Consider a convolutional layer with one filter W of size $22$ applied to a $33$ input matrix

X:

X $=$

$$

$$

$510$

$243$

$024$

$$

$$

and filter:

W $=$

$$

$21$

$11$

$$

The output of the convolution is passed through a sigmoid activation function, resulting in

the output matrix Y $.$ Assume the gradient of the loss with respect to Y is:

$$L

$$Y

$=$

$$

$10$

$12$

$$

$($a$)$ Perform the forward pass and compute Y using a valid convolution. $[5]$

$($b$)$ Using backpropagation, compute the gradients of the loss with respect to the filter W

and the input X$.[15$Consider a convolutional layer with one filter W of size $22$ applied to a $33$ input matrix

X:

X $=$

$$

$$

$510$

$243$

$024$

$$

$$

and filter:

W $=$

$$

$21$

$11$

$$

The output of the convolution is passed through a sigmoid activation function, resulting in

the output matrix Y $.$ Assume the gradient of the loss with respect to Y is:

$$L

$$Y

$=$

$$

$10$

$12$

$$

$($a$)$ Perform the forward pass and compute Y using a valid convolution. $[5]$

$($b$)$ Using backpropagation, compute the gradients of the loss with respect to the filter W

and the input X$.[15$