Compute the forward pass of the following part of a convolutional net:
If I is the following image patch:
1 3 2 4 6 4
4 8 3 1 0 2
2 1 4 3 9 1
4 7 2 3 9 2
and W is the following 3-by-3 filter matrix:
-1 0 1
-1 0 1
-1 0 1
Compute J, K, and O. You are not doing any zero padding while doing the convolution. Assume stride size 1 for the convolution. Assume a 2-by-2 max pooling with stride 2. Write J, K, and O below.
Now assume that the ideal output IO=[7,10]. Also assume the loss as 0.5 times the square of the Euclidean distance between IO and O. Compute back-propagation for O, K, J, and W.