1: repeat 2: Select at random lang j ∈ L 5: loss += Lr(ti, tj) refinement loss 9: Update all M parameters to minimize loss 10: orthogonalize(M) see §3.3 11: until convergence When learning MWEs, however, it is desirable to go beyond aligning each language with the target space individually, and instead utilize the relations between all languages as we did in MAT.
we in this section propose a generalization of the existing refinement methods to incorporate a multilingual objective.