Title: Transferable Unsupervised Robust Representation Learning. Abstract: Robustness is an important, and yet, under-explored aspect of unsupervised representation learning, which has seen a lot of recent developments. In this work, we address this gap by developing a novel framework: Unsupervised Robust Representation Learning (URRL), which combines unsupervised representation learning's pretext task and robust supervised learning (e.g., AugMix).  Moreover, it is commonly assumed that there needs to be a trade-off between natural accuracy (on clean data) and robust accuracy (on corrupted data). We upend this view and show that URRL improves both the natural accuracy of unsupervised representation learning and its robustness to corruptions and adversarial noise. A further challenge is that the robustness of a representation might not be preserved in the transfer learning process after fine-tuning on downstream tasks. We develop transferable robustness by proposing a task-agnostic similarity regularization during the fine-tuning process. We show that this improves the robustness of the resulting model without the need for any adversarial training or further data augmentation during fine-tuning.