In general (except when the semantic relations between A and B are symmetrical), we have the following inequality: sim r (A : B, C : D) = sim r (B : A, C : D) Therefore we do not want A:B and B:A to be represented by identical row vectors, although it would ensure that equation 8is satisfied.
in step 12 of LRA, the relational similarity between A:B and C:D is the average of the cosines, among the (num filter + 1) 2 cosines from step 11, that are greater than or equal to the cosine of the original pairs, A:B and C:D. the average includes only those alternates that are "better" than the originals.