Question 5 Gradient Computation Our Goal Is To Use A Computation Graph To Compute The Gradient Of The Following Functio 1 (79.16 KiB) Viewed 14 times
Question 5. Gradient Computation Our goal is to use a computation graph to compute the gradient of the following function: f(x, y, z) = In (070) 2 x + y and evaluate it at x = 1, y = 2, and z = = 9. (a) (3 pts) We define the variables q, r, and f below to represent the intermediate computa- tions. For each of these variables, calculate its partial derivatives with respect to its inputs. We provide the solution for the q variable to illustrate the process: q= x + y да ax aq ду = 1 p=z/q = f = ln(r)
(b) (5 pts) Now consider the computation graph shown below. Perform forward propa- gation, calculate the intermediate values for q, r, and f and add them to the graph. Then perform back propagation, using the results from part (a) and the chain rule to propagate the gradients of f backwards and fill in the blanks underlined in blue. Z= 9 Z r = x = 1 х In 1 q= + y = 2 у
(c) (2 pts) Supply the final answers below: af дх af ਰy = df dz =
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