CAST: Non-Privileged Clipped Asymmetric Self-Teaching with Advantage Flipping for GRPO

Reinforcement learning with verifiable rewards (RLVR), especially Group Relative Policy Optimization (GRPO), has been widely used to improve reasoning in large language models. However, outcome-level rewards provide only sparse supervision, and group-relative advantages vanish when all sampled trajectories for a prompt are either correct or incorrect. On-Policy Self-Distillation (OPSD) offers dense token-level guidance, but its token preferences are not necessarily aligned with trajectory correctness; empirical diagnostics show that OPSD signals behave differently on correct and incorrect rollouts, with teacher-positive and teacher-negative gap signals exhibiting different noise profiles. These diagnostics are conducted under an OPSD-style privileged teacher context for analysis only, whereas CAST training uses answer-free self-teacher scoring.Motivated by these observations, this work proposes CAST, an answer-free self-distillation method for GRPO-style RLVR. CAST keeps the verifier-grounded GRPO objective, but uses a stop-gradient self-teacher to shape token-level advantages according to trajectory correctness. Unlike prior self-distilled RLVR methods, CAST does not require reference-solution-conditioned teacher scoring, keeps the self-teacher log-probability gap active throughout training, and applies bidirectional local advantage sign reversal: teacher-negative tokens in correct trajectories can receive negative token-level advantages, while teacher-positive tokens in incorrect trajectories can receive bounded positive local advantages. For zero-variance all-correct and all-wrong groups, CAST assigns bounded sign-constrained base advantages, so these otherwise zero-gradient groups can contribute verifier-signed token feedback. Experiments on mathematical reasoning show that CAST improves RLVR training while retaining a lightweight, verifier-grounded trajectory-level objective.