# R3S: Refining and Recovering Reinforcement Signals for Multilingual Understanding and Reasoning

arXiv: https://arxiv.org/abs/2602.05940 · HTML: https://mlsanity.com/paper/2602.05940/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 8 of its 12 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 8 of 8)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [COMET: A Neural Framework for MT Evaluation](https://mlsanity.com/paper/2009.09025/) (2020)
- [MMLU-ProX: A Multilingual Benchmark for Advanced Large Language Model Evaluation](https://mlsanity.com/paper/2503.10497/) (2025)
- [MAPO: Advancing Multilingual Reasoning through Multilingual Alignment-as-Preference Optimization](https://mlsanity.com/paper/2401.06838/) (2024)
- [Understand, Solve and Translate: Bridging the Multilingual Mathematical Reasoning Gap](https://mlsanity.com/paper/2501.02448/) (2025)
- [Learn Globally, Speak Locally: Bridging the Gaps in Multilingual Reasoning](https://mlsanity.com/paper/2507.05418/) (2025)
- [MMATH: A Multilingual Benchmark for Mathematical Reasoning](https://mlsanity.com/paper/2505.19126/) (2025)
- [When Models Reason in Your Language: Controlling Thinking Language Comes at the Cost of Accuracy](https://mlsanity.com/paper/2505.22888/) (2025)

## Built on by (most cited first, 5 of 5)

- [What Makes Good Multilingual Reasoning? Disentangling Traces with Measurable Features](https://mlsanity.com/paper/2604.04720/) (2026)
- [Learning When to Translate for Multilingual Reasoning](https://mlsanity.com/paper/2606.02465/) (2026)
- [AdaMame: A Training Recipe for Adaptive Multilingual Reasoning](https://mlsanity.com/paper/2606.15080/) (2026)
- [RP-OPSD: Reasoning-Pivot-Guided On-Policy Self-Distillation for Multilingual Reasoning Transfer](https://mlsanity.com/paper/2608.06347/) (2026)
- [GRPO Beyond English: A Large-Scale Study of GRPO in Non-English and Multilingual Settings](https://mlsanity.com/paper/2608.13698/) (2026)

## Abstract (arXiv)

Large reasoning models often default to English reasoning when processing non-English questions, yet their performance drops substantially when reasoning in the question language. Even with the same reasoning language, semantically equivalent English and non-English questions still exhibit a clear performance gap. Together, these phenomena reveal two distinct bottlenecks: target-language question understanding and target-language reasoning. Existing methods typically optimize only one of these capabilities. However, simply combining them may not be sufficient to optimize both effectively, as answer correctness alone cannot distinguish failures in question understanding from those in reasoning. We propose R3S, a reinforcement learning framework that disentangles the optimization of the two capabilities. R3S refines translation rewards derived from downstream reasoning accuracy through English-solvability filtering and recovers target-language RLVR signals using self-generated English hints. Together, these designs require neither external model feedback nor external multilingual training data. Experiments across three backbone models and five languages show that R3S improves language-consistent accuracy over the target-language RLVR baseline on MMATH by an average of 10.3 percentage points, while maintaining near-perfect language consistency. Consistent gains on MMLU-ProX further demonstrate its generalization beyond math problems.