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arxiv: 2605.09548 · v1 · submitted 2026-05-10 · 💻 cs.CL

Recognition: no theorem link

Crosslingual On-Policy Self-Distillation for Multilingual Reasoning

Yihong Liu , Raoyuan Zhao , Michael A. Hedderich , Hinrich Sch\"utze
Authors on Pith no claims yet

Pith reviewed 2026-05-12 04:41 UTC · model grok-4.3

classification 💻 cs.CL
keywords multilingual reasoningself-distillationlow-resource languagesmathematical reasoningcrosslingual transferon-policy learningLLM reasoning
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The pith

COPSD uses a model's own English reasoning as teacher to improve its low-resource language math performance via on-policy token distillation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces Crosslingual On-Policy Self-Distillation (COPSD) to close the gap in mathematical reasoning between high-resource and low-resource languages for large language models. The same model serves as both student and teacher: the student receives only the low-resource problem statement, while the teacher is given privileged access to the English translation and reference solution. Training matches the full token-level output distributions between them on the student's own rollouts, supplying dense supervision instead of sparse outcome rewards. Experiments across 17 low-resource African languages demonstrate consistent gains in reasoning accuracy for multiple model sizes, outperforming Group Relative Policy Optimization. The method also yields better answer-format compliance, stronger test-time scaling, and improved results on harder multilingual benchmarks, with the largest benefits for the lowest-resource languages.

Core claim

COPSD lets a single model transfer its high-resource English reasoning behavior to low-resource languages by minimizing full-distribution token-level divergence on student rollouts, where the teacher alone receives the problem translation and reference solution in English.

What carries the argument

Crosslingual On-Policy Self-Distillation (COPSD): on-policy self-distillation that minimizes token-level output divergence between a student seeing only the low-resource input and a teacher given English translation plus reference solution.

If this is right

  • Consistent accuracy gains on low-resource mathematical reasoning across different model sizes.
  • Substantial outperformance of GRPO on 17 African languages.
  • Improved adherence to answer formats and stronger test-time scaling.
  • Generalization to harder multilingual reasoning benchmarks, with especially large gains for lower-resource languages.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach might extend to non-math reasoning tasks such as code generation or logical inference by supplying analogous privileged English context during distillation.
  • It could lower the need for external translators or parallel data by relying on the model's internal crosslingual knowledge.
  • Removing the reference solution from the teacher's context while keeping only the translation might still yield partial gains but would likely reduce reliability.

Load-bearing premise

The teacher's privileged English context generates supervision that transfers useful reasoning patterns to the student's low-resource generations without harmful biases or inconsistencies introduced by translation or the reference solution.

What would settle it

Training with COPSD on the same low-resource languages and models but measuring no increase (or a decrease) in math problem accuracy compared to standard supervised fine-tuning or GRPO would show the crosslingual distillation signal is not reliably beneficial.

Figures

Figures reproduced from arXiv: 2605.09548 by Hinrich Sch\"utze, Michael A. Hedderich, Raoyuan Zhao, Yihong Liu.

