The results suggest that dense credit assignment through distillation can be effective when its likelihood-based scores are empirically validated as meaningful proxies for outcome-relevant credit, when this alignment does not hold.
Abstract
On-policy self-distillation aims to improve upon reinforcement learning from verifiable rewards (RLVR) by providing token-level scores derived from privileged information, such as reference solutions or critic feedback. These scores are treated as estimates of token-level action values, yet they answer a fundamentally different question: how the model's prediction changes when its input context is enriched, rather than how the expected outcome changes when a token is changed. We examine this gap along three dimensions: (i) whether the token-level score tracks task success; (ii) whether feedback generated from the same rollout causes the score to reflect agreement with its own description, and whether using feedback from other rollouts in the group mitigates this self-referential effect; and (iii) what behavior the resulting training objective actually reinforces. In experiments on AIME 2025, the implemented score distinguishes correct from incorrect rollouts at approximately chance level (AUC=0.505); using feedback from a different rollout does not consistently improve this discrimination; and all training configurations achieve only 24.2-33.9% Avg@4, compared with 64.2% for outcome-only GRPO. Moreover, the highest-entropy token decile accounts for 57-71% of the total absolute token-advantage mass, despite the score being least informative about reasoning quality in this regime. By contrast, similar experiments on SciKnowEval Biology improves held-out Avg@8 by 28.0%, while its corresponding trajectory scores achieve AUCs of 0.81-0.92. Together, these results suggest that dense credit assignment through distillation can be effective when its likelihood-based scores are empirically validated as meaningful proxies for outcome-relevant credit. When this alignment does not hold, however, the resulting supervision can fail to generalize and may substantially underperform outcome-based RL.
Group-relative residual calibration can incorporate verifier outcomes without discarding dense token-level guidance, and demonstrates that group-relative residual calibration can incorporate verifier outcomes without discarding dense token-level guidance.
Zhu Zhang, Ji-Xun Wang, Xiao-An Xu et al.· 1 citation
This review treats collapse as a symptom governed by three levers: where the signal is applied, that is, how tokens are weighted; what the teacher is shown, that is, the nature of the privileged information; and when the signal changes, that is, the teacher's dynamics and the decay of guidance.
Evidence Anchors are constructed, which are concise, step-level evidence snippets extracted from the web, as privileged information that captures key reasoning steps without revealing the entire answer path, and SSPO, which converts teacher-student disagreement into step-level advantage weights within GRPO, applied exclusively to incorrect trajectories.
Haoze Wu, Chuqiao Kuang, Tianyi Zhuang et al.· 0 citations
Reinforcement learning with verifiable rewards (RLVR) is central to improving long-CoT reasoning in large language models. Critic-free methods such as GRPO convert response-level rewards into advantages and uniformly broadcast them across tokens, overlooking their unequal contributions to the final outcome. On-policy self-distillation (OPSD) instead provides dense distributional supervision by minimizing the forward KL divergence between an unprivileged policy and a privileged self-teacher, implicitly assuming that the resulting likelihood shifts encode reliable answer-aligned information. We test this premise by fixing each sampled trajectory and re-scoring it under two opposing outcome conditions, one asserting correctness and the other incorrectness. Most affected tokens shift in the same direction under both conditions, with few sign reversals and substantial overlap in the induced optimization signals. Large shifts also concentrate on highly substitutable surface-form tokens, whereas tokens carrying problem-specific reasoning content are less sensitive. These findings show that privileged shifts fail to provide reliable answer-aligned directions, while their magnitudes primarily reflect counterfactual sensitivity rather than token-level learning value. Based on these observations, we propose Counterfactual Sensitivity Credit Reallocation (CSCR), a simple extension of GRPO that reduces credit for highly sensitive tokens and renormalizes token-level advantages to preserve both the original credit budget and verifier-determined direction. On long-CoT mathematical reasoning benchmarks, CSCR consistently outperforms GRPO baseline with the same number of policy updates. Targeted ablations further corroborate our diagnosis: privilege-induced directions are unreliable, moderate downweighting is most effective, and stronger modulation destabilizes optimization.
Reinforcement learning with verifiable rewards (RLVR) offers a verifier-bounded performance ceiling for training multi-turn tool-use agents, yet its trajectory-level credit assignment conflates heterogeneous per-turn outcomes into a single reward signal. On-policy distillation provides dense per-token supervision but is either teacher-bounded or prone to gradient concentration collapse. We introduce $\textbf{CrEST}$, a hierarchical credit assignment framework that retains RL's verifier-bounded ceiling while incorporating dense token-level signals from a privileged self-teacher. $\textbf{CrEST}$ resolves credit at two levels: turn-segmented verified advantages address inter-turn dilution, while entropy-gated self-teacher modulation refines intra-turn token contributions. Experiments on BFCL V3 and WildToolBench show that $\textbf{CrEST}$ consistently outperforms both RL and distillation baselines across two model scales, with the largest gains on long-trajectory and strict session-level metrics. Our work demonstrates that the teacher's role in policy optimization can be reduced from determining update directions to modulating update magnitudes, unlocking dense credit assignment without sacrificing the verifier-bounded ceiling.
Zechuan Wang, Siyuan Lu, Hongxuan Zhang et al.· 1 citation
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