How to modify implicit-sinkhorn for point cloud registration?

[EryiXie]

Hi, thank you for this brilliant work.
I am currently trying to use your method for point cloud registration, similar to the way mentioned in your work (adapted to networks like RPMNet). However there is one thing that confuses me a little bit, that is:
In point cloud registration, the source and target point cloud contains sometimes points that are not able to be matched, which in the case of RPMNet are taken care of by adding a dummy column and a dummy row. And the Sinkhorn normalization skips the dummy column and row, so that potentially multiple unmatched points can map themself to the dummy space. (If I understand it correctly)
https://github.com/yewzijian/RPMNet/blob/b1c9ee0290a4f1f6515b22d496f8e1768c661c91/src/models/rpmnet.py#L63-L91

I am wondering how should I modify your implicit-sinkhorn to adapt to dummy padding, especially for the gradient computation in the "backward" function.