1 Our contributions are: (a) In §2, we show that the monolingual word embeddings used in <cite>Conneau et al. (2018)</cite> are not approximately isomorphic, using the VF2 algorithm (Cordella et al., 2001 ) and we therefore introduce a metric for quantifying the similarity of word embeddings, based on Laplacian eigenvalues. (b) In §3, we identify circumstances under which the unsupervised <cite>bilingual dictionary induction (BDI)</cite> algorithm proposed in <cite>Conneau et al. (2018)</cite> does not lead to good performance.