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(25 points) This question aims to provide an exercise on the Backpropagation algorithm. A neural network with one hidden layer and sigmoid activation function is shown below. Assume the learning rate eta is set to 0.5, and at the end of some iteration of Backpropagation, the network weights are as follows: (w1, w2, w3, w4, w5, w6, b1, b2, b3)=(0.15, 0.20, 0.25, 0.30, 0.40, 0.45, 0.35, 0.35, 0.60). The next input instance is (x1, x2) = (0.05, 0.1) with target output labeled 0.01 (the probability it belongs to the target class). Calculate the updated values of w5 and w1 based on this input instance and the above set of weights, according to the update rule of Backpropagation. (Note: your solution should first show the forward pass in calculating the output and total error, next show the backward pass in calculating the weight change to w5, and then the weight change to w1. Updates to w5 and w1 are representative to other parameters in the same layer, and therefore, calculations for other parameters are omitted in this question.)

          (25 points) This question aims to provide an exercise on the Backpropagation algorithm. A neural network with one hidden layer and sigmoid activation function is shown below. Assume the learning rate eta is set to 0.5, and at the end of some iteration of Backpropagation, the network weights are as follows: (w1, w2, w3, w4, w5, w6, b1, b2, b3)=(0.15, 0.20, 0.25, 0.30, 0.40, 0.45, 0.35, 0.35, 0.60). The next input instance is (x1, x2) = (0.05, 0.1) with target output labeled 0.01 (the probability it belongs to the target class). Calculate the updated values of w5 and w1 based on this input instance and the above set of weights, according to the update rule of Backpropagation. (Note: your solution should first show the forward pass in calculating the output and total error, next show the backward pass in calculating the weight change to w5, and then the weight change to w1. Updates to w5 and w1 are representative to other parameters in the same layer, and therefore, calculations for other parameters are omitted in this question.)

(25 points) This question aims to provide an exercise on the Backpropagation algorithm. A neural network with one hidden layer and sigmoid activation function is shown below. Assume the learning rate eta is set to 0.5, and at the end of some iteration of Backpropagation, the network weights are as follows: (w1, w2, w3, w4, w5, w6, b1, b2, b3)=(0.15, 0.20, 0.25, 0.30, 0.40, 0.45, 0.35, 0.35, 0.60). The next input instance is (x1, x2) = (0.05, 0.1) with target output labeled 0.01 (the probability it belongs to the target class). Calculate the updated values of w5 and w1 based on this input instance and the above set of weights, according to the update rule of Backpropagation. (Note: your solution should first show the forward pass in calculating the output and total error, next show the backward pass in calculating the weight change to w5, and then the weight change to w1. Updates to w5 and w1 are representative to other parameters in the same layer, and therefore, calculations for other parameters are omitted in this question.)

Added by Carolina D.

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