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

TL;DR

SpatialMath introduces a framework that integrates spatial visual comprehension into symbolic reasoning, significantly improving performance on geometry problems by extracting and infusing spatial representations into reasoning chains.

Contribution

The paper presents SpatialMath, a novel framework that combines spatial perception modules with symbolic reasoning, along with a new dataset MATHVERSE-PLUS for vision-intensive mathematical problems.

Findings

SpatialMath outperforms baseline models by up to 10 percentage points.

Enhanced spatial representations improve reasoning accuracy.

The framework demonstrates robustness in vision-intensive mathematical tasks.

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.