Title: A Probabilistic Framework For Modular Continual Learning. Abstract: Continual learning (CL) algorithms seek to accumulate and transfer knowledge across a sequence of tasks and achieve better performance on each successive task. Modular approaches, which use a different composition of modules for each task and avoid forgetting by design, have been shown to be a promising direction to CL. However, searching through the large space of possible module compositions remains a challenge. In this work, we develop a scalable probabilistic search framework as a solution to this challenge. Our framework has two distinct components. The first is designed to transfer knowledge across similar input domains. To this end, it models each module’s training input distribution and uses a Bayesian model to find the most promising module compositions for a new task. The second component targets transfer across tasks with disparate input distributions or different input spaces and uses Bayesian optimisation to explore the space of module compositions. We show that these two methods can be easily combined and evaluate the resulting approach on two benchmark suites designed to capture different desiderata of CL techniques. The experiments show that our framework offers superior performance compared to state-of-the-art CL baselines.