Mitigating Distribution Sharpening in Math RLVR via Distribution-Aligned Hint Synthesis and Backward Hint Annealing
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910115337076736 |
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| author | Xie, Pei-Xi Lin, Che-Yu Yang, Cheng-Lin |
| author_facet | Xie, Pei-Xi Lin, Che-Yu Yang, Cheng-Lin |
| contents | Reinforcement learning with verifiable rewards (RLVR) can improve low-$k$ reasoning accuracy while narrowing solution coverage on challenging math questions, and pass@1 gains do not necessarily translate into better large-$k$ performance. Existing hint-based approaches can make challenging questions trainable, but they leave two issues underexplored: teacher-student distribution mismatch and the need to reduce hint exposure to match no-hint evaluation. We address these issues through two components. Distribution-Aligned Hint Synthesis (DAHS) constructs verified teacher hints conditioned on student-style responses. Backward Hint Annealing (BHA) anneals hint exposure across difficulty buckets and uses per-question hint dropout to preserve no-hint updates throughout RL training. We evaluate the method in math RLVR under the DAPO training framework across AIME24, AIME25, and AIME26 using $\texttt{Qwen3-1.7B-Base}$ and $\texttt{Llama-3.2-1B-Instruct}$. On $\texttt{Qwen3-1.7B-Base}$, our method improves both pass@1 and pass@2048 relative to DAPO across the three AIME benchmarks. On $\texttt{Llama-3.2-1B-Instruct}$, the gains are concentrated in the large-$k$ regime. These results suggest that, in math RLVR, hint scaffolding is effective when it restores learnable updates on challenging questions early in training and is then gradually removed before no-hint evaluation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07747 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mitigating Distribution Sharpening in Math RLVR via Distribution-Aligned Hint Synthesis and Backward Hint Annealing Xie, Pei-Xi Lin, Che-Yu Yang, Cheng-Lin Artificial Intelligence Computation and Language Machine Learning Reinforcement learning with verifiable rewards (RLVR) can improve low-$k$ reasoning accuracy while narrowing solution coverage on challenging math questions, and pass@1 gains do not necessarily translate into better large-$k$ performance. Existing hint-based approaches can make challenging questions trainable, but they leave two issues underexplored: teacher-student distribution mismatch and the need to reduce hint exposure to match no-hint evaluation. We address these issues through two components. Distribution-Aligned Hint Synthesis (DAHS) constructs verified teacher hints conditioned on student-style responses. Backward Hint Annealing (BHA) anneals hint exposure across difficulty buckets and uses per-question hint dropout to preserve no-hint updates throughout RL training. We evaluate the method in math RLVR under the DAPO training framework across AIME24, AIME25, and AIME26 using $\texttt{Qwen3-1.7B-Base}$ and $\texttt{Llama-3.2-1B-Instruct}$. On $\texttt{Qwen3-1.7B-Base}$, our method improves both pass@1 and pass@2048 relative to DAPO across the three AIME benchmarks. On $\texttt{Llama-3.2-1B-Instruct}$, the gains are concentrated in the large-$k$ regime. These results suggest that, in math RLVR, hint scaffolding is effective when it restores learnable updates on challenging questions early in training and is then gradually removed before no-hint evaluation. |
| title | Mitigating Distribution Sharpening in Math RLVR via Distribution-Aligned Hint Synthesis and Backward Hint Annealing |
| topic | Artificial Intelligence Computation and Language Machine Learning |
| url | https://arxiv.org/abs/2604.07747 |