Confused about the shape of relative position encoding about axial-deeplab HOT 4 OPEN

Does (C, W) mean global position encoding?
Note that our positional encoding is relative and shared across the other axis. For example, in w-axis attention, each pixel corresponds to W other pixels and W relative positions, so there are (W, W) relative positional encodings in total.

from axial-deeplab.

Does (C, W) mean global position encoding?
Note that our positional encoding is relative and shared across the other axis. For example, in w-axis attention, each pixel corresponds to W other pixels and W relative positions, so there are (W, W) relative positional encodings in total.

Thanks for your helpful reply. I did mean global position encoding by (C, W).
I am also confused about the following line:

from axial-deeplab.

They are randomly initialized, but for different position they have different relative positional encoding while the same relative distance ones should share the weights.

from axial-deeplab.

Note that our positional encoding is relative and shared across the other axis. For example, in w-axis attention, each pixel corresponds to W other pixels and W relative positions, so there are (W, W) relative positional encodings in total.

If the span-size K is smaller than the width W, then do we have the size of (C,W,K) for the relative position encoding matrix?
So that it's einsumed with the query like Q (H,(W,C)) * r^q ((W,C),K) -> A (H,W,K)? (A: attention matrix)

from axial-deeplab.