Despite the impressive reasoning abilities demonstrated by large language models (LLMs), empirical evidence indicates that they are not language agnostic as expected, leading to performance declines in multilingual settings, especially for low-resource languages. We attribute the decline to the model's inconsistent multilingual understanding and reasoning alignment. To address this, we present Pivot-Aligned Self-Feedback Multilingual Reasoning (PASMR), aiming to improve the alignment of multilingual math reasoning abilities in LLMs. This approach designates the model's primary language as the pivot language. During training, the model first translates questions into the pivot language to facilitate better alignment of reasoning patterns. The reasoning process in the target language is then supervised by the pivot language's reasoning answers, thereby establishing a cross-lingual self-feedback mechanism without relying on external correct answers or reward models. Extensive experimental results demonstrate that our method enhances both the model's understanding of questions and its reasoning capabilities, leading to notable task improvements.

翻译：尽管大型语言模型（LLM）已展现出令人瞩目的推理能力，但实证研究表明，其并非如预期般具备语言无关性，在多语言场景（尤其是低资源语言）中常出现性能下降。我们将此问题归因于模型在多语言理解与推理对齐方面存在不一致性。为此，本文提出枢轴对齐自反馈多语言推理方法（PASMR），旨在提升LLM在多语言数学推理任务中的对齐能力。该方法将模型的主要语言设定为枢轴语言。在训练过程中，模型首先将问题翻译至枢轴语言，以促进推理模式的对齐；随后，目标语言的推理过程将受到枢轴语言推理答案的监督，从而建立起不依赖外部正确答案或奖励模型的跨语言自反馈机制。大量实验结果表明，本方法能同时增强模型对问题的理解能力与推理能力，在多语言数学推理任务上取得显著提升。