I am trying to perform a convolution over the Height and Width dimensions of a batch of input tensor cubes using kernels (which I have made myself) for every depth slice, without any movement of the kernel in the 3rd dimension (in this case the depth).
So say I had a batch of 3 tensor cubes:
import torch 

batch = torch.rand((3,4,4,4))

I would like to convolve each cube with some 2D kernels (1 for each batch member):
weights = torch.rand((3,4,4))

but convolve only in the Height and Width dimensions somehow. I suspect using some variant of the following code block:
kernels = torch.nn.Parameter(weights,requires_grad=False)

output = torch.nn.functional.conv3d(batch,weights,padding=1)

Is there a preferred/optimal way to do this? The only way I can see is to perform a 3D convolution but somehow set the stride to be [0,1,1] which I don’t think PyTorch will allow me to do.
Perhaps this is in fact a very simple problem and one can do this with 2D convolutions and I would love to know how, but the key points here are:


The output should have the same shape as the input (obviously padding helps but you can’t just run a 2D convolution over each batch member or the depth axis will come out as 1?)


Each batch member should be convolved with its own kernel.


Many thanks in advance!

Edit:
I’ve been playing around and think I may have this working using the following code:
import torch 
from functions import makebeam

batch = torch.rand((8,1,30,30,30))

weights = torch.rand((1,1,1,3,3))

conv = torch.nn.Conv3d(1,1,4,padding=[0,1,1],bias=False)

with torch.no_grad():
    conv.weight = torch.nn.Parameter(weights,requires_grad=False)

output = conv(batch)
print(output.shape)

Although I am still confused as to how passing a 2D kernel to a 3D convolution over a 3D tensor performs a convolution over each depth slice