# TAPO: Translation Augmented Policy Optimization for Multilingual Mathematical Reasoning

arXiv: https://arxiv.org/abs/2603.25419 · HTML: https://mlsanity.com/paper/2603.25419/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 27 of its 50 references that are in the map.
- First posted on arXiv 26 Mar 2026.

## Placed in

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

## Builds on (most cited first, 27 of 27)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Group-in-Group Policy Optimization for LLM Agent Training](https://mlsanity.com/paper/2505.10978/) (2025)
- [RL's Razor: Why Online Reinforcement Learning Forgets Less](https://mlsanity.com/paper/2509.04259/) (2025)
- [RLVMR: Reinforcement Learning with Verifiable Meta-Reasoning Rewards for Robust Long-Horizon Agents](https://mlsanity.com/paper/2507.22844/) (2025)
- [MT-R1-Zero: Advancing LLM-based Machine Translation via R1-Zero-like Reinforcement Learning](https://mlsanity.com/paper/2504.10160/) (2025)
- [Language Versatilists vs. Specialists: An Empirical Revisiting on Multilingual Transfer Ability](https://mlsanity.com/paper/2306.06688/) (2023)
- [Learn Globally, Speak Locally: Bridging the Gaps in Multilingual Reasoning](https://mlsanity.com/paper/2507.05418/) (2025)
- [Language Matters: How Do Multilingual Input and Reasoning Paths Affect Large Reasoning Models?](https://mlsanity.com/paper/2505.17407/) (2025)
- [Think Natively: Unlocking Multilingual Reasoning with Consistency-Enhanced Reinforcement Learning](https://mlsanity.com/paper/2510.07300/) (2025)
- [MMATH: A Multilingual Benchmark for Mathematical Reasoning](https://mlsanity.com/paper/2505.19126/) (2025)
- [When Less Language is More: Language-Reasoning Disentanglement Makes LLMs Better Multilingual Reasoners](https://mlsanity.com/paper/2505.15257/) (2025)
- [Why Do Multilingual Reasoning Gaps Emerge in Reasoning Language Models?](https://mlsanity.com/paper/2510.27269/) (2025)
- [Cross-lingual Collapse: How Language-Centric Foundation Models Shape Reasoning in Large Language Models](https://mlsanity.com/paper/2506.05850/) (2025)
- [Beyond English-Centric Training: How Reinforcement Learning Improves Cross-Lingual Reasoning in LLMs](https://mlsanity.com/paper/2509.23657/) (2025)
- [Making Qwen3 Think in Korean with Reinforcement Learning](https://mlsanity.com/paper/2508.10355/) (2025)

## Built on by (most cited first, 6 of 6)

- [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)
- [Translate-R1: Cost-Aware Translation Tool Use via Reinforcement Learning](https://mlsanity.com/paper/2606.06835/) (2026)
- [Soft Token Alignment for Cross-Lingual Reasoning](https://mlsanity.com/paper/2606.26466/) (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 Language Models (LLMs) have demonstrated remarkable proficiency in English mathematical reasoning, yet a significant performance disparity persists in multilingual contexts, largely attributed to deficiencies in language understanding. To bridge this gap, we introduce Translation-Augmented Policy Optimization (TAPO), a novel reinforcement learning framework built upon GRPO. TAPO enforces an explicit alignment strategy where the model leverages English as a pivot and follows an understand-then-reason paradigm. Crucially, we employ a step-level relative advantage mechanism that decouples understanding from reasoning, allowing the integration of translation quality rewards without introducing optimization conflicts. Extensive experiments reveal that TAPO effectively synergizes language understanding with reasoning capabilities and is compatible with various models. It outperforms baseline methods in both multilingual mathematical reasoning and translation tasks, while generalizing well to unseen languages and out-of-domain tasks.