Align to the Pivot: Dual Alignment with Self-Feedback for Multilingual Math Reasoning

TL;DR

This paper introduces PASMR, a novel training method that improves multilingual math reasoning in large language models by aligning reasoning patterns through a pivot language and self-feedback, especially benefiting low-resource languages.

Contribution

The paper proposes a new training approach that enhances multilingual reasoning in LLMs by using a pivot language and self-feedback, without external supervision.

Findings

Improved reasoning accuracy across multiple languages.

Enhanced understanding of questions in low-resource languages.

Significant performance gains demonstrated in experiments.

Abstract

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.