Peijie Wang

Shuo Lu, Jianjie Cheng, Yinuo Xu et al.

Multimodal large language models (MLLMs) have achieved strong performance on perception-oriented tasks, yet their ability to perform mathematical spatial reasoning, defined as the capacity to parse and manipulate two- and three-dimensional relations, remains unclear. Humans easily solve textbook-style spatial reasoning problems with over 95\% accuracy, but we find that most leading MLLMs fail to reach even 60\% on the same tasks. This striking gap highlights spatial reasoning as a fundamental weakness of current models. To investigate this gap, we present MathSpatial, a unified framework for evaluating and improving spatial reasoning in MLLMs. MathSpatial includes three complementary components: (i) MathSpatial-Bench, a benchmark of 2K problems across three categories and eleven subtypes, designed to isolate reasoning difficulty from perceptual noise; (ii) MathSpatial-Corpus, a training dataset of 8K additional problems with verified solutions; and (iii) MathSpatial-SRT, which models reasoning as structured traces composed of three atomic operations--Correlate, Constrain, and Infer. Experiments show that fine-tuning Qwen2.5-VL-7B on MathSpatial achieves competitive accuracy while reducing tokens by 25\%. MathSpatial provides the first large-scale resource that disentangles perception from reasoning, enabling precise measurement and comprehensive understanding of mathematical spatial reasoning in MLLMs.

Peijie Wang, Ming-Liang Zhang, Jun Cao et al.

Multimodal Large Language Models (MLLMs) have achieved remarkable progress but continue to struggle with geometric reasoning, primarily due to the perception bottleneck regarding fine-grained visual elements. While formal languages have aided plane geometry understanding, solid geometry which requires spatial understanding remains largely unexplored. In this paper, we address this challenge by designing a unified formal language that integrates plane and solid geometry, comprehensively covering geometric structures and semantic relations. We construct GDP-29K, a large-scale dataset comprising 20k plane and 9k solid geometry samples collected from diverse real-world sources, each paired with its ground-truth formal description. To ensure syntactic correctness and geometric consistency, we propose a training paradigm that combines Supervised Fine-Tuning with Reinforcement Learning via Verifiable Rewards. Experiments show that our approach achieves state-of-the-art parsing performance. Furthermore, we demonstrate that our parsed formal descriptions serve as a critical cognitive scaffold, significantly boosting MLLMs' capabilities for downstream geometry reasoning tasks. Our data and code are available at Geoparsing.