In the paper they try with the rows ordered at random and with rows ordered using some similarity criteria. They get slightly better results with the ordered version.

I'm still not convinced that it is a good idea to use the "convolutional" part that in some sense compare one rows with their neighbor rows. They get some results that are slightly better than other methods, but the improvement is not very clear. (Perhaps the CNN is just calculating an average of the neighbor rows?)

EDIT: Remember that you can edit your comment.