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I have a simple question.

Why only convolution is used in CNN? There are a lot of possible rules for combining a filter and an image. Why is pixel-wise convolution the standard? For example, dropout or max-pooling are another typical layers. I want to do some research regarding special convolutions, for example, rotated convolutions or adding some "deformation parameters" to convolutions instead of data augmentation. This make sense? Is there literature regarding this?

Thanks a lot.

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