TAPO: Translation Augmented Policy Optimization for Multilingual Mathematical Reasoning

TL;DR

TAPO is a reinforcement learning framework that enhances multilingual mathematical reasoning in LLMs by integrating translation quality and explicit alignment strategies, significantly improving performance across languages.

Contribution

Introduces TAPO, a novel reinforcement learning approach that combines translation quality rewards with an understand-then-reason paradigm for multilingual reasoning.

Findings

Outperforms baseline methods in multilingual reasoning tasks

Generalizes well to unseen languages and out-of-domain tasks

Effectively integrates translation and reasoning capabilities

Abstract

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.