Question 4: Given the input matrix X and kernel K: X = \begin{bmatrix…

Given the input matrix $X$ and kernel $K$:

$X = \begin{bmatrix} 2 & 1 & 0 & 1 \\ 0 & 1 & -1 & 0 \\ 3 & 2 & 1 & -1 \\ 1 & 0 & -2 & 2 \end{bmatrix}, \quad K = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$

• Perform convolution of $K$ over $X$ with stride $= 1$ and no padding to get matrix $A$.
• Apply average pooling on all of $A$ to produce scalar $B$.
• Apply the ReLU activation on $B$ to obtain final output $\hat{y}$.

If $\frac{\partial L}{\partial \hat{y}} = 2$, compute $\frac{\partial L}{\partial K_{11}}$, where $K_{11}$ is the centre element of the kernel. Submit the final answer correct to two decimal places.