Title: Theoretical foundations of curriculum learning in linear RNNs
Primary area: learning theory
Keywords: curriculum learning, learning speed, pretraining, theory, linear RNNs

Abstract: Pretraining models with a curriculum of simpler tasks is a common approach to speed up training. However, it is unclear what aspects of task structure drive learning speed, and how to practically choose the curriculum based on theoretical principles. Using recent advances in the analysis of learning trajectories in linear RNNs (Proca et al., 2025), we study a simple but informative example of performing two integration tasks in sequence, and ask what aspects of their task structure lead to faster overall learning of the second ``target'' task. We show both analytically and through simulations that even for tasks that are similar in their geometry, sequencing them based on the strength and scale of the input-to-target correlations can provably enhance learning speed. A surprising result from our theory that goes against conventional wisdom is that training intermediate tasks to suboptimal accuracies can be more beneficial to learning speed, rather than training them to convergence. These results provide foundational insight into how task similarity forms both a theoretical and practical basis for curriculum learning.