MAPO: Advancing Multilingual Reasoning through Multilingual Alignment-as-Preference Optimization

Though reasoning abilities are considered language-agnostic, existing LLMs exhibit inconsistent reasoning abilities across different languages, e.g., reasoning in a pivot language is superior to other languages due to the imbalance of multilingual training data.To enhance reasoning abilities in non-pivot languages, we propose an alignment-as-preference optimization framework. Specifically, we adopt an open-source translation model to estimate the consistency between answers in non-pivot and pivot languages. We further adopt the answer consistency as the preference for DPO or PPO thus optimizing the lesser reasoning. Experiments show that our method significantly improves the model's multilingual reasoning, with better reasoning consistency across languages. Our framework achieved a 13.7% accuracy improvement on out-of-domain datasets MSVAMP while preserving the competitive performance on MGSM. Moreover, we find that iterative DPO is helpful for further alignment and improvement of the model's multilingual mathematical reasoning ability, further pushing the improvement to 16.7%