Title: Exclusive Supermask Subnetwork Training for Continual Learning. Abstract: Continual Learning (CL) methods mainly focus on avoiding catastrophic forgetting and learning representations that are transferable to new tasks. Recently, Wortsman et al. (2020) proposed a CL method, SupSup, which uses a randomly initialized, fixed base network (model) and finds a supermask for each new task that selectively keeps or removes each weight to produce a subnetwork. They prevent forgetting as the network weights are not being updated. Although there is no forgetting, the performance of supermask is sub-optimal because fixed weights restrict its representational power. Furthermore, there is no accumulation or transfer of knowledge inside the model when new tasks are learned. Hence, we propose ExSSNeT (Exclusive Supermask SubNEtwork Training), that performs exclusive and non-overlapping subnetwork weight training. This avoids conflicting updates to the shared weights by subsequent tasks to improve performance while still preventing forgetting. Furthermore, we propose a novel KNN-based Knowledge Transfer (KKT) module that dynamically initializes a new task's mask based on previous tasks for improving knowledge transfer. We demonstrate that ExSSNeT outperforms SupSup and other strong previous methods on both text classification and vision tasks while preventing forgetting. Moreover, ExSSNeT is particularly advantageous for sparse masks that activate 2-10% of the model parameters, resulting in an average improvement of 8.3% over SupSup. Additionally, ExSSNeT scales to a large number of tasks (100), and our KKT module helps to learn new tasks faster while improving the overall performance.