  Massively multilingual language models such as multilingual BERT offer
state-of-the-art cross-lingual transfer performance on a range of NLP tasks.
However, due to limited capacity and large differences in pretraining data
sizes, there is a profound performance gap between resource-rich and
resource-poor target languages. The ultimate challenge is dealing with
under-resourced languages not covered at all by the models and written in
scripts unseen during pretraining. In this work, we propose a series of novel
data-efficient methods that enable quick and effective adaptation of pretrained
multilingual models to such low-resource languages and unseen scripts. Relying
on matrix factorization, our methods capitalize on the existing latent
knowledge about multiple languages already available in the pretrained model's
embedding matrix. Furthermore, we show that learning of the new dedicated
embedding matrix in the target language can be improved by leveraging a small
number of vocabulary items (i.e., the so-called lexically overlapping tokens)
shared between mBERT's and target language vocabulary. Our adaptation
techniques offer substantial performance gains for languages with unseen
scripts. We also demonstrate that they can yield improvements for low-resource
languages written in scripts covered by the pretrained model.
