The Path Not Taken: RLVR Provably Learns Off the Principals

The recent paper on Reinforcement Learning with Verifiable Rewards (RLVR) sheds light on its unique learning dynamics, which diverge from traditional methods like Supervised Fine-Tuning (SFT). By employing a Three-Gate Theory, the authors explain how RLVR achieves effective learning through minimal updates in weight space, focusing on off-principal directions. This approach not only challenges the notion of sparsity as a mere artifact but also provides a comprehensive understanding of RLVR's optimization regime. The findings could have profound implications for the development of AI systems, enhancing their reasoning capabilities while maintaining efficiency in parameter adjustments.