Math-PUMA：增强数学推理的渐进式向上多模态对齐
Math-PUMA: Progressive Upward Multimodal Alignment to Enhance Mathematical Reasoning
AI总结：
提出Math-PUMA方法，通过三阶段训练（含KL散度模态对齐）提升多模态大语言模型的数学推理能力，有效缩小图文模态间的性能差距并超越多数开源模型。
摘要：
多模态大语言模型（MLLMs）擅长解决基于文本的数学问题，但由于主要在自然场景图像上训练，它们在处理数学图表时存在困难。对于人类而言，视觉辅助通常会提升问题解决能力，但当信息从文本模态转向视觉模态时，MLLMs的表现反而变差。这种下降主要归因于它们在图像和文本对齐方面的缺陷。为了应对上述挑战，我们提出了Math-PUMA，一种专注于渐进式向上多模态对齐的方法。该方法旨在通过三阶段训练过程提升MLLMs的数学推理能力，其中第二阶段是关键的对齐阶段。我们首先利用大量文本数学问题集来增强语言模型的数学推理能力。随后，我们构建了一个包含不同程度文本和视觉信息的多模态数据集，通过将每个问题以至少两种形式呈现来创建数据对。通过利用下一个token预测分布的Kullback-Leibler (KL) 散度来对齐视觉和文本模态，确保了一致的问题解决能力。最后，我们使用高质量的多模态数据对MLLMs进行多模态指令微调。在多个数学推理基准上的实验结果表明，使用Math-PUMA训练的MLLMs超越了大多数开源MLLMs。我们的方法有效缩小了不同模态呈现问题的性能差距。代码和数据可在以下网址获取：https://github.com/wwzhuang01/Math-PUMA。
英文摘要：
Multimodal Large Language Models (MLLMs) excel in solving text-based mathematical problems, but they struggle with mathematical diagrams since they are primarily trained on natural scene images. For humans, visual aids generally enhance problem-solving, but MLLMs perform worse as information shifts from textual to visual modality. This decline is mainly due to their shortcomings in aligning images and text. To tackle aforementioned challenges, we propose Math-PUMA, a methodology focused on Progressive Upward Multimodal Alignment. This approach is designed to improve the mathematical reasoning skills of MLLMs through a three-stage training process, with the second stage being the critical alignment stage. We first enhance the language model's mathematical reasoning capabilities with extensive set of textual mathematical problems. We then construct a multimodal dataset with varying degrees of textual and visual information, creating data pairs by presenting each problem in at least two forms. By leveraging the Kullback-Leibler (KL) divergence of next-token prediction distributions to align visual and textual modalities, consistent problem-solving abilities are ensured. Finally, we utilize multimodal instruction tuning for MLLMs with high-quality multimodal data. Experimental results on multiple mathematical reasoning benchmarks demonstrate that the MLLMs trained with Math-PUMA surpass most open-source MLLMs. Our approach effectively narrows the performance gap for problems presented in different modalities. The code and data are available at: \url{https://github.com/wwzhuang01/Math-PUMA}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
