This work presents a method for adapting a single, fixed deep neural network\nto multiple tasks without affecting performance on already learned tasks. By\nbuilding upon ideas from network quantization and pruning, we learn binary\nmasks that piggyback on an existing network, or are applied to unmodified\nweights of that network to provide good performance on a new task. These masks\nare learned in an end-to-end differentiable fashion, and incur a low overhead\nof 1 bit per network parameter, per task. Even though the underlying network is\nfixed, the ability to mask individual weights allows for the learning of a\nlarge number of filters. We show performance comparable to dedicated fine-tuned\nnetworks for a variety of classification tasks, including those with large\ndomain shifts from the initial task (ImageNet), and a variety of network\narchitectures. Unlike prior work, we do not suffer from catastrophic forgetting\nor competition between tasks, and our performance is agnostic to task ordering.\nCode available at https://github.com/arunmallya/piggyback.\n