Abstract: In this talk, we aim to quantify the robustness of distributed training against worst-case failures and adversarial nodes. We show that there is a gap between robustness guarantees, depending on whether adversarial nodes have full control of the hardware, the training data, or both. Using ideas from robust statistics and coding theory we establish robust and scalable training methods for centralized, parameter server systems. Perhaps unsurprisingly, we prove that robustness is impossible when a central authority does not own the training data, e.g., in federated learning systems.