Question: Consider we have a cross - entropy loss function for binary classification: L = [ ln ( ) + ( 1 ) ln ( 1

Consider we have a cross

-

entropy loss function for binary classification:

= [

() + (1)

(1)],

where

is the probability out from the output layer activation function. We've built a computation graph of the network as shown below. The blue letters below are intermediate variable labels to help you understand the connection between the network architecture graph above and the computation graph.

When

= 1,

what is the gradient of the loss function w

.

.

. 11 ?

Write your answer to three decimal places.

Note: Please use the computation graph method. One can calculate the gradient directly using chain rules, but if the computation graph is not used at all, it will not score properly. Try to fill the red boxes above. This question does not need coding and the answer can be easily obtained analytically.

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