to b5? (10 points) (e) What is the gradient of this loss for this example with respect to w,3? (10 points) (f) What is the gradient of this loss for this example with respect to w2,4? (10 points) Consider the following neural network with weights w for the edges and offset b for the nodes: 1 W = 0.4 1,3 W = 0.6 1,4 b= -0.3 3,5 Y3 W = 2.0 b = 0.0 Y_ b = 0.4 5 W23=-0.7 W2=-0.5 Y W4.5 1.0 4 Assume that the outputs of nodes Y3, Y4, and Y are based on rectified linear functions: Y3 = max(0,W,3 b3 Y5 = max (0, 2,40% a + b) or Y = max (0. + D). For the following problems, consider input values X = 1 and X2 = 1: (a) What is the value of Y3 for this input? (6 points) (b) What is the value of Y4 for this input? (6 points) (c) What is the value of Y5 for this input? (6 points) Assuming the desired output is 0.6 and the squared loss function, loss (Y5, 0.6) = (Y5 -0.6), is used: (d) What is the gradient of this loss for this example with respect to b5? (10 points) (e) What is the gradient of this loss for this example with respect to w,3? (10 points) (f) What is the gradient of this loss for this example with respect to w2,4? (10 points)