Language as a Latent Variable for Reasoning Optimization

TL;DR

This paper explores how language functions as a latent variable influencing reasoning in multilingual models, introducing a novel RL framework that enhances reasoning accuracy across languages without relying on chain-of-thought annotations.

Contribution

It proposes polyGRPO, a reinforcement learning method that leverages language variation as an exploration signal to improve multilingual reasoning performance.

Findings

Non-English responses often outperform English on reasoning tasks.

Unconstrained language conditions yield the best reasoning accuracy.

polyGRPO improves multilingual math problem accuracy by over 6%.

Abstract

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.