Figure 1
Figure 1. Figure 1: Radar comparison of Qwen3-1.7B perfor￾mance on AfriMGSM under a 4096-token generation budget. Each axis corresponds to one of the 17 low￾resource African languages, with axis-specific scaling based on the maximum observed performance for that language. COPSD consistently outperforms both the base and GRPO-trained models across languages. underrepresented languages (Hwang et al., 2025; Yong et al., 2025; Gh… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of COPSD. Each problem is translated into a low-resource language as the student’s input. The same LLM acts as both student and teacher: the student generates an on-policy rollout, while the teacher evaluates it with privileged English context and the reference solution. By minimizing per-token divergence along the rollout, COPSD transfers English-accessible reasoning behavior to improve reasoning… view at source ↗
Figure 3
Figure 3. Figure 3: Average training dynamics across languages [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Test-time scaling results on Pass@12 for three representative languages: Amharic (AMH), Ewe (EWE), [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Average repeat rate comparison on Qwen3-1.7B with 4-grams. COPSD consistently re￾duces repetition compared to the base model and GRPO. out training.6 Compared with both the base model and GRPO, COPSD consistently maintains the lowest repeat rate across training steps. Impor￾tantly, lower repeat rates should not be interpreted simply as greater lexical diversity; rather, for rea￾soning in low-resource langu… view at source ↗
Figure 6
Figure 6. Figure 6: Pass@12 improvements of COPSD over the base model on PolyMath across low-, medium-, and high-difficulty settings under 8,192-token generation budget. Each plot compares Base and COPSD for 8 languages spanning different resource levels. COPSD yields consistent gains across resource levels and difficulty levels, with especially substantial improvements for lower-resource languages such as Swahili (SWA) and T… view at source ↗
Figure 1
Figure 1. Figure 1: Language-specific prompting components used for language control. Panel (a) lists the instruction appended to each input, which asks the model to reason step by step and place the final answer in \boxed{}. Panel (b) lists the prompt-hacking prefixes inserted immediately after <think> to steer the explicit reasoning trace toward the target language [PITH_FULL_IMAGE:figures/full_fig_p014_1.png] view at source ↗
Figure 9
Figure 9. Figure 9: Repeat rate across different n-gram settings (n = 2 to 6) and model sizes. COPSD consistently reduces repetition compared to both the base and GRPO. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Per-language training dynamics for Qwen3-1.7B across all African languages under a 1024-token generation budget. Solid lines show Pass@12 and dashed lines show format rate. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Per-language training dynamics for Qwen3-4B across all African languages under a 1024-token generation budget. Solid lines show Pass@12 and dashed lines show format rate. 19 [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Per-language training dynamics for Qwen3-8B across all African languages under a 1024-token generation budget. Solid lines show Pass@12 and dashed lines show format rate. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Per-language test-time scaling results on Pass@12 for [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Per-language test-time scaling results on Pass@12 for [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Per-language test-time scaling results on Pass@12 for [PITH_FULL_IMAGE:figures/full_fig_p023_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Translation prompt template used to translate English training questions into a target language. The [PITH_FULL_IMAGE:figures/full_fig_p023_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Student-policy prompt. The left panel shows the instantiated Swahili prompt used in training and [PITH_FULL_IMAGE:figures/full_fig_p024_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Teacher-policy prompt. The teacher receives privileged information, including the English translation of [PITH_FULL_IMAGE:figures/full_fig_p024_18.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes Crosslingual On-Policy Self-Distillation (COPSD), a self-distillation procedure in which the same LLM acts as both student and teacher: the student receives only the low-resource-language problem statement, while the teacher is given privileged crosslingual context consisting of an English translation and reference solution. Training minimizes full-distribution token-level KL divergence on the student's own on-policy rollouts. Experiments across 17 low-resource African languages and multiple model sizes report consistent gains in mathematical reasoning, outperformance relative to Group Relative Policy Optimization (GRPO), improved answer-format adherence, stronger test-time scaling, and generalization to harder benchmarks, with larger gains for lower-resource languages. Code and data are released.

Significance. If the central claim holds, COPSD offers a practical, dense-supervision alternative to outcome-only RL for closing the multilingual reasoning gap without external data or unstable policy optimization. The open release of code and data, together with evaluation on 17 languages and multiple model scales, strengthens the work's reproducibility and potential impact for low-resource settings.

