  Recent multilingual pre-trained language models have achieved remarkable
zero-shot performance, where the model is only finetuned on one source language
and directly evaluated on target languages. In this work, we propose a
self-learning framework that further utilizes unlabeled data of target
languages, combined with uncertainty estimation in the process to select
high-quality silver labels. Three different uncertainties are adapted and
analyzed specifically for the cross lingual transfer: Language
Heteroscedastic/Homoscedastic Uncertainty (LEU/LOU), Evidential Uncertainty
(EVI). We evaluate our framework with uncertainties on two cross-lingual tasks
including Named Entity Recognition (NER) and Natural Language Inference (NLI)
covering 40 languages in total, which outperforms the baselines significantly
by 10 F1 on average for NER and 2.5 accuracy score for NLI.
