Yongzhen Guo

Hao Liang, Meiyi Qiang, Yuying Li et al.

With the rapid development of large language models (LLMs), the quality of training data has become crucial. Among the various types of training data, mathematical data plays a key role in enabling LLMs to acquire strong reasoning abilities. While high-quality open-source data is important, it is often insufficient for pre-training, necessitating the addition of synthetic math problems. However, synthetic math questions and answers can introduce inaccuracies, which may degrade both the training data and web data. Therefore, an effective method for cleaning synthetic math data is essential. In this paper, we propose the MathClean benchmark to evaluate the effectiveness of math data cleaning models. The MathClean benchmark consists of 2,000 correct questions and 2,000 erroneous questions with additional 2,000 correct and erroneous answers sourced from augmented data based on GSM8K and MATH. Moreover, we also annotate error types for each question or answer, since it can assess whether models can correctly identify the error categories for future improvements. Finally, we present comprehensive evaluations using state-of-the-art (SOTA) models. Our results demonstrate that even strong models like GPT-o1 and DeepSeek-R1 perform poorly on this benchmark, highlighting the utility of MathClean. Our code and data is available at https://github.com/YuYingLi0/MathClean.

Yuying Li, Siyi Qian, Hao Liang et al.

Geometric reasoning remains a core challenge for Multimodal Large Language Models (MLLMs). Even the most advanced closed-source systems, such as GPT-O3 and Gemini-2.5-Pro, still struggle to solve geometry problems reliably, despite exhibiting strong textual reasoning abilities on tasks like the International Mathematical Olympiad (IMO). This gap suggests that the bottleneck lies in understanding geometric diagrams rather than reasoning itself. Since geometric figures can often be faithfully described in concise textual form, converting visual content into captions offers a promising direction. Motivated by this insight, we introduce CapGeo, a caption-assisted reasoning framework that bridges visual and textual modalities. Experiments show substantial improvements when models are equipped with captions: Qwen2.5-VL-72B improves from 8.6% (vision-only) to 59.0%, while Claude-Opus-4 rises from 44.8% to 73.0%. To systematically evaluate and identify high-quality geometric captioning models, we further propose CapGeo-Bench, a dataset of 4,641 curated figure-caption pairs. Crucially, CapGeo-Bench incorporates a keypoint-based evaluation metric that correlates strongly with downstream CapGeo performance, enabling reliable assessment of geometric captioning ability. Together, our framework and benchmark highlight a new pathway toward advancing geometric reasoning in MLLMs.