image is (H, W) and kernel is (K, K). Convolve them with stride 1 and no padding, and return the 2-D result of shape (H-K+1, W-K+1).

F.conv2d works on 4-D batched input, so the single image and single kernel have to gain batch and channel dimensions on the way in and lose them again on the way out.

Note that F.conv2d computes a cross-correlation rather than a true convolution -- it does not flip the kernel -- which is what every deep learning framework means by "convolution".

Input

image =
tensor([[ 0.,  1.,  2.,  3.],
        [ 4.,  5.,  6.,  7.],
        [ 8.,  9., 10., 11.],
        [12., 13., 14., 15.]])
kernel =
tensor([[ 1.,  0.],
        [ 0., -1.]])

Output

tensor([[-5., -5., -5.],
        [-5., -5., -5.],
        [-5., -5., -5.]])