多语言数学推理：提升印地语和英语开源LLMs的能力
Multilingual Mathematical Reasoning: Advancing Open-Source LLMs in Hindi and English
AI总结：
本研究旨在提升开源LLMs在印地语和英语中的数学推理能力，通过课程学习、分解策略和结构化解决方案设计，使WizardMath 7B在英语数据集上超越Gemini准确率6%，并在印地语数据集上匹配其性能。
摘要：
大型语言模型（LLMs）在语言任务上表现优异，但在数学推理方面存在困难，特别是在印地语等非英语语言中。本研究旨在提升较小、资源高效的开源LLMs在印地语和英语中的数学推理能力。我们使用零样本、少样本思维链（CoT）方法和监督微调评估了OpenHathi 7B、LLaMA-2 7B、WizardMath 7B、Mistral 7B、LLeMMa 7B、MAmmoTH 7B、Gemini Pro和GPT-4等模型。我们的方法结合了课程学习，逐步在难度递增的问题上训练模型；一种新颖的分解策略以简化复杂算术运算；以及将解决方案划分为阶段的结构化解决方案设计。我们的实验取得了显著的性能提升。WizardMath 7B在英语数据集上超过Gemini的准确率+6%，并在印地语数据集上匹配Gemini的性能。采用结合英语和印地语样本的双语方法取得了与单语言模型相当的结果，证明了在两种语言中学习数学推理的能力。本研究突显了在开源LLMs中改进数学推理的潜力。
英文摘要：
Large Language Models (LLMs) excel in linguistic tasks but struggle with mathematical reasoning, particularly in non English languages like Hindi. This research aims to enhance the mathematical reasoning skills of smaller, resource efficient open-source LLMs in both Hindi and English. We evaluate models like OpenHathi 7B, LLaMA-2 7B, WizardMath 7B, Mistral 7B, LLeMMa 7B, MAmmoTH 7B, Gemini Pro, and GPT-4 using zero-shot, few-shot chain-of-thought (CoT) methods, and supervised fine-tuning. Our approach incorporates curriculum learning, progressively training models on increasingly difficult problems, a novel Decomposition Strategy to simplify complex arithmetic operations, and a Structured Solution Design that divides solutions into phases. Our experiments result in notable performance enhancements. WizardMath 7B exceeds Gemini's accuracy on English datasets by +6% and matches Gemini's performance on Hindi datasets. Adopting a bilingual approach that combines English and Hindi samples achieves results comparable to individual language models, demonstrating the capability to learn mathematical reasoning in both languages. This research highlights the potential for improving mathematical reasoning in open-source LLMs.
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