About

We optimize operation CoordConv from the paper https://arxiv.org/pdf/1807.03247.pdf. For this purpose we use simple math:

• convolution for input with c1 + c2 channels can be expressed as the sum of convolutions for input with c1 and c2 channels separately.

• for channel matrix which has equal rows (0, 1, .. n) or equal columns (0, 1, .. n)^T (these matrices are added in the CoordConv defining the coordinates) convolution operation equals to

• matrix with columns alpha * (0, 1, .., n)^T + alpha0

• matrix with rows beta * (0, 1, .., n) + beta0 correspondingly. Bias can be ignored due to bias in the convolution layer which comes before this operation.

In the coordconv/modules a layer CoordXY is provided which adds necessary result to the standard convolution to obtain CoordConv. With comparison to the original paper, optimized version of operation is simpler, more efficient, and has less number of parameters.

Dependencies

• python 3.6

• pytorch 0.4