Abstract: Global co-occurrence information is the primary source of structural information on multilingual corpora, and we find that analogical/parallel compound words across languages have similar co-occurrence counts/frequencies (normalized) giving weak but stable self-supervision for cross-lingual transfer. Following the observation, we aim at associating contextualized representations with relevant (contextualized) representations across languages with the help of co-occurrence counts. The result is MLM-GC (MLM with Global Co-occurrence) pre-training that the model learns local bidirectional information from MLM and global co-occurrence information from a log-bilinear regression. Experiments show that MLM-GC pre-training substantially outperforms MLM pre-training for 4 downstream cross-lingual tasks and 1 additional monolingual task, showing the advantages of forming isomorphic spaces across languages.