arXiv Machine Learning By Bang Xie, Hao Liu, Zhiyuan Peng, Xin Yin, Chenhao Ying, Yuan Luo, Senjian Zhang, Wei Chen

From Reasoning Strings to Partial Orders: Verifier-Certified Rule Transport through Quotient Policy Optimization

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The paper introduces Verifier-Certified Rule Transport (VCRT), a method that uses native verifiers to replay adjacent operation pairs and identify commutation certificates or anti-diamonds, thereby distinguishing true logical dependencies from mere serialization choices in reinforcement learning with verifiable rewards. VCRT assigns policy credit based on the total probability mass of each certified orbit and imposes constraints on post-swap consistency, source retention, and policy drift. In leave-one-environment-out transfer experiments across ProofWriter, CLRS, and Lean, VCRT achieves a 77.60% macro pass rate, outperforming the strongest baseline by 13.06 points, with the largest gains observed in Lean.

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