ml-recall

#automatic-differentiation

6 questions from Optimization & Calculus, Neural Network Basics, Deep Learning Frameworks

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6 questions · 6 min · score and explanations at the end

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Question 1: Short answer

mediumAI-checkedOptimization & Calculus

Forward-mode automatic differentiation evaluates $f(x_1, x_2) = \ln x_1 + x_1 x_2$ at $(x_1, x_2) = (e^2, \pi)$ through the trace $v_1 = \ln x_1$ , $v_2 = x_1 x_2$ , $f = v_1 + v_2$ , carrying a tangent $\dot v$ along with every value. With the seeds $\dot x_1 = 1$ and $\dot x_2 = 0$ , what tangent $\dot f$ comes out? Round to 3 decimals.

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