major comments (2)
  1. [Method] Method section (COPSD description): the teacher is conditioned on the English reference solution while the student sees only the low-resource problem; token-level divergence on student rollouts can therefore reward reproduction of the known correct answer path rather than induction of language-internal reasoning steps. This risks answer leakage, especially given imperfect translations or style mismatches in low-resource languages. No ablation that removes the reference solution from the teacher (or substitutes a no-reference teacher) is reported, leaving the interpretation of the gains over GRPO open to the alternative explanation of privileged-answer mimicry.
  2. [Experiments] Experiments and results sections: the headline claims of 'consistent improvements across model sizes' and 'substantially outperforms GRPO' on 17 languages rest on quantitative results that, per the abstract, lack reported error bars, statistical significance tests, or per-language breakdowns. Without these, it is difficult to assess whether the observed deltas are robust or driven by a subset of languages or model scales.
minor comments (2)
  1. [Abstract] The abstract states improvements but supplies no numerical deltas, baseline scores, or key metrics; adding one or two representative numbers (e.g., average accuracy lift on the 17-language suite) would improve readability.
  2. [Method] Notation for the divergence objective and rollout sampling procedure could be clarified with an explicit equation or pseudocode block to make the on-policy self-distillation step easier to replicate.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment below and indicate where we will revise the manuscript to strengthen the presentation and address the concerns raised.

read point-by-point responses

  1. Referee: [Method] Method section (COPSD description): the teacher is conditioned on the English reference solution while the student sees only the low-resource problem; token-level divergence on student rollouts can therefore reward reproduction of the known correct answer path rather than induction of language-internal reasoning steps. This risks answer leakage, especially given imperfect translations or style mismatches in low-resource languages. No ablation that removes the reference solution from the teacher (or substitutes a no-reference teacher) is reported, leaving the interpretation of the gains over GRPO open to the alternative explanation of privileged-answer mimicry.

    Authors: We appreciate the referee's point on potential answer leakage. The design intentionally provides the teacher with privileged crosslingual context (English translation plus reference solution) to generate high-quality reasoning distributions that the student can distill from its own on-policy rollouts. This enables dense supervision without external data. However, we acknowledge that the current experiments do not isolate whether gains arise from reasoning transfer versus direct mimicry of the reference path, particularly with imperfect translations. We will add an ablation in the revised manuscript that removes the reference solution from the teacher's prompt (retaining only the English translation) and compare performance against the full COPSD setup and GRPO. This will clarify the contribution of each component. revision: yes

  2. Referee: [Experiments] Experiments and results sections: the headline claims of 'consistent improvements across model sizes' and 'substantially outperforms GRPO' on 17 languages rest on quantitative results that, per the abstract, lack reported error bars, statistical significance tests, or per-language breakdowns. Without these, it is difficult to assess whether the observed deltas are robust or driven by a subset of languages or model scales.

    Authors: We agree that additional statistical details would improve the robustness assessment. The reported results are averages over the 17 languages, but we did not include per-language tables, standard deviations across runs, or formal significance tests in the main text or appendix for space reasons. In the revision we will add (i) a per-language breakdown table with mean and standard deviation (computed from the multiple model scales and seeds where available), (ii) error bars on all main figures, and (iii) paired statistical tests (e.g., Wilcoxon signed-rank) comparing COPSD against GRPO and other baselines. These additions will be placed in the results section and appendix. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the proposed method or claims

full rationale

The paper describes COPSD as a procedural training recipe: the same model acts as student (receiving only the low-resource problem) and teacher (receiving privileged English translation plus reference solution), with training via token-level divergence minimization on student-generated rollouts. This is a standard on-policy distillation setup with no mathematical derivation chain, no fitted parameters renamed as predictions, and no self-referential quantities. The performance claims rest on empirical results across 17 languages and model sizes rather than any reduction to the method's own inputs by construction. No load-bearing self-citations or ansatz smuggling appear in the description. The approach is self-contained as an independent training procedure.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on standard machine-learning assumptions such as the utility of token-level KL divergence for distillation and the transferability of reasoning via English references, but introduces no new free parameters, axioms, or invented entities.

pith-pipeline@v0.9.0 · 5510 in / 1103 out tokens · 43530 ms · 2026-05-12T04:41:02.027860+00:00 · methodology

discussion (0)

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Reference graph

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