# Does a rotational convolutional filter exist in neural networks?

Traditionally, a convolutional filter is one where you take a matrix of numbers, multiply it with a subset of the data, and then sum it up. Then you move the filter left to right and top to bottom in a sweeping fashion to generate a smaller (or equal) grid.

But I wonder if there are filters that work in rotations meaning, consider a 2x2 filter containing these parameters.

a, b
d, c


And consider a 4x4 input data. Normally, in the CNN world, after applying the filter to the input, I would get a 3x3 output, which is the result of the sweeping I described earlier.

Now say, instead of sweeping across, I would like to rotate the weight before I apply, and I do not do sweeping, I rotate the matrix for each of the 4 corners in the 4x4 input.

Meaning, I would apply to the top-left these values

a, b
d, c


then to bottom-left these values which is the above rotated

b, c
a, d


then to the bottom-right

c, d
b, a


then to the top-right

d, a
c, b


so I end with another 2x2 matrix after applying the above filter to the 4x4 input.

Does such filter have a name already?

• You might need to do your own coding of the software implementation, but nothing keeps this from being a viable neural network that shares CNN’s idea of weight sharing and dropping parameters. Perhaps start by drawing out your filter layer like I show here.
– Dave
Jul 23 at 17:00
• I figured out a pretty clever way to use existing CNN filters. I just have to wrangle my data. Jul 24 at 14:20