Recent research has attempted to induce unsupervised bilingual lexicons by aligning monolingual word vector spaces (Zhang et al., 2017a;<cite> Conneau et al., 2018</cite>; Aldarmaki et al., 2018; Artetxe et al., 2018a; Alvarez-Melis and Jaakkola, 2018; Mukherjee et al., 2018) . Given a pair of languages, their word alignment is inherently a bi-directional problem (e.g. EnglishItalian vs Italian-English). However, most existing research considers mapping from one language to another without making use of symmetry.