If I'm understanding correctly (I haven't read it in depth yet): Points are processed as local clusters. Each cluster of points is ordered according to a trans

If I'm understanding correctly (I haven't read it in depth yet): Points are processed as local clusters. Each cluster of points is ordered according to a transformation matrix X. This produces a "canonical" ordering so the processing of points in these local clusters do not need to be invariant to the order since the order now has consistency and meaning. It's kind of like placing each point into a regular grid like an image before running the convolution. The trick is which points to put in which grid cell which is determined by the transformation matrix X. This takes advantage of locality which PointNet does not, if I recall correctly. By acting locally and stacking many layers of these you can produce a hierarchy of more and more abstract clusters of points, each with an inherent relationship to nearby clusters of points. In addition, the transformation matrix also appears to act as an attention over the points in the cluster.