# Cross-lingual Self-Consistency for Multilingual Reasoning with Language Models

arXiv: https://arxiv.org/abs/2606.01464 · HTML: https://mlsanity.com/paper/2606.01464/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 19 of its 28 references that are in the map.
- First posted on arXiv 31 May 2026.

## Placed in

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

## Builds on (most cited first, 19 of 19)

- [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)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Language Models are Multilingual Chain-of-Thought Reasoners](https://mlsanity.com/paper/2210.03057/) (2022)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [The Unreasonable Effectiveness of Entropy Minimization in LLM Reasoning](https://mlsanity.com/paper/2505.15134/) (2025)
- [Maximizing Confidence Alone Improves Reasoning](https://mlsanity.com/paper/2505.22660/) (2025)
- [PolyMath: Evaluating Mathematical Reasoning in Multilingual Contexts](https://mlsanity.com/paper/2504.18428/) (2025)
- [Self-Questioning Language Models](https://mlsanity.com/paper/2508.03682/) (2025)
- [Crosslingual Reasoning through Test-Time Scaling](https://mlsanity.com/paper/2505.05408/) (2025)
- [A Survey of Multilingual Reasoning in Language Models](https://mlsanity.com/paper/2502.09457/) (2025)
- [How Far Can Unsupervised RLVR Scale LLM Training?](https://mlsanity.com/paper/2603.08660/) (2026)
- [BenchMAX: A Comprehensive Multilingual Evaluation Suite for Large Language Models](https://mlsanity.com/paper/2502.07346/) (2025)
- [MindMerger: Efficient Boosting LLM Reasoning in non-English Languages](https://mlsanity.com/paper/2405.17386/) (2024)
- [MMATH: A Multilingual Benchmark for Mathematical Reasoning](https://mlsanity.com/paper/2505.19126/) (2025)
- [Could Thinking Multilingually Empower LLM Reasoning?](https://mlsanity.com/paper/2504.11833/) (2025)
- [Cross-Lingual Optimization for Language Transfer in Large Language Models](https://mlsanity.com/paper/2505.14297/) (2025)

## Built on by (most cited first, 3 of 3)

- [Distill Where the Student Goes: Teacher-Regularized RL for English-Evidence Cross-Lingual RAG](https://mlsanity.com/paper/2607.02966/) (2026)
- [GRPO Beyond English: A Large-Scale Study of GRPO in Non-English and Multilingual Settings](https://mlsanity.com/paper/2608.13698/) (2026)
- [Multilingual Verifier Bias in RLVR: Benchmark, Rollout Diagnosis, and the Cross-Lingual Selection Bottleneck](https://mlsanity.com/paper/2608.20362/) (2026)

## Abstract (arXiv)

Despite expanding their multilingual coverage, the advanced reasoning capabilities of LLMs remain largely confined to a few high-resource languages like English. To address this, we propose an unsupervised Reinforcement Learning (RL) approach to enhance multilingual reasoning by enforcing cross-lingual self-consistency: the principle that a model should produce the same final answer for equivalent problems in different languages. Existing methods are limited by the scarcity of multilingual reasoning data and show weak generalization to unseen languages. Our approach requires neither gold answers nor parallel data, and it achieves average gains of up to 21.7% on MGSM across 10 languages. In addition, our method demonstrates strong generalization, with an 18.2% mean improvement on MGSM languages unseen during training, and up to 6.2% gain on 3 out-of-distribution benchmarks. These results show the potential of consistency-based methods to improve the multilingual capabilities of LLMs without requiring supervised data.