Crosslingual On-Policy Self-Distillation for Multilingual Reasoning
Authors: Yihong Liu, Raoyuan Zhao, Michael A. Hedderich, Hinrich Schütze
Organizations: Center for Information and Language Processing, LMU Munich · Munich Center for Machine Learning (MCML)
Abstract
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.
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 have achieved substantial progress in reasoning capabilities. Yet in low-resource native settings, many suffer from cross-lingual collapse, reverting to English during intermediate steps that require complex logical reasoning. This presents a cold-start bottleneck for policy optimization, whereas standard fine-tuning risks catastrophic forgetting due to cross-lingual representation drift. To address these challenges, we introduce the Onramp-Sequence Cross-Distillation (OSCD), a post-training algorithm that projects high-resource reasoning trajectories into low-resource vocabulary subspaces during generative training rollouts via an integrated translator agentic loop, ensuring the stable and efficient translation of dynamically generated reference samples for fine-tuning. This is coupled with joint-embedding semantic alignment of both reference and target-language reasoning traces, thereby bridging the pairwise cross-lingual representational gaps. Comprehensive evaluations using the AIME25 and HMMT25 benchmarks demonstrate that OSCD yields up to 3.2 times overall improvements in native Southeast Asian languages for mathematical reasoning, of which the joint-embedding semantic alignment component contributes up to 6.4% improvements in linguistic debiasing over translation-only baselines.
Sean Gip Lim, William Chandra Tjhi, Hai Leong Chieu
Large language models exhibit substantial performance variation across languages, even when solving semantically equivalent tasks. Existing analyses often treat this phenomenon as an observational disparity caused by differences in pretraining data, tokenization, or benchmark coverage. We study a complementary hypothesis: high-resource languages (HRLs) may more reliably elicit latent computations useful for task-specific (i.e. mathematical) reasoning, while lower-resource languages (LRLs) may under-activate those computations despite expressing the same task. To test this hypothesis, we introduce a mechanistic intervention framework for identifying and transferring task-relevant sparse latent features across languages. Using sparse autoencoders over residual-stream activations, we isolate features enriched in successful HRL task-specific reasoning while filtering out source-language and generic-generation features. We then construct steering directions from these features and inject them during LRL inference. The resulting interventions test whether the selected features are functionally involved in the observed reasoning gap: suppressing them should impair source-language reasoning, while activating them should partially recover target-language reasoning beyond random and non-task controls. Our framework reframes some cross-lingual reasoning gaps as failures of mechanism elicitation rather than capability absence, and offers a causally testable route to feature-mediated transfer without translation, fine-tuning, or changing the user-facing language.