# Language as a Latent Variable for Reasoning Optimization

arXiv: https://arxiv.org/abs/2604.21593 · HTML: https://mlsanity.com/paper/2604.21593/

## Key facts

- Cited by 2 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 38 references that are in the map.
- First posted on arXiv 23 Apr 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)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [FastText.zip: Compressing text classification models](https://mlsanity.com/paper/1612.03651/) (2016)
- [Magistral](https://mlsanity.com/paper/2506.10910/) (2025)
- [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)
- [Language Imbalance Driven Rewarding for Multilingual Self-improving](https://mlsanity.com/paper/2410.08964/) (2024)
- [BenchMAX: A Comprehensive Multilingual Evaluation Suite for Large Language Models](https://mlsanity.com/paper/2502.07346/) (2025)
- [Multilingual Large Language Models: A Systematic Survey](https://mlsanity.com/paper/2411.11072/) (2024)
- [Could Thinking Multilingually Empower LLM Reasoning?](https://mlsanity.com/paper/2504.11833/) (2025)
- [Empowering Multi-step Reasoning across Languages via Tree-of-Thoughts](https://mlsanity.com/paper/2311.08097/) (2023)
- [Language of Thought Shapes Output Diversity in Large Language Models](https://mlsanity.com/paper/2601.11227/) (2026)

## Built on by (most cited first, 2 of 2)

- [Translate-R1: Cost-Aware Translation Tool Use via Reinforcement Learning](https://mlsanity.com/paper/2606.06835/) (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)

As LLMs reduce English-centric bias, a surprising trend emerges: non-English responses sometimes outperform English on reasoning tasks. We hypothesize that language functions as a latent variable that structurally modulates the model's internal inference pathways, rather than merely serving as an output medium. To test this, we conducted a Polyglot Thinking Experiment, in which models were prompted to solve identical problems under language-constrained and language-unconstrained conditions. Results show that non-English responses often achieve higher accuracy, and the best performance frequently occur when language is unconstrained, suggesting that multilinguality broadens the model's latent reasoning space. Based on this insight, we propose polyGRPO (Polyglot Group Relative Policy Optimization), an RL framework that treats language variation as an implicit exploration signal. It generates polyglot preference data online under language-constrained and unconstrained conditions, optimizing the policy with respect to both answer accuracy and reasoning structure. Trained on only 18.1K multilingual math problems without chain-of-thought annotations, polyGRPO improves the base model (Qwen2.5-7B-Instruct) by 6.72% absolute accuracy on four English reasoning testset and 6.89% in their multilingual benchmark. Remarkably, it is the only method that surpasses the base LLM on English commonsense reasoning task (4.9%), despite being trained solely on math data-highlighting its strong cross-task generalization. Further analysis reveals that treating language as a latent variable expands the model's latent reasoning space, yielding consistent and generalizable improvements in reasoning performance.