Do MLLMs Really Understand Space? A Mathematical Reasoning Evaluation

2026-02-12

AI Summary

This work addresses the limited capability of multimodal large language models (MLLMs) in reasoning about spatial relationships within two- and three-dimensional mathematical contexts. To tackle this challenge, the authors propose MathSpatial, a novel framework that introduces a decoupled perception-and-reasoning evaluation paradigm and formalizes spatial reasoning through a structured trajectory—Correlate-Constrain-Infer—to accurately model the underlying cognitive process. The framework encompasses the MathSpatial-Bench benchmark, the MathSpatial-Corpus training dataset, and the MathSpatial-SRT inference methodology, with fine-tuning conducted on Qwen2.5-VL-7B. Experimental results demonstrate that the fine-tuned model achieves substantially higher spatial reasoning accuracy while reducing token consumption by 25%, thereby exposing fundamental limitations of current MLLMs in spatial reasoning tasks.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Large language models for search

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 and comprehensive understanding of mathematical spatial reasoning in MLLMs.

Problem

• spatial reasoning
• multimodal large language models
• mathematical reasoning
• perception-reasoning gap

Innovation

• spatial reasoning
• multimodal large language models
• structured reasoning traces
• reasoning-perception disentanglement
• MathSpatial