Title: Do MLLMs Really Understand Space? A Mathematical Reasoning Evaluation
Primary area: datasets and benchmarks
Keywords: Spatial Reasoning，Multimodal Large Language Models

Abstract: 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 of spatial reasoning skills in MLLMs. More broadly, MathSpatial offers a comprehensive foundation for understanding how MLLMs handle mathematical spatial reasoning. Our code and datasets will be released upon paper acceptance.