Imagine, based on some criteria, we have three vectors (vec1, vec2, vec3) for the word king, and we call these three vectors as local vectors for the king. Which way is sufficient to generate a global (single, or unique) vector for the word king from these three local vectors (vec1, vec2, vec3) that can be used in downstream task. There are three possible options:
Concat(vec1, vec2, vec3)
average(vec1, vec2, vec3)
sum(vec1, vec2, vec3)
are they sufficient? WHY? any reference?
You haven't stated how those 3 vectors were created, and that matters. If the method they were created meant they all shared, in some important sense, the "same coordinate system", then it might be appropriate to add or average them.
But, if they're derived in unrelated ways, and thus their individual coordinates aren't part of the same self-consistent/comparable system, then concatenation makes more sense, preserving their individual information – forwarding all that info to downstream steps, without any assumptions about what's more important, nor allowing any 'cancelling-out' of position info from the random/arbitrary interaction of unrelated coordinate-systems.
Also, if vec1, vec2, and vec3 are of different-dimensionalities, concatenation always works, but sum/average won't.
(I could possibly give more reasoning if you added more concrete information about the different sources of vec1, vec2, vec3.)
