  The brittleness of finetuned language model performance on
out-of-distribution (OOD) test samples in unseen domains has been well-studied
for English, yet is unexplored for multi-lingual models. Therefore, we study
generalization to OOD test data specifically in zero-shot cross-lingual
transfer settings, analyzing performance impacts of both language and domain
shifts between train and test data. We further assess the effectiveness of
counterfactually augmented data (CAD) in improving OOD generalization for the
cross-lingual setting, since CAD has been shown to benefit in a monolingual
English setting. Finally, we propose two new approaches for OOD generalization
that avoid the costly annotation process associated with CAD, by exploiting the
power of recent large language models (LLMs). We experiment with 3 multilingual
models, LaBSE, mBERT, and XLM-R trained on English IMDb movie reviews, and
evaluate on OOD test sets in 13 languages: Amazon product reviews, Tweets, and
Restaurant reviews. Results echo the OOD performance decline observed in the
monolingual English setting. Further, (i) counterfactuals from the original
high-resource language do improve OOD generalization in the low-resource
language, and (ii) our newly proposed cost-effective approaches reach similar
or up to +3.1% better accuracy than CAD for Amazon and Restaurant reviews.
