  The vision transformer (ViT) has achieved state-of-the-art results in various
vision tasks. It utilizes a learnable position embedding (PE) mechanism to
encode the location of each image patch. However, it is presently unclear if
this learnable PE is really necessary and what its benefits are. This paper
explores two alternative ways of encoding the location of individual patches
that exploit prior knowledge about their spatial arrangement. One is called the
sequence relationship embedding (SRE), and the other is called the circle
relationship embedding (CRE). Among them, the SRE considers all patches to be
in order, and adjacent patches have the same interval distance. The CRE
considers the central patch as the center of the circle and measures the
distance of the remaining patches from the center based on the four
neighborhoods principle. Multiple concentric circles with different radii
combine different patches. Finally, we implemented these two relations on three
classic ViTs and tested them on four popular datasets. Experiments show that
SRE and CRE can replace PE to reduce the random learnable parameters while
achieving the same performance. Combining SRE or CRE with PE gets better
performance than only using PE.
