Curriculum Learning Boosts AI Compositional Generalization Exponentially

Compositional generalization, the ability of AI to break down complex problems into simpler, solvable parts and then combine those solutions, is a cornerstone of advanced reasoning. However, the theoretical understanding of when and why this decomposition leads to more efficient learning has been limited. This research explores compositional generalization through the lens of simulating semiautomata, a model encompassing state tracking and modular arithmetic. It introduces an autocurriculum-based approach that recursively decomposes longer sequences into shorter sub-problems, learns their solutions, and then composes them. This method achieves dramatically better statistical complexity, requiring only subpolynomial supervision tokens compared to the linear requirement of direct simulation. It also significantly reduces the coverage requirements for reference models in reinforcement learning settings, demonstrating an exponentially weaker condition for effective learning.