A similar property holds for the other direction of the loop (from B to A and then from A back to B).
we use the Sinkhorn distance (Cuturi, 2013) to capture the distributional similarity between two set of embeddings after transformation, which we found empirically superior to the KL-divergence (Zhang et al., 2017a) and distance to nearest neighbor (Artetxe et al., 2017;Conneau et al., 2017) with regards to the quality of learned transformation as well as the robustness under different training conditions.