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Deep Learning · Quiz 2 · 16 Mar 2025 · January 2025 term

Question 10: Given an input array X and a kernel/filter K as follows:…

Question 10

+3 marksNumerical answer

Given an input array XX and a kernel/filter KK as follows:

X=[10−211201−1−1100101]X = \begin{bmatrix} 1 & 0 & -2 & 1 \\ 1 & 2 & 0 & 1 \\ -1 & -1 & 1 & 0 \\ 0 & 1 & 0 & 1 \end{bmatrix}

K=[101001101]K = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 0 & 1 \end{bmatrix}

Based on the above data, answer the given subquestions.

Pass BB through the sigmoid (logistic) function with weight equal to 1 and no bias to get the final output y^\hat{y}.

LL is some loss function that depends on y^\hat{y}. Given that ∂L∂y^=−1\frac{\partial L}{\partial \hat{y}} = -1, determine the value of ∂L∂K00\frac{\partial L}{\partial K_{00}} where K00K_{00} is the element of KK at index (0,0)(0,0). Note that we use zero-indexing here.

Enter your answer correct up to 3 digits after the decimal.

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Correct answer: -0.126 (accepted within ±0.01)

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Question 10 of 23 in the IIT Madras BS Deep Learning (Deep Learning) Quiz 2 paper sat on 16 Mar 2025, in the January 2025 term (IIT M DEGREE AN EXAM QDB2 16 Mar 2025). It carries 3 marks.

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