This makes sense, if one considers that the two copies are identical then the softmax outputs would be identical and the difference is zero everywhere. However, by subtracting a scaled copy, the normalization of the difference seems to really boost the signal value(s) over the "noise", making the signal stand out compared to pre-normalization.
softmax(A) - softmax(lambda * A)
And as so happens, normalizing the output of that that with my test vectors seems to really boost the output the largest component if A and B are equal.I wonder if there's a metaphor here for our own experience and utility in "surprise".
Like if one attention head is surprised by what another learns, up-weight it. But if they both find the same, assume it's not very surprising and down-weight it.
Admittedly, "surprise" is something that has a big section of my knowledgebase[1][2][3] (both as a subjective feeling and adaptive function of our minds, one of the most complex adaptive system we know of)
[1] https://plus.maths.org/content/information-surprise
[2] https://blakeelias.name/papers/Multi-Agent-Cooperation-Intri...
[3] https://complexity.simplecast.com/episodes/81/transcript