Deep neural network (DNN) accelerators are specialized hardware for inference and have received considerable attention in the past years. Here, in order to reduce energy consumption, these accelerators are often operated at low voltage which causes the included accelerator memory to become unreliable. Additionally, recent work demonstrated attacks targeting individual bits in memory. The induced bit errors in both cases can cause significantly reduced accuracy of DNNs. In this paper, we tackle both random (due to low-voltage) and adversarial bit errors in DNNs. By explicitly taking such errors into account during training, wecan improve robustness significantly.