# Breaking Language Barriers in Multilingual Mathematical Reasoning: Insights and Observations

arXiv: https://arxiv.org/abs/2310.20246 · HTML: https://mlsanity.com/paper/2310.20246/

## Key facts

- Cited by 59 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 45 references that are in the map.
- First posted on arXiv 31 Oct 2023.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 22 of 22)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [GLM-130B: An Open Bilingual Pre-trained Model](https://mlsanity.com/paper/2210.02414/) (2022)
- [The Flan Collection: Designing Data and Methods for Effective Instruction Tuning](https://mlsanity.com/paper/2301.13688/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Language Models are Multilingual Chain-of-Thought Reasoners](https://mlsanity.com/paper/2210.03057/) (2022)
- [RRHF: Rank Responses to Align Language Models with Human Feedback without tears](https://mlsanity.com/paper/2304.05302/) (2023)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [Preference Ranking Optimization for Human Alignment](https://mlsanity.com/paper/2306.17492/) (2023)
- [BayLing: Bridging Cross-lingual Alignment and Instruction Following through Interactive Translation for Large Language Models](https://mlsanity.com/paper/2306.10968/) (2023)
- [Large Language Models Meet Harry Potter: A Bilingual Dataset for Aligning Dialogue Agents with Characters](https://mlsanity.com/paper/2211.06869/) (2022)

## Built on by (most cited first, 30 of 59)

- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [MAPO: Advancing Multilingual Reasoning through Multilingual Alignment-as-Preference Optimization](https://mlsanity.com/paper/2401.06838/) (2024)
- [PolyMath: Evaluating Mathematical Reasoning in Multilingual Contexts](https://mlsanity.com/paper/2504.18428/) (2025)
- [Multilingual Large Language Model: A Survey of Resources, Taxonomy and Frontiers](https://mlsanity.com/paper/2404.04925/) (2024)
- [xCoT: Cross-lingual Instruction Tuning for Cross-lingual Chain-of-Thought Reasoning](https://mlsanity.com/paper/2401.07037/) (2024)
- [Crosslingual Reasoning through Test-Time Scaling](https://mlsanity.com/paper/2505.05408/) (2025)
- [Understand, Solve and Translate: Bridging the Multilingual Mathematical Reasoning Gap](https://mlsanity.com/paper/2501.02448/) (2025)
- [Question Translation Training for Better Multilingual Reasoning](https://mlsanity.com/paper/2401.07817/) (2024)
- [PLUG: Leveraging Pivot Language in Cross-Lingual Instruction Tuning](https://mlsanity.com/paper/2311.08711/) (2023)
- [Linguistic Generalizability of Test-Time Scaling in Mathematical Reasoning](https://mlsanity.com/paper/2502.17407/) (2025)
- [Compress to Impress: Unleashing the Potential of Compressive Memory in Real-World Long-Term Conversations](https://mlsanity.com/paper/2402.11975/) (2024)
- [mCoT: Multilingual Instruction Tuning for Reasoning Consistency in Language Models](https://mlsanity.com/paper/2406.02301/) (2024)
- [GraphWiz: An Instruction-Following Language Model for Graph Problems](https://mlsanity.com/paper/2402.16029/) (2024)
- [Multilingual Routing in Mixture-of-Experts](https://mlsanity.com/paper/2510.04694/) (2025)
- [Language Imbalance Driven Rewarding for Multilingual Self-improving](https://mlsanity.com/paper/2410.08964/) (2024)
- [DialogGen: Multi-modal Interactive Dialogue System for Multi-turn Text-to-Image Generation](https://mlsanity.com/paper/2403.08857/) (2024)
- [A Survey on Human Preference Learning for Large Language Models](https://mlsanity.com/paper/2406.11191/) (2024)
- [Bridging the Language Gaps in Large Language Models with Inference-Time Cross-Lingual Intervention](https://mlsanity.com/paper/2410.12462/) (2024)
- [LangBridge: Multilingual Reasoning Without Multilingual Supervision](https://mlsanity.com/paper/2401.10695/) (2024)
- [MindMerger: Efficient Boosting LLM Reasoning in non-English Languages](https://mlsanity.com/paper/2405.17386/) (2024)
- [Is Bigger and Deeper Always Better? Probing LLaMA Across Scales and Layers](https://mlsanity.com/paper/2312.04333/) (2023)
- [SLAM: Towards Efficient Multilingual Reasoning via Selective Language Alignment](https://mlsanity.com/paper/2501.03681/) (2025)
- [MMATH: A Multilingual Benchmark for Mathematical Reasoning](https://mlsanity.com/paper/2505.19126/) (2025)
- [AdaMCoT: Rethinking Cross-Lingual Factual Reasoning through Adaptive Multilingual Chain-of-Thought](https://mlsanity.com/paper/2501.16154/) (2025)
- [Getting More from Less: Large Language Models are Good Spontaneous Multilingual Learners](https://mlsanity.com/paper/2405.13816/) (2024)
- [Cross-lingual Collapse: How Language-Centric Foundation Models Shape Reasoning in Large Language Models](https://mlsanity.com/paper/2506.05850/) (2025)
- [From Good to Great: Improving Math Reasoning with Tool-Augmented Interleaf Prompting](https://mlsanity.com/paper/2401.05384/) (2023)
- [CALM: Unleashing the Cross-Lingual Self-Aligning Ability of Language Model Question Answering](https://mlsanity.com/paper/2501.18457/) (2025)
- [LayAlign: Enhancing Multilingual Reasoning in Large Language Models via Layer-Wise Adaptive Fusion and Alignment Strategy](https://mlsanity.com/paper/2502.11405/) (2025)
- [Rewarding Graph Reasoning Process makes LLMs more Generalized Reasoners](https://mlsanity.com/paper/2503.00845/) (2025)

## Abstract (arXiv)

Existing research predominantly focuses on developing powerful language learning models (LLMs) for mathematical reasoning within monolingual languages, with few explorations in preserving efficacy in a multilingual context. To bridge this gap, this paper pioneers exploring and training powerful Multilingual Math Reasoning (xMR) LLMs. Firstly, by utilizing translation, we construct the first multilingual math reasoning instruction dataset, MGSM8KInstruct, encompassing ten distinct languages, thus addressing the issue of training data scarcity in xMR tasks. Based on the collected dataset, we propose different training strategies to build powerful xMR LLMs, named MathOctopus, notably outperform conventional open-source LLMs and exhibit superiority over ChatGPT in few-shot scenarios. Notably, MathOctopus-13B reaches 47.6% accuracy which exceeds ChatGPT 46.3% on MGSM testset. Beyond remarkable results, we unearth several pivotal observations and insights from extensive experiments: (1) When extending the rejection sampling strategy to the multilingual context, it proves effective for model performances, albeit limited. (2) Employing parallel corpora for math Supervised Fine-Tuning (SFT) across multiple languages not only significantly enhances model performance multilingually but also elevates their monolingual performance. This indicates that crafting multilingual corpora can be regarded as a vital strategy for enhancing model performance in a specific language, especially in mathematical reasoning tasks. For instance, MathOctopus-7B improves its counterparts that trained on English from 42.2% to 50.8% on GSM8K testset. Codes are available at https://github.com/microsoft/MathOctopus.