Technical Summary: LUAR – Learning When to Translate for Multilingual Reasoning

Problem Statement

Reasoning Language Models (RLMs) have demonstrated strong capabilities on complex reasoning tasks by generating intermediate reasoning traces. However, they exhibit significant performance gaps in multilingual settings, particularly for low-resource languages. Recent studies indicate that these gaps are often driven not by a lack of reasoning capability, but by failures in language understanding when processing non-English inputs.

While translating non-English inputs into English can mitigate these understanding failures, indiscriminately translating every query is inefficient and unnecessary, as RLMs can often reason reliably from the original language. The core challenge is to enable RLMs to selectively invoke translation only when their direct understanding of the input is unreliable, without relying on external detectors that introduce latency or requiring the model to relearn language understanding from scratch.

Methodology: LUAR Framework

The authors propose LUAR (Language Understanding Boundary-aware Reinforcement Learning), a two-stage training framework that teaches RLMs to recognize their own language-understanding boundaries and invoke an external translator only when necessary.

1. Outcome-Based Boundary Estimation

LUAR defines a query as falling outside the model's language-understanding boundary if access to an English translation substantially improves the model's ability to solve it. This is estimated empirically by:

• Sampling $N/2$ responses via direct reasoning (original language).
• Sampling $N/2$ responses via translator-augmented reasoning (prepending a reference English translation to the trace).
• Calculating the correctness fractions $d_{acc}(q)$ and $t_{acc}(q)$.
• Assigning a translation-usefulness label $u(q) = 1$ if $t_{acc}(q) \ge d_{acc}(q) + \delta$ (where $\delta=0.5$), indicating translation is beneficial.

2. Two-Stage Training Procedure

Stage I: Translator-Call Supervised Fine-Tuning (SFT)

• Goal: Warm up the model's action space to include translator calls.
• Process: The model is fine-tuned on correct responses sampled from either direct or translator-augmented modes.
• Selection Rule: A "soft" rule is used to select the training target mode ($m(q)$): if $t_{acc}(q) > d_{acc}(q)$, the model is trained on a translator-augmented trace; otherwise, a direct trace. This exposes the model to both reasoning paths without enforcing a strict boundary yet.

Stage II: Boundary-Aware Online Reinforcement Learning (GRPO)

• Goal: Optimize the decision of when to call the translator.
• Process: The model is trained using Group Relative Policy Optimization (GRPO).
• Reward Function: A boundary-aware reward $r(q, y_i)$ is defined to jointly score task correctness and translator-call decisions:
  • Correct + Useful Call ($u(q)=1$): Reward $1 + \gamma$ (Bonus).
  • Correct + No Call: Reward $1$ (Base).
  • Correct + Unnecessary Call ($u(q)=0$): Reward $1 - \gamma$ (Penalty).
  • Incorrect/Invalid: Reward $0$.
• This encourages the model to call the translator only when it empirically leads to a higher probability of a correct answer, while avoiding calls when direct reasoning suffices.

Key Contributions

1. A New Perspective on Multilingual Reasoning: The paper reframes multilingual reasoning gaps as issues of language-understanding boundaries, proposing that RLMs should learn to detect when they fall outside these boundaries rather than simply improving general multilingual comprehension.
2. LUAR Framework: The introduction of a two-stage training pipeline (SFT + Boundary-Aware GRPO) that internalizes the decision to invoke translation directly within the reasoning trace, eliminating the need for separate external detectors.
3. Selective Translation Policy: Demonstrating that RLMs can learn a policy that concentrates translator calls on low-resource languages where direct reasoning fails, while preserving direct reasoning for high-resource languages and unseen low-resource languages.

Experimental Results

The framework was evaluated on Qwen3-4B and Qwen3-8B across PolyMath (mathematical reasoning) and MMLU-ProX-Lite (STEM reasoning) benchmarks covering 10 typologically diverse languages.

• Performance Gains: LUAR outperformed standard GRPO, prompt-based methods (Self-Assessment, Native Tool Use), external detector-based methods (Selective Translation), and other training-based baselines (Boundary-SFT, Q-ALIGN, TAPO).
  • On Qwen3-4B, LUAR achieved an average accuracy of 54.39% (translating only 20.3% of examples), significantly outperforming the base model (44.93%) and the full-translation baseline (55.39% with 100% translation cost).
  • On Qwen3-8B, LUAR achieved 70.46% average accuracy.
• Mode Selection: LUAR achieved the highest mode-selection macro-F1, indicating it correctly identified when translation was useful.
• Generalization: The model successfully generalized to unseen low-resource languages (Yoruba, Zulu), substantially improving accuracy on these languages (e.g., 56.27% on Yoruba and 87.20% on Zulu for Qwen3-4B) where direct reasoning was weakest.
• Efficiency: LUAR demonstrated lower inference latency (9.32s) compared to the base model (11.77s) and external selective translation (14.09s), attributed to shorter reasoning traces when translation is avoided.

Significance and Claims

The paper claims that LUAR provides a selective approach to multilingual reasoning, allowing RLMs to learn to invoke translation only when their direct understanding is unreliable. This approach:

• Bridges the gap between high-resource and low-resource language performance without requiring massive target-language training data.
• Avoids unnecessary overhead by not translating inputs that the model can already understand.
• Generalizes effectively to unseen languages, suggesting that the learned policy captures a robust signal of language-understanding boundaries rather than overfitting to specific training languages.

The authors conclude that treating language understanding as a boundary condition that can be detected and acted upon via tool use (translation) is a promising direction for building robust multilingual reasoning models. They note limitations regarding the diversity of language families covered and the scope of tasks (currently focused on math and STEM), suggesting future work could extend this boundary-aware policy to broader reasoning tasks.