RP-OPSD: Reasoning-Pivot-Guided On-Policy Self-Distillation for Multilingual Reasoning Transfer
Authors: Xinye Wang, Junxiao Liu, Shujian Huang
Organizations: National Key Laboratory for Novel Software Technology, Nanjing University
Abstract
Multilingual reasoning transfer is crucial for extending reasoning capabilities of large language models (LLMs) beyond high-resource languages. On-policy self-distillation (OPSD) and its variants have emerged as a promising paradigm, providing dense token-level supervision on student-generated rollouts, yet their objectives do not explicitly prioritize reasoning signals most critical to cross-lingual transfer. We characterize that target-language reasoning comprises the generation of both surface text and reasoning pivots, which are decisions that advance or redirect the reasoning process and shape subsequent inference. This motivates concentrating privileged distillation around such pivots. We therefore propose RP-OPSD, Reasoning-Pivot-guided On-Policy Self-Distillation, using the distributional shift between matched teacher views with and without an English reference solution as an operational proxy to guide privileged distillation and reference anchoring. Experiments on mathematical reasoning benchmarks covering 17 languages and multiple difficulty levels show that our method outperforms strong multilingual reasoning baselines and OPSD variants. Further analysis reveals that RP-OPSD concentrates privileged distillation on reasoning-control and problem-condistioned state-update tokens, while downweighting it for tokens that mainly support surface realization. Our code is available at https://github.com/NJUNLP/RP-OPSD.
Large language models (LLMs) have achieved remarkable progress in mathematical reasoning, but this ability is not equally accessible across languages. Especially low-resource languages exhibit much lower reasoning performance. To address this, we propose Crosslingual On-Policy Self-Distillation (COPSD), which transfers a model's own high-resource reasoning behavior to low-resource languages. COPSD uses the same model as student and teacher: the student sees only the low-resource problem, while the teacher receives privileged crosslingual context, including the problem translation and reference solution in English. Training minimizes full-distribution token-level divergence on the student's own rollouts, providing dense supervision while avoiding the sparsity and instability of outcome-only reinforcement learning (RL). Experiments on 17 low-resource African languages show that COPSD consistently improves low-resource mathematical reasoning across model sizes and substantially outperforms Group Relative Policy Optimization (GRPO). Further analyses show that COPSD improves answer-format adherence, strengthens test-time scaling, and generalizes to harder multilingual reasoning benchmarks, with especially large gains for lower-resource languages. We make our code and data available at: https://github.com/cisnlp/COPSD.
On-Policy Distillation (OPD) is emerging as a promising alternative to reinforcement learning for LLM post-training, yet its effectiveness in multilingual settings remains underexplored. We study OPD and its advanced variant, On-Policy Delta Distillation (OPD2), for mathematical reasoning in English, Korean, and Japanese. OPD2 improves OPD by using the probability gap between a post-trained teacher and its base model as the learning signal. Experiments with Qwen3 show that OPD2 consistently outperforms the original OPD, with particularly strong improvements in Korean and Japanese, and generally narrows the English-Korean performance gap. We further find that English-only OPD can also increase performance for Korean and Japanese, but often shifts the responses toward English, highlighting the importance of multilingual data to preserving target-language responses.
On-policy self-distillation (OPSD) improves the reasoning performance of large language models (LLMs) by providing dense token-level supervision for on-policy rollouts. However, existing OPSD methods often yield limited gains on in-domain reasoning and generalize poorly to out-of-domain problems. We identify two key causes: conditioning the self-teacher on a verified solution encourages imitation of training-domain reference trajectories rather than error-specific correction, and applying distillation to the full response can overwrite valid reasoning prefixes and reinforce overfitting. We propose Reflective On-policy Self-Distillation (ROSD), a framework that turns reference-solution imitation into targeted reasoning correction through reflection-guided, error-localized distillation. For each rollout, ROSD uses a self-reflector to extract a corrective idea and locate the first erroneous span. The corrective idea guides the self-teacher toward targeted supervision, while the localized error span restricts distillation to where correction is needed. This design corrects flawed reasoning while preserving valid prefixes. Experiments on multiple in-domain and out-of-domain reasoning benchmarks show that ROSD yields stronger in-domain reasoning performance overall and substantially better out-of-domain generalization than standard OPSD. Code is available at https://github.com/ZiqiZhao1/ROSD.