Title: XLA: A Robust Unsupervised Data Augmentation Framework for Cross-Lingual NLP. Abstract: Transfer learning has yielded state-of-the-art (SoTA) results in many supervised NLP tasks. However,  annotated data for every target task in every target language is rare, especially for low-resource languages. We propose XLA, a novel data augmentation framework for self-supervised learning in zero-resource transfer learning scenarios. In particular, XLA aims to solve cross-lingual adaptation problems from a source language task distribution to an unknown target language task distribution, assuming no training label in the target language task. At its core, XLA performs simultaneous self-training with data augmentation and unsupervised sample selection. To show its effectiveness, we conduct extensive experiments on zero-resource cross-lingual transfer tasks for Named Entity Recognition (NER), Natural Language Inference (NLI) and paraphrase identification on Paraphrase Adversaries from Word Scrambling (PAWS). XLA achieves SoTA results in all the tasks, outperforming the baselines by a good margin. With an in-depth framework dissection, we demonstrate the cumulative contributions of different components to XLA's success. 