Future work should move beyond the restrictive assumption by exploring new methods that can, e.g., 1) increase the isomorphism between monolingual spaces (Zhang et al., 2019) by distinguishing between language-specific and language-pairinvariant subspaces; 2) learn effective non-linear or multiple local projections between monolingual spaces similar to the preliminary work of Nakashole (2018); 3) similar to Vulić and Korhonen (2016) and Lubin et al.
even in these settings when the comparison to the weakly supervised FULL-SUPER+SYM is completely fair (i.e.,  (c) Swedish→ L2 Figure 3: A comparison of BLI scores on "easy" (i.e., similar) language pairs between the fully UNSUPERVISED model and a weakly supervised model (seed dictionary size |D 0 | = 200 or |D 0 | = 500) which relies on the self-learning procedure with the symmetry constraint (FULL+SL+SYM).