SpatialMath: Spatial Comprehension-Infused Symbolic Reasoning for Mathematical Problem-Solving

2026-01-24

AI Summary

This work addresses the challenge faced by existing small-to-medium-scale multimodal language models in accurately interpreting images and effectively integrating visual perception with symbolic reasoning on visually dense mathematical tasks, such as geometry. To this end, we propose SpatialMath, a framework that employs a dedicated spatial-aware module to extract structured spatial representations from diagrams and deeply integrates them into the symbolic reasoning chain, enabling vision-driven, structured mathematical reasoning. We introduce MATHVERSE-PLUS, a new dataset featuring fine-grained visual explanations and annotated reasoning paths, and train our model using supervised fine-tuning and data augmentation strategies. Experimental results demonstrate that our approach achieves up to a 10-percentage-point improvement over strong baselines on visually intensive mathematical reasoning tasks, validating the effectiveness of the proposed joint perception-reasoning architecture.

Technology Category

• Computer Vision: Visual Reasoning & Symbolic Representations
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

Multimodal Small-to-Medium sized Language Models (MSLMs) have demonstrated strong capabilities in integrating visual and textual information but still face significant limitations in visual comprehension and mathematical reasoning, particularly in geometric problems with diverse levels of visual infusion. Current models struggle to accurately decompose intricate visual inputs and connect perception with structured reasoning, leading to suboptimal performance. To address these challenges, we propose SpatialMath, a novel Spatial Comprehension-Infused Symbolic Reasoning Framework designed to integrate spatial representations into structured symbolic reasoning chains. SpatialMath employs a specialized perception module to extract spatially-grounded representations from visual diagrams, capturing critical geometric structures and spatial relationships. These representations are then methodically infused into symbolic reasoning chains, facilitating visual comprehension-aware structured reasoning. To this end, we introduce MATHVERSE-PLUS, a novel dataset containing structured visual interpretations and step-by-step reasoning paths for vision-intensive mathematical problems. SpatialMath significantly outperforms strong multimodal baselines, achieving up to 10 percentage points improvement over supervised fine-tuning with data augmentation in vision-intensive settings. Robustness analysis reveals that enhanced spatial representations directly improve reasoning accuracy, reinforcing the need for structured perception-to-reasoning pipelines in MSLMs.

Problem

• multimodal language models
• visual comprehension
• mathematical reasoning
• geometric problems
• spatial reasoning

Innovation

• spatial comprehension
• symbolic reasoning
• multimodal language models
• geometric problem solving
• perception-to-reasoning pipeline