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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?

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    $\begingroup$ 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. $\endgroup$
    – Dave
    Commented Jul 23, 2021 at 17:00
  • $\begingroup$ I figured out a pretty clever way to use existing CNN filters. I just have to wrangle my data. $\endgroup$
    – xiaodai
    Commented Jul 24, 2021 at 14:20

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I think group CNN is close. It has rotation and symmetry

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